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hello welcome back everybody i'm Jason and today we're going to tackle a topic that is honestly very passionate for me it's a topic that I've been interested in since a very early age and that is electricity and magnetism have you ever wondered why exactly we call it electromagnetic radiation electromagnetic why do we combine these two words well that's what we're going to talk about today we're going to explore one of the most beautiful and profound
0:29
discoveries in the history of science and that is the connection between electricity and magnetism and the idea that electricity and magnetism are actually two sides of the same coin or in other words two sides of the same phenomena [Music] [Applause] [Music] [Applause] so the road map here is I like to give you some background some historical background how it was all discovered how it was put together we're going to talk a fair amount about Maxwell's equations
1:11
and using them to really try to understand the connection between electricity and magnetism and then I'm actually going to show you that connection through some really cool demos in effects in electricity and magnetism so you can see for yourself how they're connected together so let's start at the beginning for literally thousands of years humans knew about electricity as separate phenomena from magnetism in other words electricity and magnetism were sort
1:38
of separate things that were interacted with and sort of discovered at different points in history the ancient Greeks actually found strange rocks that they called load stones that attracted iron and they knew that amber when you rub the amber it could actually attract very light objects sort of like magically attracting them through some sort of force but nobody suspected that these
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different phenomena were actually connected until that is a cold winter's day in 1820 now I want you to picture this danish scientist Hans Christian Urst is giving a lecture and he's demonstrating electrical current flowing through a wire much like I might do for you here and I will do for you here pretty soon in just a minute now by pure chance he notices something really weird during his demonstration his compass needle moves whenever he turns the electric current on or off
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now this discovery was totally accidental but it revealed something absolutely revolutionary the idea that electric currents create magnetic fields and that the magnetic field surrounding an electric current can interact with or affect a compass put in near proximity so these two effects that everybody thought were totally separate things actually were connected that's a big deal and as we're going to see very soon we use these interactions and these phenomena of almost
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every invention in the modern day now I want you to keep in your mind the idea here that electric current generates a magnetic field because I'm actually going to show you that in just a minute with a demo that we'll do now as is always the case multiple people are usually involved in the big picture discoveries so enter Michael Faraday you may have heard of Michael Faraday as in the Faraday cage among other things one of science great experimentalists now in 1831 Faraday
3:35
wondered about this connection between electricity and magnetism if electricity can create magnetism the question that you naturally have is could magnetism then go backwards and create electricity can you go both directions through many many many experiments Faraday discovered that moving a magnet through a coil of wire actually produced an electric current in the wire but only when the magnet was moving that's important only when the magnet is moving relative to the wire this
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was the principle of electromagnetic induction and it changed our world literally forever so I want to stop here and take note of the duality that exists here what we basically figured out up to this point in history is that if you take a magnet and you move it near a wire electricity is flowing then in the wire that's a direct result of that right but think about what electricity is it's moving charges so moving a magnet near a wire generates electricity in the wire which
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is moving charges now if you go the other way we already knew and I'm going to show you in a minute that if we have electricity in a wire which is moving charges in a wire it creates a magnetic field around the wire notice that no matter which way you go some sort of relative motion is happening either the magnet is moving relative to the electrons in the wire and causing them to then move or we say that the moving charges in the wire create their own magnetic field right so
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something is moving either way i want you to keep track of that it's a little bit beyond the scope of what I want to talk about today but relative motion Einstein proved much much later with this theory of relativity that depending on your frame of reference you can prove that depending on how you're moving relative to the wire or relative to the charges you can prove that electricity and magnetism in fact are actually the same phenomena they look different to us because we
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are moving in a reference frame totally separate from any of the charges or the magnets that are actually moving in front of us but from a larger standpoint it can be proven using relativity theory that electricity and magnetism really are two different manifestations for lack of a better word of the underlying electromagnetic force now I'm being honest when I say I don't think it's an understatement that the connection between electricity and magnetism that we're
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talking about here quite literally is powering our modern world let me give you a few examples every electric generator in every power plant works on this principle even if it's a nuclear power plant it's basically heating up steam and the steam is turning a generator what's inside of the generator there's a magnet and a coil of wire and they're rotating relative to one another generating the
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electricity if it is a steam engine of some kind that generates electricity again it's turning a motor if it's hydroelect electric power plant it's turning a motor the only example I can think of when you don't need to really rotate a motor is for for instance a solar panel or for a radioactive thermo electric generator like we use on space probes that uses a a radioactive power source that literally heats up a wire but for every domestic production of power that you
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can really think of nuclear coal gas whatever any of the conventional methods it's almost always turning a generator so this connection between electricity and magnetism really touches everything so that's going one way you use some external force to rotate a coil of wire or a magnet near near each other and you generate electricity if you go the other direction then you have an electric motor you use electricity to flow through a wire in proximity to a magnet
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and the magnetic forces from the magnetic fields then cause a rotation that is what we call an electric motor and I think you can see electric motors are used in literally everything that moves in the modern world another example is the transformer that's outside of your house that steps down the high voltage power from the power plant to a lower voltage that can be safely used in your house that is the process of induction and the connection between electricity and magnetism
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that allows that voltage conversion to happen how about something simpler like the wireless charging pad that you might put your phone on or something else to charge that inductive process happens through the connection between electricity and magnetism even the common speaker a speaker is a magnet and a coil of wire we run electricity the sound wave is converted to electricity through the coil and it vibrates from the magnetic forces and the interaction there it vibrates the cone
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and that's what generates the sound so even the common speaker whether it's a speaker in your ear or a speaker that fills an auditorium is using the connection between electricity and magnetism so now we know that the phenomena are connected experimentally but the story actually gets even better in the 1860s James Clerk Maxwell came along and did something incredible he took all of these
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experimental observations and he wrote them down as four elegant mathematical equations honestly I think they're some of the most beautiful sets of equations that we have in math in science in physics now Maxwell's equations what they do is they show that the electricity and the magnetism are not just related they were fundamentally the same force which is what I alluded to earlier so James Clark Maxwell went there Einstein attacked it from relativity theory but now we know that
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they're essentially unified under the common framework called the electromagnetic phenomena now this is not an entire course on electricity and magnetism or Maxwell's equations but I can't resist i'm going to put Maxwell's equations up for you and I want to talk through them and even if you don't understand every symbol please just listen to my verbal description of what they're saying and I think you'll appreciate the beauty in what they're trying to convey so Maxwell's
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equations consist of four equations two of them are a little bit shorter looking and two of them are longer now the upside down triangle is a vector calculus operation that you learn about in advanced calculus all you need to know is that the upside down triangle is basically taking the derivative in calculus but it's a little more complicated because it's taking the derivative in multiple different directions also this dot that's there is not necessarily a multiplication
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like you're thinking about from seventh grade it's a vector operation called the dot product that you learn about when you get into more advanced math um the X down there is not the multiplication you're thinking about either it's a vector operation called the crossroduct now the E's and the H's those are vector fields the E that you see when they're bolded like that that's the electric field which is a vector field at every point in space surrounding all of us is an
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electric field value but not just a value it has a length and it has a direction that it points right so depending on what's going on like if you have a charged particle here the electric field will be radially pointing out all in all directions emanating from it whereas somewhere in deep space where there's nothing going on the value of the electric field might be zero you also have this
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h which is the magnetic field and we all play with magnets so you can sort of envision that uh vector field surrounding the magnet which you may have seen in other experiments actually I'm going to do a little more with that with you today and show you what that magnetic field looks like but it's a vector field as well because it points in a certain direction and it has a value here's what
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you need to know the top equation is called Gaus's law it's called the div of E that's what the upside down triangle is the div of E that means the outward flow of the electric field how much of the electric field is is penetrating a space going radially outward that's what the upside down triangle dotted with E means and over on the right hand side it's equal to the top term is the charge
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density and the bottom is just a constant of nature called the permitivity it's just a constant so it doesn't really you don't really have to worry about that what the top equation is saying is that the electric field radially pointing outwards is exactly equal through a surface to how much charge is on the inside so the top equation in words is telling you that electric fields are produced by charges in mathematical terms that's what it says the outward flow of the electric
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field is equal to the charge density or the amount of charge you have in a region of space if you don't have any charges anywhere then uh and we're talking about nothing else happening right just totally empty space no waves no electromagnetic waves nothing else happening if you don't have any charges then you don't have any electric field radiating through a boundary like this all right it says that electric fields are caused by charges now the second equation the div of h is
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the outward flow of the magnetic field the outward flow of the magnetic field and that's always equal to zero now what I mean by the outward flow is do I have a net flow coming out from a point that's what I'm trying to say we know magnetic fields can exist around the magnet but they're always in closed loops right that that's not an outward flow that's just looping out and coming back in
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what it's saying here for the second uh equation Gals's law for magnetism what it's saying is the outward flow of a mag of a magnetic field is always zero because there is no such thing as a magnetic charge we know there's electric charges like electrons and protons but so far in nature we've never found a magnetic charge magnet magnetism only comes from the flow of charges uh uh inside of a wire or microscopically inside of a bar magnet the spins are all aligned in such
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a way that creates the magnetic field on the outside so the top equation the electric field radially flows outward as a result of charges somewhere that's what the top equation says the second equation says the radial flow of magn magnetic fields never happens because it's always equal to zero and so there's no magnetic charges it's called a magnetic monopole they don't exist we've never found it okay so that's the top two equations the next equation starts to talk about
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the connection between electricity and magnetism the triangle with the cross is pronounced the curl of E the curl of E is literally like if you were to take your fingers and rotate it uh with with your thumb pointing in a certain direction the curl of your fingers would be the curling literally the vector field curling around a point that's what it means the curl of E is equal to uh the mu here is just a constant it's called the the the per the permeability it
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doesn't matter it's just a number so forget about that the uh partial the symbol there with the h is the partial derivative of h with respect to t that's the derivative and it's a derivative of a vector field what it means is how does the magnetic field h change with respect to time so the third equation says the curling or the uh of the electric field how much the tendency is for an
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electric field to be in curling situation is going to be proportional to how much the magnetic field is changing so if the magnetic field is changing with time then it causes an electric field to curl in other words it generates an electric field so a changing magnetic field causes an electric field that's what we said in words earlier that whenever you move the magnet with respect to the wire it
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causes an electric field which causes an electric current this is the equation that's basically talking about that when you change h with respect to time which happens if you move a magnet across a region very quickly then there's a negative sign there but throwing away the negative and throwing away the constant what it's basically saying is a changing magnetic field causes an electric field
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in a curling fashion now the last equation is the total inverse of that what it's saying is that a curling uh a curling rotational magnetic field is equal to not one thing but two possible situations the first one is called J that is called the current density or the electric current flowing through a wire so even if nothing else is happening if a constant current J is flowing in a wire it will generate a magnetic field and that magnetic field will curl around the wire i'm going
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to show you a demo in just a minute where I run a current through the wire and we're going to see that the magnetic field curls around the wire but it it can be generated by a constant current but it can also be generated by the next term which forget about the epsilon that's the uh permitivity that's just a that's just a constant forget about that the partial E with respect to T is how the
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electric field is changing with time so the last equation basically says the following a magnetic field is generated by either J a flowing current in a wire or by a changing electric field that's what it's saying so if we read the two bottom equations a little bit faster to internalize it this is what it's saying an electric field is generated by a changing magnetic field and then that last equation a magnetic field is generated by a current flowing or a changing electric field
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so a changing electric field causes a magnetic field but a changing magnetic field causes an electric field this is why they're connected together because when one changes it causes the other one to pop up and be generated but as that one is changing as it arises it causes the other field to be uh influenced as well this connection between the two is what's going to uh cause electromagnetic waves to be able to travel through space which is a combination of the electric field
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and the magnetic field propagating so just to wrap up in a pretty bow what I just said Maxwell's equations predicted that changes in electric and magnetic fields would propagate through space as waves at the speed of light these equations when you manipulate them using the tools of calculus what you can prove is that the speed of the disturbance through the electric and magnetic field or through the electromagnetic field always propagates at the speed of light which matches our
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external measurements for the speed of light when we measure it in the real world so we know that these equations must be very close to how reality behaves because from them we can calculate the speed of light which matches our observations so all of the waves that we have different labels for are really all electromagnetic waves of different frequencies or different wavelengths same thing
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so I want you to think about that the light that you see with your eyes the radio waves that travel through space for the radio stations X-rays that we use at the doctor's office gamma rays anything else infrared they're all manifestations of the same electromagnetic wave and it goes even deeper than this when we get to quantum mechanics we learn that the electromagnetic force is carried the actual force is mediated or carried by particles called photons you may have heard
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the word photons so every time you see light or every time you feel warmth from the sun or every time you use your microwave or something mundane like this you're experiencing electromagnetic interaction at the quantum level so now that we've had a good overview and introduction of how we kind of got here what I'd like to do is show you what I think are some really cool demos that show
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visually what the magnetic field looks like around a permanent magnet and also how electric current can generate magnetic fields as shown and given by Maxwell's equations and then we'll finally wrap it up by taking a stab at trying to explain everybody's favorite question from when they're four or five years old how do magnets work all right so here what we're going to do is bridge the gap between permanent magnets and magnetic fields generated by electric currents it was one
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of the most important discoveries of the last couple hundred years that electricity flowing in a wire generates a magnetic field around the wire we use this from everything from electric motors to generators so very very important here I have a piece of copper wire i'll put it against the white background so you can see it a little bit better here it's just uh supported there and what I'm going to do is run an electric current through this now I have to say this i don't want
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anybody to ever try this at home because I have to put quite a bit of electric current through the wire in order for us to measure the magnetic field now this isn't hooked up to anything so I can of course touch it i'm going to put this little cardboard backing down and then on top of the cardboard backing I have a sheet of paper and the sheet of paper is um has a hole put put the uh a backing down we're going to sprinkle the iron filings on there in a second next I have a
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uh some test equipment here we'll talk about more what what this is all doing later here we have a power supply we can supply current through there and we have the the scope and the function generator here in a minute we'll use to drive the electromagnet we have a few things we're going to do first we're going to drive a direct current through this wire so uh I have the uh the black uh
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lead which I'm just going to clip down below onto the bottom of the wire this is a bare wire with no insulation and then the top one here I'm going to I think put it right here all right so I'm going to clip that now that we have electric current flowing in this wire right here you can see over on the u uh on the power supply over here we're sending 9 amps of current so if you know anything
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about electricity 9 amps of current is a lot of electric current so never ever ever try this kind of thing at home uh it's something that um that I don't want anyone doing that's why I'm doing the video so you can learn from me doing it and you don't have to do it yourself so 9 amps of current now this uh wire is now generating a magnetic field around it so we have here a compass when we
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bring the compass close we can see that as I move the compass around the wire it is now affected by the magnetic field we'll come on this side you can see as I go around uh here it's pointed in that direction when I go here it starts to move and when I go around the other side it's pointed in another direction i actually have a a separate compass i'm going to show you two different compasses so we can just make sure the effect is real all right here's a separate compass i just
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wanted to do it with two compasses just to show you so here's the compass when I bring it close to the wire look what happens when I bring this thing and follow it around the wire you can see it's clearly affected by some sort of invisible field which we call of course a magnetic field uh uh around the wire there if I were to disconnect this okay and there's no other magnets around this
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is what the compass is doing without any current flowing in the wire you can see I can move it on both sides and effectively it's pointed towards north as soon as I put electric current through this thing then of course it's being deflected quite a bit as I move around there right of course the more electric current we're going to learn the higher the magnetic field so the more deflection
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on a compass we have so the next thing we want to do is see what what does this look like right now we know that magnetic fields have to form closed circles so because of the symmetry of the wire there's only really one way it can do that let's see if our intuition is correct so we'll sprinkle these guys right and it's a little difficult to get it to to look perfect right because this
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is not a super strong magnetic field just with a single wire like this you can sort of start it to to see it take shape but what I'll do is I'll just tap it like this and now we can see it look what's going on here if you go very close to the wire you can see it's forming these concentric rings here so the magnetic field that is formed around a wire is given by what's called the right- hand rule if
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the electric current is going in the direction of your thumb then your fingers are curling in the direction of the magnetic field here the positive current is going through the red wire so really the current's going down through the page and the magnetic field is curling in a circle in the direction I have here now if I tap it a few more times you know I can probably get it to to to even do maybe a little bit more clear something like this so the magnetic field around a wire
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carrying electric is curling in a circle uh around the wire all right okay now we have what we call an electromagnet so this is a fancy looking device but basically what it is is a coil of wire so this is a coil of wire wound around a magnetic uh core there so as we run the uh electricity through the wire we're going to draw pictures in a little while but what it does is it takes the magnetic
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field that's generated by the electricity and because of the way it's wound it concentrates the magnetic field inside of the coil and so we have this uh steel here so the magnetic field will be concentrated there the more current we run through the electromagnet the stronger the magnetic field and so we should be able to lift objects with this and that's what we're going to do next so we
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we'll hook it up here and what we'll do is we'll connect uh the uh power supply to the terminals now we have really two of them we have another one on the other side but we won't be using uh that one here and then we'll turn the electricity on and see what we get all right so what we're going to do is we'll take first of all we'll take our our paper clips we'll put them underneath here
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and we'll turn the uh current on here the voltage up to a maximum of 6 volts that's as much current the voltage driven driving the current here that's as much as as this thing can take we're at 2 volts now nothing has happened 3 volts nothing has happened four volts nothing has happened yeah we start getting some action around 4 volts uh there here we're up at 5 volts we we turn the current down and we release the uh we release them here so we'll try it one more time and uh see if
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we can get it to attract there and as the current goes up the magnetic field is going up which is concentrated inside this coil let's see what we just go straight up to five here and of course it uh lifted them all up there and we can go down to zero and we can drop them now notice what's happening when we go to zero some of the some of the paper clips are still sort of attracted uh there and that's because as the core there is magnetized when you release the current or
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turn the current down some portion of the steel or whatever material is in there the the iron that's in the steel remains magnetized and so you can still get a weak magnetic effect even after you turn it off often times that will go away go away after a while so let me take these paper clips away and I'll put these lightweight discs that are down there uh and we'll see if we can do the same
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thing i just think these are just just neat to watch it's really the same exact demo so we'll go up uh see this is 2 volts 3 volts you can see the current here 1.3 amps right here this thing can go up to a maximum of uh 6 volts uh there about two or three uh amps there so we're up there right around six volts this is about the limit of what this thing can do and you can see not only is it
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uh uh magnetized but the the uh discs that are down there once they become magnetized they they are further attracting the other disc down below as we showed in the previous demos we can turn this off and we can release uh this guy and you can see there's some residual magnetization let me just kind of knock these off right and we'll do it again i just think it's worth doing a couple of different a couple of different times so we'll go straight up and then straight down up and
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down now what I'd like to do is remove these and put some iron filings down below and see if we can lift those up and what that looks like okay here we have the iron filings let's go up and see what happens here that's one volt two volts oh starting to be pulled up i think that's kind of a neat little neat little demo all by itself and up around five and a half volts you can see it's starting to lift it up now we can release it of course you can kind of like make a dance
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you can go up like this and then down and go up again and then down like this all right let me disconnect this and I want to try to see if we can get a picture of the magnetic field inside this electromagnet all right now the first thing I'd like to do first of all we're going to turn the electromagnet back on uh and we'll try to get a picture of what the field is doing here so here I have my little handydandy plate here i'll shake it up here and see if I can slip this thing down
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underneath and see if we can get a picture and you can see immediately what's going on here is it's pulled up like this and you can see that the magnetic field is circular in nature down there and as you as you drag this thing through you can just see the ripple effect of the magnetic field and how it attracts the iron filings in there it's just kind of mesmerizing to watch now the next
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thing I like to do is turn it sideways and see if we can get a profile view of what the magnetic field is doing all right let's try it first with our little plate here we're going to turn the the uh voltage on up to 6 volts that's about uh five let's do five and a half volts about 2 amps 2.2 amps something like that so a lot less than what we had before here I'm going to put my little board little thing down here and you can see I can't get it too close but you can see the
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magnetic field appearing right here in fact I think it's going to be a little easier to see let me grab a sheet of paper let me grab a sheet of paper i think it'll be a lot easier to see so what I'll do is I'll put a piece of paper on top shake it up and we'll put this right down on top and you'll you can see the field here it's kind of coming out and around and entering into the other side you can see the curved nature of it like this as we move it around you can see it
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kind of sliding back and forth now I'd like to do the exact same thing with the iron filings uh here so I'm gonna open this up and try to hold it steady here and see what we get little harder to see the reason it's a little harder to see is because the magnetic field is is strongest inside of that coil and we're looking kind of at the side of the coil so it's kind of coming out of one side of the coil coming around and entering into the other side of the coil
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there and that's where the magnetic field is the strongest it's almost like there's a bar magnet here now and notice the connection we're going to talk about the connection between circulating currents and permanent magnets in a little bit but the uh the uh effectively the magnetic field is coming out of one end here and going into the other outside of this electromagnet it's actually not that strong it's mostly concentrated inside the coil now what I'd like to do is I'd like to
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hook my signal generator up to this electromagnet which can't push as much current but we can get it to pulsate and see if we can find uh do some neat interactions with pulsating magnetic fields all right here we have something really neat so here we have the um the electromagnet and it's being driven not by the DC power supply but by an by a function generator so I can drive different uh uh different waveforms through here when I press the button here I'm going to drive it with
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a square pulse to turn it on then off on then off and so on so what I'm going to do is I'm going to get down here i've got the iron filings that I've sprinkled on this piece of paper and if I can do it without messing anything up I'm going to push it underneath the electromagnet here and you can see that there's some residual magnetism going on from before but it's basically off right now now let's see what happens when we turn the output of the function generator on so we'll
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turn it on we can see on the scope here let's give it a second it's catching up there and uh it's a square pulse and the period of this uh pulse here is I think I put it to uh 2 seconds so this thing repeats this onoff period repeats every two seconds now if we take a look at what's going down under here right you can see that the iron filings are being attracted and then repelled attracted repelled attracted repelled right that's just I think honestly so incredibly cool you can
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sort of visualize when you see it on off like that that the uh the field is coming on and then off and you can see it directly in the attraction of the iron filings right there okay now let's play with it a little bit more let's turn the um what's called the duty cycle of this function generator so right now it's half the time on half the time off so we'll change it uh we'll go over here to uh
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duty cycle and we'll change it from 50% we'll just go down here to like I don't know 25% or something like that it takes a little time to get down there all right so there we're at 25% and let's see what the difference is right here so now it's on off on looks like it's off it's off more than it's on so for 25% of the time it's going to be on and then it's going to mostly be off so on off and
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then mostly off then on off mostly off so let's change the duty cycle the other direction we'll go up past 50% and we'll go to let's see if I can do 70 just type 75% let's see what 75% duty cycle does so this should flip it the other way let's take a look at it so it's mostly on now on and then off on and then off on and then off and so on so let's change the duty cycle back to 50% so that means half of the time the pulse is on and half the time's off now let's change the
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waveform entirely from a square pulse to a sine wave so we can go over here to waveforms right and instead of a square we can do a sign and let's see if we can detect what's happening down here so now you can see it's raising up very gradually and then relaxing so a sign is a much more of a smooth curve so it's on and then off and then on and instead of punch punch punch punch like this all right let's check another uh guy here uh in fact let's increase the frequency
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a little bit or the period let's just play with this a little bit um let's see how far we can you know what let's go to waveforms first let's try a triangle uh wave see if we can detect the difference in the triangle wave let's do that so you can see it's just on and then going down just kind of a ramp up and then down you can see the triangle wave triggered there in the oscilloscope up to its peak and then down and then up and so on so let's go back to the square pulse
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let's let it kind of settle down there all right let's try to increase the frequency so instead of uh the period here is uh two seconds let's bring the period down to one second to make it happen a little bit faster so we'll go up here to uh period and from 2 seconds let's drop it down to one second and let's see what happens so on off on off on off and so on so we're increasing the frequency i actually don't know how fast we can drive this thing and and see the results of it
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let's just try half a second let's go over here to period whoops period and we'll go 0.5 seconds and we can just see it going much much much faster all right and let's go over here and let's drop it down to 0.25 seconds so we'll go uh 0.25 seconds we're making it shorter and shorter and shorter and shorter like that boom boom boom boom boom boom boom now let's change it to a sine wave just for giggles we'll go
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to waveform we'll change it to a sine wave at this higher frequency we can see how it's going up down up down up down up down like that all right let's go back to a pulse and of course we can now that we're increasing the frequency we need to change our scope so we can see it a little bit better all right now let's go over here to waveforms let's go back to square wave and instead of 0.25 let's go to 0.1 seconds so a tenth of a second uh here whoa look at that
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boom boom boom boom boom boom boom it's like a like a a beating heart super fast beating heart all right how far can we go i actually don't know uh 0.1 let's uh let's go 0.05 I guess 0.05 that's cutting it in half again let's see what this looks like seconds whoa check it out it's fluttering oh that's so neat i have not actually practiced this uh ahead of time i mean I did it but I didn't try all the different frequencies let's drop it from 0.05 to 0.03
35:59
0.03 seconds and now it's just so fast that we can't even really we can't even really tell let's change it to a sine wave and we'll wrap it up we'll leave it at this frequency we'll change it to a sine wave and see what we have and it's again it's so fast it's flickering it's so fast that we can't really uh we can't really discern it all right so let me shut it down and we'll go ahead and conclude now I have to say I'm super pleased with this and I had a lot of fun doing
36:27
these i had done some of them ahead of time but not all of them and certainly didn't do the very high frequency uh business we just did here here so I was surprised myself and excited by it so what I want to really um drive home is that magnetism and electricity are really two sides of of the same coin really and that's why you hear electromagnetism thrown around so much electric current can generate a magnetic field later we're going to learn that a magnetic field can actually
36:55
generate an electric current also that's not part of what we've done here but it's something we'll do later right but I want you to understand that understanding how a coil of wire concentrates a magnetic field inside of it is how a lot of our modern technology works motors generators and other devices uh run on this concept and as we talk about permanent magnets which we'll do in just a few minutes we're going to talk about how the motion of the electrons are mimicking
37:21
little coils of wire so sort of so to speak to generate the magnetic field in a permanent magnet so the first thing I want to talk about is what everybody knows and is interested in and that is that magnets attract and repel each other so here I have two bar magnets notice I have a north and a south pole and you can see that uh when we get them close together these guys are it looks a little bit better this way that they repel each other notice that when you have south
37:46
facing south they re repel each other but when you turn it around to a north side of the magnet uh then of course it doesn't repel each other anymore it attracts each other now we have uh some a little bit stronger magnets here look at these these influence each other farther away and they just look magical the way in which they work so here we have the two north sides facing each other if we put the two south sides facing each other we get repulsion so like
38:11
sides of the magnet repel each other but when we have a north facing a south side it doesn't repel each other anymore it attracts it attracts so here we have a magnet attracting and repelling another magnet if we turn them sideways we can get similar behavior south uh touching north north touching south they attract each other and and it's very strong actually hard to pull apart but if we turn
38:32
this around so that we have south and south facing and north and north facing then of course this is really impressive and fun to do they just totally repel each other you can get you know in this case several centimeters of distance between them uh there all right the next thing I want to do is I want to put these aside we're going to go back to our uh slightly weaker magnet here and here we
38:51
have uh I have over here uh these uh disc magnets with a hole in them and uh even though they're not labeled there is a north and a south side it's not particularly it's not labeled but there's a north and a south side to this and you can see that these are magnets also uh track the magnet there now the interesting thing we can do is we can connect them like a car and we can actually use the magnet underneath to sort of propel the wheels so to speak on the car so let's see if we
39:15
can get that to work and if we kind of push it over here there's a little bit of repulsion I'm feeling but then when I get past it here it get you can kind of see it kind of like scootering that way so what's really going on is it's sort of uh it's attracting it here and then when it gets to the middle of the magnet I'm starting to feel a repulsive force but when it gets over the hump of the repulsion then it's kind of pushing it you can see it kind of like oscillating back and
39:37
forth right there that's kind of neat too actually you can see see that effect right there because there's an attractive force right there out of the north pole of the magnet uh there is an invisible field that is coming out of here and entering into the south pole right we can't see it but we see its effects by its attraction and repulsion of other magnets and other metals and the field is
39:56
actually coming out of the north pole and entering into the south pole so the directionality makes it a vector field we use the word vector it just means it has a direction associated with it so this field is pointing out of the north pole and it loops around and points in to the south pole all right the next thing I want to do is pull out uh slightly different magnets these are uh disc
40:18
magnets they're a little bit stronger and they're hollow in the center and they're pretty strong and you can see how hard that I have to kind of pull to get them to come apart actually it's very difficult you mostly have to slide them here so if I put this guy on the bottom here and then put this one on top then I feel a repulsive force and you can see it's basically levitating right
40:38
there now what's neat about this is I can sort of bounce it up and down i can feel it it's like very springy it's like a mattress or something it's very springy like this so what we have inside here are the same poles either both north or both south uh and that's why they're repelling each other like this if I were to flip it over and then they would be attracting and they would have opposite poles opposite attracts in terms of magnetic uh magnetic fields as well all right now
41:02
I mentioned before to you that the magnetic field is is exiting or coming out of the north pole and then coming back around and connecting back in through the south pole one thing I want you to remember is that all magnetic fields have to form closed circles right they don't just emanate from a point like electric fields do they're they they they form closed loops always right and uh so here
41:23
is the bar magnet so that's what we visualize here so here's a here's a another bar magnet into the shape of a cylinder what I want to do is visualize this field in a three-dimensional shape here is iron filings we're going to do a lot with iron filings but here is just a uh a fluid fil box here full of iron filings so with no magnet inside you can see what's going on here let's drop this thing
41:45
in here and see what happens we'll drop it in there and look at what happens there the magnetic you can see the magnetic field uh immediately appear in fact it's a little more impressive if if I close it off here and you can see it's sort of attracting inside of there now and if I give it a nice little shake and I'll try to get the angle with a couple of different cameras so there's there's sort of a side view there let me kind of let it go so you can sort of see that and then
42:09
we'll do it with sort of the top view there and so you can see that it's the the field is exiting and coming around you can see the curved nature of the field as it comes and and sort of enters into the bottom so we're going to draw more pictures but I think this is like the best thing that I really want you to drill into your head look at how the field is very curved like that and kind
42:31
of like angular and then going into the bottom so if you can imagine these lines coming out of the top and then flowing into the bottom then the next thing you need to know is that the magnet is the strongest or the magnetic field is the strongest where these field lines are concentrated so you can sort of see actually well let me go and let it do its thing but you can kind of see that the
42:51
the bunching up is starting to happen near the near the ends so if you can imagine all of these uh all of these lines entering into the pole then they're all going to get crowded near the pole uh either the north or the south pole and the more crowded or the more dense those field lines are the stronger the field i'll say that again the more crowded or dense the the the the magnetic field lines are is where the magnet is the strongest and you can kind of see it now that I've
43:18
just sort of sort of let it settle right here you can see uh along the bottom a really nice curved you can see that sort of the curved magnetic fields like less dense there but near the poles everything is bunched up that's because there's more field lines kind of concentrated there and so a higher field strength if you want to know uh the word of the day which I love this word when we talk about magnetic fields and electric fields also we talk about the flux density when you hear
43:44
about something uh you hear the term flux density it just means the density of the field line see these these lines are called magnetic flux it's got a cool name magnetic flux so the flux density is just how many lines are in a just like regular density in a volume or or you could talk about surface area if you're talking about the lines cutting through a surface area so flux density uh let's talk about field lines uh penetrating a surface area there and so the flux density is
44:10
highest where these field lines are entering into a pole because they're crowded and concentrated uh over a smaller area but out away from the pole they're more spread out and so the magnet is less uh strong or less intense uh near the sides and more intense or more strong near the poles all right so so far we've had magnets attracting or repelling other magnets now we also want to play
44:34
with other situations here so here we have some paper clips these are coated so they're colorful but inside of course they're metal paper clips and uh then we can take the magnets and actually even though these are not magnetic you can see they're not attracting each other we can uh obviously use a magnet to lift them up now this is a pretty weak magnet but still works pretty good let's grab our
44:55
uh stronger magnet and see how that looks we'll just kind of bring this down here and we get a little closer and of course we start to pick these guys up and I think we even have a better magnet probably for this demo these are already together but we can just get it a little closer and we can immediately see that's pretty neat we'll do that one more time so you can see that as the uh magnet is stronger it can exert a force over a longer distance a magnetic force but
45:19
what's interesting about it so there are there are different materials that are that are able to be attracted by a mag a magnet we call those magnetic materials and some materials are not right uh for instance some examples iron is magnetic inside of this uh container is little filings of iron little tiny chips of iron that's why they're able to be influenced by the magnetic field uh nickel
45:42
is another metal that's able to be magnetized or attracted by a a magnet cobalt is another one also steel steel is able uh usually to be magnetized or to be u attracted well steel contains uh iron and so that's the reason why or if it contains any magnetic material if it's an alloy right but some uh materials are not able to be magnetized for instance copper is not able to be magnetized um
46:05
aluminum if you get aluminum can it's not able to be magnetized either all right so here I have some copper wire there's no insulation on this so that's why it looks beautiful in copper uh there we're actually going to use this wire later to make our uh uh to to to run an electric current and see the magnetic field that surrounds a wire that's why I have it out and here we have our paper clips now if I run uh of course the magnet over the paper clips of course they they attract
46:30
but I can run my magnet along the copper all day long and and nothing happens it's it's it's not magnetic at all this is the more strong magnet I have it's just not uh affected by it at all aluminum is the same way now what the I'm not going to explain in great detail why certain metals are able to be magnetized and aren't i will tell you that all of magnetism is a quantum mechanical effect it has to do with the electrons which are uh in the atoms or surrounding the atoms
46:58
and specifically it has to do with what we call the spin of the electrons i don't want to get too much into it now i'll touch on it later but there's a a a characteristic of electrons called spin and when the uh spins are all aligned uh in the material then we can magnetize the material or if they're able to be aligned in the same direction right but when they're unable to be aligned then you have random directions of electron spin and so you don't see any observable
47:24
mag magnetism from the outside from a macroscopic point of view from the whole substance and uh uh uh copper and aluminum and some of the others are not able to be uh spin aligned from the outside like this whereas whatever this paperclip is made of probably steel or something are the electrons that are in there it's not magnetic now but when we bring the magnet close to it it's able to align
47:47
the electron spins in these paper clips and then so they become magnetized and of course magnets can be attracted and so it it attracts right now I have something else I want to uh attract and repel i just think they're neat um just another metal here it's probably steel although I didn't make them so I don't really know um it's just fun if you uh take this guy of course you can you know
48:09
you can attract them and notice what's happening here this is actually kind of interesting notice that the uh this let's let's look at the one on the end here the one on the end is able to be attracted to the one next door even though the one next door let's remove these two away from the magnet uh are these magnetic no they're not magnetic so these two these two little disc here they are not magnetic right but whenever they are touching uh one of the uh pieces that are touching
48:38
the magnet then they are able to turn into magnets so what's happening whenever you attract a piece of metal is the magnetic field emanating from the permanent magnet where I'll just give the punch line away and the permanent magnet are materials where all of the electron spins are already aligned in the same direction or a whole great many of them are aligned in the same direction so the magnetic uh field can emanate and permeate the space around the permanent magnet whenever you
49:04
have a material come into contact with that that's able to be magnetized then temporarily their electron spins can be aligned in the same way so they can turn into magnets sort of temporarily when they're in the vicinity of the magnetic field but when we remove these guys from the magnetic field as we you know they're all sticking together here we can just kind of like pull them away and
49:24
then suddenly everything literally falls apart they're not magnets anymore so sort of a temporary effect now since we're talking about magnetic attraction we've picked up paper clips we picked up these little discs here is what we call iron filings now we're going to use these a lot uh in just a few minutes to visualize the magnetic field uh here but uh I do want to share with you and
49:45
just show you how it's just sort of fascinating to watch you bring a magnet near this iron which is able to be magnetized and it you can just see it almost vacuuming it up like a you know just like a vacuum cleaner and you can kind of hang them off of Notice that the iron the the pieces of iron that are attached to the bottom uh are temporarily magnetized able to attract further pieces so it's
50:06
able to temporarily uh magnetize the iron now eventually the the little uh the little uh stellag tites or whatever you want to call it they get so long that they they can't they can no longer pick up anything else because the it has to be close to the parent magnet in order to be magnetized so the effect does wear off you can't build these things forever but we can do some impressive things like
50:27
that's pretty neat now we can kind of hoover them all up here let me hold that down and let's just pick them all up that's just kind of neat to look at you can just see you can just see the the back and forth dancing that's going on here as we pick them up there so we can kind of kind of do that and then we'll bring this to the side and we'll put that away and clean it up later now the next
50:45
thing we want to talk about is to try to visualize this and we've used several ways we want to just drill at home that there is some sort of invisible field around this because if we have a compass let me move the magnet away the this compass is going to point to the magnetic north pole of the earth uh in my vicinity so you can see it's kind of pointing off in that direction so notice it's pointing in that direction if I move it over here it's pointing in the same direction if I
51:09
move it over here same direction over here same direction because it's pointed to the strongest magnetic field that it feels which is the Earth's magnetic field so no matter where I move it I mean I'm wiggling it a little bit well once it settles it points in the same direction now if I bring a a new magnet here there is a magnetic field emanating and and permeating and surrounding that
51:29
space here and now let me move this over here and we'll put this over here and what happens as we get closer to this magnet right you can see it's sort of locked in place let me move the magnet out of the way and we can see that the effect that it has here let's move it over here now it's pointing to the magnetic north as we put the magnet here you can see it just changed now as we move the
51:50
magnet uh around here you can see it's just locked on it's locked on to what it sees nearby because the magnetic field coming out of this thing is uh much much stronger than the uh locally because it's closer to the magnetic field of earth the magnetic field of earth is strong enough to uh protect us from the solar wind and it's it's it's a strong magnetic field but locally this magnet
52:14
since it's so much closer is kind of overwhelming it here now as the as we move farther away uh it does uh continue to respond but notice it's kind of like wiggling more it's not like it's maybe not like quite as locked on it's moving but it's just not as locked on when you bring this thing close it is absolutely locked on to moving um as we move around here so I'm going to do the same thing when we do the electromagnet with the wire we're going to do it with the compass we'll do
52:41
it with the iron filings to show you and prove to you that not only are permanent magnets able to be uh formed and created but when we create we run an electric current through a wire we're going to be able to measure and observe that there is a magnetic field surrounding the wire that's going to be a huge clue as to how these magnets work because if we can run an electric current through a wire and generate a magnetic field then it's a good guess that maybe there's something to
53:07
do with electrons inside the permanent magnet that's also generating a magnetic field and we're going to connect those two things together as we go along in the further demos so now what we want to do is visualize the magnetic field with sprinkling the iron filings and so we're just kind of getting a little more and we'll use different shaped magnets as well so here we have our north south magnet remember this is the one that's not so strong so I'm going to place it under a sheet
53:28
of paper and I'll sprinkle these iron filings on top and when we sprinkle the iron filings on top hopefully we will see the magnetic field that this magnet has sort of like come into focus here get a few more on there i start I can start start to sort of see it now yeah you can see that good and you can give the the paper a little kind of a little shake helps it also right so you can see that here was the north pole of the magnet you can even see the S for the south here that the
53:58
magnetic field is emanating from here and going and traveling around and entering in through the south pole and the same kind of thing is happening right here right this is very very similar to what we already saw with our cube magnet i'll put it right on top in three dimensions you can see it's it's happening going from north to south in three dimensions all throughout space there this is just
54:17
a flat representation of the same thing so let's go and do the same thing again with our stronger bar magnet all right here's our stronger bar magnet and we'll put it underneath and we should basically see the same sort of thing uh but I just want to give you exposure to what what it looks like but it should look a little more intense uh we'll we'll we'll kind of like see notice how when
54:37
we sprinkle it we don't have to shake the paper it's like immediately locking into place it's like a really really really nice looking magnetic field here and that's because this magnet is stronger so as soon as the iron hits the paper it's immediately magnetized and locked into place we can give a little a little shaking here or whatever if we want to to see it but you can see how intense the magnetic field near is the north and the south here all these field lines
55:00
are coming and entering into the north and the south pole the density or the flux density of the magnetic field dictates how strong the field is so the the field is strongest here and here and it's weaker uh here and of course as you go farther out the field lines are spread even more out farther out and so it's it's weaker out there i have one more even stronger bar magnet we'll do that one next all right now this one's not labeled north and south but there is a north and a south
55:25
pole here i don't I just don't know which is which but it's there this is called a neodymium magnet which is a rare earth magnet and it's stronger than any of the other ones so I put that under there let's see what this looks like we should see the same thing but we should see it lock into place really really quickly let's see notice that this one is so strong that we can't even really
55:44
visualize the field that much the reason you can't visualize the field that much is because um it's attracting it so incredibly uh uh uh fast uh that you really can't can't see much of anything it's just attracting it to it now you can sort of see that the shape of it you can see that uh it's it's radially coming out here but again it's so strong that it's just pulling it in immediately so it's
56:05
actually a little more fun to look at the other magnets now this one is actually so strong i want to show you what happens when I lift it up just because of the iron there i've actually lifted the magnet off of the underlying paper uh here if I reach down below it's actually attracted it's It's not even going to come off the paper you can see me trying to pull it it's very difficult to
56:25
pull it off this is a really strong magnet in fact we can see what it looks like to try to suck these guys up over here you can just see it just you know just like a vacuum cleaner you can just pull it all up there all right all right i have another cool toy here this is uh iron filings inside of a uh sort of a transparent plate there and there's sort of oil or fluid in there and if you shake
56:47
this thing up and just kind of get it going and you can get it to evenly disperse throughout there it's just different ways of visualizing things i want to if I'm going to do this I want to do it right i want to do it with a bunch of different ways to visualize you're going to see the same thing but it's just really neat to see th this just sort of snap into place let's look at the magnetic field right there and you can see that the magnetic field sort of snaps into place you
57:08
give a little little shake shake now remember this is our less strong magnet actually I think it's going to work better if we go this way uh so let's go long ways here we'll go right down on top of it and let's see if we can see the magnetic field and you can of course you can see it emanating and coming from the from one pole into the other from the north coming out into the south same
57:25
sort of thing let's do the same exact thing with our slightly stronger magnet we'll again go this direction let's make it north south like this see what this looks like okay we'll go right on top of it and you can see it uh you can see the magnetic field coming out notice it's so strong that you can't see it after a few minutes so when you use this one it's actually a little bit better
57:45
to kind of keep it separated from like maybe like that far away then you can really see the field very very very clearly and check it out as you move it around it's so neat to watch the field sort of propagate through the iron filings in fact that's so cool i think we're going to do it again so we start over here this time and let's just sort of race through and watch the magnetic field
58:04
propagate through and affect the iron filings that are above like that all right now if you remember the really really really strong magnet we had a hard time visualizing because it was attracting so kind of violently for lack of a better word so we'll do the same thing we'll see how fast it happens boom it's just done it attracts it so fast you can't really see it uh so what we can do to visualize it a little better is because we couldn't really see it better uh before we could
58:29
just keep it separated from the top like maybe this far away and you can it's still starting to suck it in from all directions in fact this one is so strong it's it's it's emanating very far away so we're going to see it better when we turn it lengthwise like this let me mix these iron fings up a little bit more let's see if we can see it right there you can see that magnetic field really
58:49
really really uh clearly get a little closer and you can just see it starting to suck it in there so that's a neodymium magnet which is a rare earth magnet okay here's our disc magnet with the circle in the middle now it's not labeled north and south but I can tell you how this works is that one side of this disc is the north side and one the other side would be like the south side now I don't know
59:10
which is which but one of them is north and one of them is south so if you can imagine the field is coming out of the north side and entering into the south side but it's doing that all the way around it's coming out of one side of the disc and and going and going around to the other side and also going through the center and reaching around as well you can almost think of it like like if this is the north uh pole here of a bar magnet we know that the field comes out and into
59:35
the south side it's just this one is constructed in a way where it's you we take the bar magnet you make it really really small and then you make a a disc of it so it comes around like that let's see if we can visualize the magnetic field using our iron filings and see if we can see if if our uh idea makes sense here so we have the bar magnet there or the circle magnet there put some iron filings on top now it's going to be difficult to see the full extent of it because
59:58
we're looking kind of down right as we said before we are uh it's coming out of the top going through the table and back through the bottom so we're not really able to see you would have to look from the side to be able to see the profile maybe we'll try it i I think it's going to be difficult to see but maybe we'll try it anyway uh and we can see that it's doing something like that we can do the same
1:00:19
thing with the fluid uh cavity all right here we go take two we'll put this guy right on top and we see Oh that's so neat looking it just sort of you could just you could just see it happen like in real time we'll do that one more time uh if I go all the way on top of it you know it just happens too fast i almost prefer to keep it far away so you can sort of see it happen starts to attract those guys you can see the middle clear out because uh it's just sort of stopping as the
1:00:46
filings get to the edge they're sort of stopping there and so the field lines are coming out and going around to the other side now I don't really know if this is going to work but let's see if we can get this to work i I've never tried it so I doubt it'll work but you know I don't know let's let's just try it um let's let's just try it let's see what it looks like when we do it from edge on oh look at that that worked way better than I thought i hadn't actually tried this before
1:01:14
so you can see the magnetic field is coming out of one side and into the other side so one side is north the other side is south or vice versa we'll do the same thing just for giggles with the fluid fil cavity all right here we have our disc magnet we'll put it like that we'll do our fluid fil cavity and see what we can see we'll get it close and what do we see yes it's exactly what we want to see so we uh we can see it kind of coming out and reaching around to the other side
1:01:40
so that is the shape of the field now you have to use your imagination because it's happening in three dimensions all around the periphery it's kind of coming out and and and also going through the middle and doing the same kind of thing there as well all right what other magnets do we have we have a horseshoe magnet this is a kind of a weak horseshoe magnet when you see a horseshoe magnet you need to think basically all that they've done is they take a north south
1:02:02
uh magnet here and they just literally bend it and they heat it up or something and they bend it into a horseshoe so it it it's nothing um it's not like a different kind of magnet or anything it's just a bent shape and of course we can do it with our our handy dandy little visualizer right here and we can see that the north and the south uh sides here we have the most concentrated uh area there and
1:02:23
of course the north is kind of connected to the south in the same way that it is here the field is coming out and into the other side so of course it's going to come out and go into the other side there but of course it also has to travel and go all the way around here all the way around the magnet it's a little bit weaker on this on the uh uh bottom side there let's try it with the iron filings i haven't actually done this one but you know we've got everything ready and I have a
1:02:44
stronger horseshoe magnet we can visualize as well so we'll do the same thing here you can see the field is definitely strongest between the ends of the north and the south but if you can visualize it it's kind of connected there but it's also kind of kind of going around very very weakly down to connect to the other side as well all right here's our final horseshoe magnet here we've got this one
1:03:06
here we'll go first from the we'll go from the top view here what does our little magnetic plate here show us of course this is a lot stronger so we can see the flux density the density of the field lines is much much uh tighter there or more uh more concentrated so we know that this magnet is stronger and it is a stronger magnet um we'll look at it with the iron filings i'm getting kind of
1:03:26
efficient at this so I can kind of kind of got the hang of it there let's see what it looks like out here away from it so the field does of course go between this where it's strongest but it does loop around and connect to the other side so remember magnetic field lines have to form closed loops we'll do it from the side view just to close it out and finish out this part all right so here we have the profile of the horseshoe magnet here again we should see the north and the south
1:03:53
connected together we'll try it with this first see what it looks like and that's exactly what we see the north and the south pole are connected by these field lines and of course the lines go all the way around but they're a little bit weaker as as they get farther away uh there so we'll do the same thing and this will be our last iron filing demo a little sad I know but that's what
1:04:10
we're going to do here so you can see same kind of thing the way you read this is you say all right uh obviously it's stronger here where everything is concentrated but as we get farther away the field lines are a little more spread out and so it's weaker but ultimately it is connecting the north and the south pole and all of these mag magnets form closed loops now if there's anything I want you to get out of this portion of sort of the demos and the lesson here is that magnetic
1:04:35
fields always always formed clos lines right and the closer the lines are together the stronger the magnetic field is in that area that means the stronger magnetic force is present on on magnetic metals and other magnets but the farther the space is uh the spacing is between the magnetic field lines the weaker it is uh a better word for that is called flux density higher flux density means
1:04:59
compacted very uh tightly uh spaced lines means strong magnet or strong magnetic field in that region but over with low flux density means lines are spaced out magnetic force magnetic field is a little bit weaker we talked about bar magnets we talked about circle magnets we talked about the compass and all of these things so let me take the demo equipment down and we'll draw some pictures of magnetic fields and tie everything together that we've learned through the demos all right
1:05:24
so here we want to put everything together first let's draw a picture of a bar magnet and the magnetic field and we'll go from there explaining everything that we saw here in our demos so here we have a bar magnet so we're just drawing a picture of what we have seen many times in the demos here now we've said that there's a north pole and a south pole these are just labels though one end is different than the other end essentially and we have seen the magnetic field
1:05:49
from these guys and so we know that it comes out of the north pole and into the south pole now there is a direction associated with magnetic fields now really it's it's also occurring inside here so I could kind of draw some dotted lines here usually you don't draw it inside though and so the lines come out of the north pole and in to the south pole like this so out of the north pole and in to the south pole if I wanted to draw more lines I could certainly do that i could say
1:06:15
well we got you know another one coming out here a little bit nearby and as we get farther away from the magnet if I were to draw another one it would have to be even farther away because remember the the density of the field lines the flux density tells us how strong the magnet is so out here things are not so dense it's fairly weak but when the lines get crowded we know that the magnet is
1:06:36
stronger there so we have more field lines coming out uh here of course making very large loops and then making their way you know back into the south pole so I'm not drawing these closed loops but all magnetic fields must form closed loops that's one of Maxwell's equations it's always true for magnetic fields all right I've danced around this a few times but I want to explicitly say we're going to explain why magnets attract each other and repel each other so in order to
1:07:05
understand that you have to understand that this magnetic field is called a vector field you can see if I pick two random points here then locally the magnetic field will be going in a different direction here as it is for instance right here or here compared to here they're pointed in different directions so the strength or the density of the lines matters for the absolute strength but the direction matters also because when you bring two magnets together their magnetic fields
1:07:33
add together as vectors add and that is going to explain why they or at least one way of explaining why they attract and repel each other so we're going to get back to that a little bit later just remember they're vector fields little arrows pointed in different directions now in addition to the bar magnet and the magnetic field that we know exists around there we also did a demo where we ran an electric current through a wire so we're going to draw that real quick so we had
1:08:00
a cardboard kind of platform this is my best uh best uh way of drawing that kind of like looking looking like this like here and that platform had a wire which was I think I'm going to use a different color uh had a wire going up which was copper and I clipped uh electrical terminals and we ran an electric current through there now for the purpose of this example let me pretend that the electric current or the current I should say is flowing up i'm going to talk a little bit more
1:08:33
about current in a second but let's call let's say the positive current flow is in the up direction the magnetic field in a wire follows as I mentioned before the right-hand rule what you do is you put your thumb in the direction uh of the positive current flow again I'm going to talk a little bit more about current in just a second because I know you probably have questions about why what's what's positive current flow just hold on to that question for a second you put your
1:08:59
thumb in the direction of the positive current flow and your fingers curl in the direction of the magnetic field so if my thumb is in the direction of the current flow my fingers curl around this wire and this tells me the direction of the magnetic field circulating like this and so if I wanted to draw those then it would be down here i'll just try to draw in the plane here uh it would look something like this right here and the arrows would look like this because they remember
1:09:26
their magnetic field is a vector field the arrows matter so if you look at my fingers they're circulating in this direction now as I get farther away from the wire the magnetic field gets weaker it's still in the same orientation it just gets weaker and we represent that by a wider spacing between the circles so as I get farther I'll draw one more maybe out here you know as we get farther
1:09:54
away from this wire the spacing between the uh the circles that are surrounding the wire get farther and farther apart so the spacing between the uh lines tells us how strong the field is they get more and more crowded as we get closer to the wire the field is stronger closer to the wire but notice they're all circulating in the same direction in accordance with the right-hand rule all right let me talk a little bit about current flow so when you take my engineering class we we
1:10:20
talk a lot more about this we know that in matter the way that we make electricity and electronics the actual charge carriers are actually electrons electrons are surrounding the atoms electrons are actually moving hopping from atom to atom so if you visualize a long series of atoms in a wire for instance copper wire the outer veence shell of those copper atoms have a lot of what we call free electrons they're electrons that are not very tightly bound to the copper atoms
1:10:50
essentially there's a lot more details we could get into that but that's a good picture for now and as we apply a voltage or an electric field across the wire it pushes one of the electrons to the next atom over but that displaces another one which is also pushed to the next atom over and it's a chain reaction you can imagine trillions of the electrons in lock step moving to the next atom over so that is what we call electric current flow that is the actual charge carrier but
1:11:17
mathematically speaking it's the same exact thing to think of a negative charge carrier moving this way as if it were an imaginary positive charge carrier moving the other way let me say that again negative charges moving this way is the same thing mathematically as a positive charge moving this way and all of our equations in physics and engineering electrical engineering are written in
1:11:41
terms of positive current flow because one reason is historical but the other reason is because the equations don't have negative signs running around everywhere so when I say the current is flowing up this wire and the right-h hand rule means my thumb is in the direction of the of the current flow this is the positive current flow we call it the whole current the actual electrons are
1:12:02
going down but it's okay because the right-h hand rule is written in terms of the positive current flow and it predicts the direction of the magnetic field you could do a right-hand rule for electron flow but then what you would do is you would have your fingers curling the wrong way and you'd have to remember to flip around the direction of the field because the magnetic field really is circulating in this manner around this wire so from now on when I say current flow I'm talking
1:12:26
about positive current flow in your mind you can replace it and say okay that's just opposite of electrons flowing it's all the same thing and it means the same thing in terms of it's just another way of looking at it it's you might say it's fictitious or a mathematical trick whatever you want to say it's fine with me i didn't make the rules i'm just trying to tell you what uh how everything is written so you can understand it this is positive current flow now this is the
1:12:51
magnetic field surrounding the wire i'm not going to write too many equations down but I want to show you what the magnetic field equation is around this wire b is the letter that we write for the magnetic field right the magnetic field B and that's equal to I'll tell you what this means in a second but mu knot multiplied times the current flowing in the wire divided by 2 pi r it's not a complicated equation that's why I want to put it on the board i'm trying to show you what
1:13:17
the magnetic field around a wire is because in a few minutes I'm going to write down what the magnetic field of a coil is and then we're going to tie that to permanent magnets and how we can understand magnetism in permanent uh and induced magnets also so what does this equation mean two is just a number it's a constant pi is just a number it's a constant so these are just constants mu not is something called the permeability and I'm not going to explain where
1:13:44
mu not comes from right now just suffice to say that in electricity and magnetism we have several constants that pop up in nature related to the speed of light into Maxwell's equations one of them is called the permeability it has to do with magnetism but for the purpose of this discussion I don't want to derive where it comes from i just want you to know it's a constant it's a number so this equation for the magnetic field is a number here a number here and a number here
1:14:08
these are all just numbers it's like three four and seven or 10 5 2 it's just numbers the only variables here are the current flowing in the wire and the radius R that's the distance away from the wire so the magnetic field strength at any point in space around this wire is directly related to how much current is flowing in the wire but it's inversely related to how far away because the R is the perpendicular distance to the wire essentially so if you keep the electric current
1:14:36
affixed constant like we had in our experiment at 9 amps then as the as the distance gets farther and farther away then the magnetic field gets weaker this is exactly what you would predict because you're dividing by a bigger and bigger number but if you hold the distance constant like if you put your finger right here and increase the current to 50 amps 100 amps 900 amps then the magnetic field will get stronger and stronger at a point so this equation makes sense it means
1:15:01
the stronger or the more current flow we have the stronger the magnetic field at a given point the farther away you get from the wire the weaker the magnetic field is that's exactly what you would have guessed if I just asked you how it worked uh before but this is what the equation predicts it's going to be important in just a second all right so now we have to talk now that we know about
1:15:21
wires and magnetic fields we also did demos with our electromagnet the electromagnet that we had is just a coil of wire and there was a core it's wound around a uh a core which is just a metal that's able to be magnetized right so let's talk a little bit about coils is very very important in modern technology because generators and uh motors run on coils of wires and magnets all right
1:15:48
so let's talk about a coil of wire so here is a little electrical terminal coming in and then your coil of wire might look like something like this now when I say it's wound on a core I literally mean that this could be some metallic core and I'm just wrapping the wire around it that's it now the act of wrapping the wire in a in in circles in a helical structure like that what it does is it concentrates the magnetic field because we know that every little part of this
1:16:13
wire is kind of emanating from it a magnetic field all through space in this concentric way but by winding it in a in a coil like this we are able to concentrate the magnetic field and make it stronger inside the coil let me show you how that works all right so what I have to do is draw a big version of this coil what I'm going to do is try to make it clear i hope I could do it so here
1:16:36
we have the coil let me draw the coil so here is one little part of the coil here is the next coil over all right here is the next coil over and I'm going to draw one more here's the last one here's the next coil over all right something like this now I'm not able to I don't want to draw it wrapping around because then that's going to make the diagram too cluttered just know that what's happening is this is going here and it's connected to here and then here connected to
1:17:08
here here and then connected to here i just don't want to clutter the diagram i'm only drawing sort of like the parts of the coil sticking out from the board all right and what I'm going to do is run an electric current through this coil anytime you see an X with a circle it means the current is going into the board and anytime you see a circle with a dot it means the current is coming out of
1:17:28
the board it's it's coming out of the board then into the board then out of the board then into the board out of the board into the board out of the board like this so it's making the coil that we are drawing up here now what is going to happen in terms of the magnetic field the right- hand rule right the right hand rule says we put our thumb in the direction of the current flow the current when it comes out of the board here is coming straight towards you my thumb
1:17:55
is pointed towards you and the magnetic field is in the direction of my curling fingers that means that there is a circulating magnetic field in this direction but this one's coming out of the board also and so we have the same thing here now where the current is going into the board the right- hand rule says our thumb goes into the board and the magnetic field circulates in this direction
1:18:18
right so it's still a circle but it's going the other way that's very important for you to know so it's still a circle but it's going the other way it's still a circle but it's going the other way it's still a circle but it's going the other way right into the board circulating like this every time the coil goes into the board like this all right but notice what's happening these coils are
1:18:41
very very close together there notice how tight it was wound on our uh on our uh coil of wire also transformers are the same way they're they're coils of wire that are wrapped like this and very close to each other the the wire is very thin and it's wrapped very very close to each other so even though I've drawn these apart really they're right next to each other so what you have remember this
1:19:01
is a vector field vector fields mean the direction matters also so if the field is going down right in this location then right next door the field is going up what happens right between these coils in between these coils I'll draw it i'll draw it in this in between these coils they cancel right in between the coils they cancel and what happens up here i'll draw it right here they cancel right
1:19:31
why because right here I have a magnetic field going up but right here I have a magnetic field going down and they're right next to each other so they add up literally it's like a it's like a rope where one person is pulling one direction and the other person's pulling the other direction if I'm pulling the same force but in two different directions they cancel and the rope doesn't move if a magnetic field is pointed this way and then right on top of it another one is pointed with
1:19:56
the same strength in the opposite direction they add to zero and so there's zero magnetic field in between there right but look at what's happening on the inside of the coil this magnetic field is pointed this direction and this one is pointed this direction because remember these are circular so it's kind of like the the the arrow is like this but look where this uh these arrows are going
1:20:17
this way and that means this one's uh pointed this direction as well so if the field is here and here and here and here on the inside of the coil it's in the same direction as they're all pointed right here so these magnetic fields are all lined up in the same direction and they're aligned in the same direction here so what you're actually going to have is you're going to have a uniform magnetic
1:20:39
field on the inside of this thing and it's going to be pointed in this direction so I'm going to try to draw equally spaced lines here like this because you can prove mathematically i'm not going to do it for you here but when you have an infinitely long coil like this then the magnetic field on the inside is everywhere uniform and it's uniform because all of these coils are adding putting a magnetic field inside in the same direction so they all add up together and in
1:21:06
between the coils they add up to zero now remember magnetic fields have to always form closed loops always so what actually happens is it's kind of like it'll be like this it'll be right next to here and then it'll loop around and connect back like this right so this will be here here here and these of course will be in this direction right here right and here you have the same exact thing
1:21:32
we have one right here and it's going to loop around right here right like this and then these are in the same direction like this right now what about these in the middle how do they close in well what's really going to happen is these are going to exit and make very very big circles to the outside i don't have enough room on my board but you get the idea they're going to make very very big loops coming around to the other side now here is the kicker here is the most important
1:21:58
thing if you make what we call the ideal coil or the ideal solenoid ideal means you can pack these uh turns very very close together and you make the coil of wire infinitely long okay we can't really build an infinitely long coil but what if we made it really really really long compared to the diameter of the coil like if the diameter were the the length of the diameter of this pen what if
1:22:21
we made it like 5 m long with the diameter of this pin and that would be a really long coil compared to its diameter you can show mathematically that if you make an ideal solenoid or an ideal coil is what it's called is the solenoid is when you make an ideal solenoid you can show mathematically that the magnetic field inside is uh high where the magnetic out magnetic field outside is exactly zero there's no magnetic field linkage now in reality it's not really zero outside because
1:22:49
you have to have closed loops but remember I said it's an infinitely long coil that means the coil goes to the end of the universe which we can never have and so you would have magnetic field lines that would be going like past alpha centauri to come back so that's just an that's just an idealization you can't have that but in an ideal solenoid the magnetic field is high on the inside and zero on the outside it's concentrating the magnetic field inside the coils now what is the
1:23:14
equation for the magnetic field here the magnetic field in this coil of wire is equal to the same uh uh permeability that we talked about earlier multiplied by the current flowing in the coil again positive current multiplied by n which is the number of turns per unit length in other words n is not just the the uh uh number of turns it's the number of turns per meter or something how tightly you can turn the things is what this is and this is the magnetic field
1:23:49
inside and the magnetic field is zero outside and this is for the ideal ideal coil now what does this tell me this tells me that if I make a very very tightly wound coil with tons and tons of turns per unit length per meter or whatever very very very tight with super thin wire uh then I'm going to have a high magnetic field on the inside if I put a lot of current through that coil the more current I put the higher the magnetic field direct relationship right and there's
1:24:23
no dependence on the distance inside there's no r like we had uh over here for the magnetic field around a wire we had the distance from the wire there's no dependence on distance here so that means that in an ideal solenoid an ideal coil of wire infinitely long as we said here then the magnetic field on the inside is uniform it there's no dependence on distance because it's uniform and
1:24:47
what's happening is you have the field cancelling on the outside and adding up on the inside because when you really think about it this uh this uh part of the coil is is pointing to the right with its field and to the left right here so you have uh pointed to the left right here and to the right right here this on the outside is pointing to the left uh a as this as we get farther and farther
1:25:07
away from this coil we can have a field pointed to the right to cancel any uh field pointing uh to the right right here so you get a a small field on the outside and the reason you get a small field on the outside is because as you get farther away from this part of the coil it's pointed to the right and this part is pointed to the left and so they add up along the outside of the coil to be
1:25:29
zero but they add up constructively on the inside so on the outside of the coil in an ideal coil that's infinitely long the magnetic field adds up to zero so there's no field outside but there's a fixed constant field inside all right now you might say man he is really diving into a ton of detail about coils the reason I want to talk about coils and so you understand the magnetic field is because it helps us to understand how permanent bar magnets work when I was young one
1:25:55
of the very first questions I ever asked anybody about science was "How do these magnets work?" I remember that i think I was four right and somebody started drawing a magnetic field right and it was just mystical to me it's still mystical to me and everything I'm about to tell you should hopefully illuminate you but ultimately magnetism is a quantum effect and none of us have a really good gut feel and understanding for quantum mechanics nobody really understands quantum
1:26:22
mechanics so I can describe this to you as best I understand it but none of us really get quantum mechanics on a gut feel level so ultimately you may understand more than you did but you may not be completely satisfied because none of us are have a gut feel for quantum mechanics and magnetism is a quantum mechanical effect okay that adds up over large distances right so I want to uh and the and the nature of the coil of the wire generating a magnetic field is going to
1:26:47
be analogous to electrons generating the magnetic field inside of a solid so before I get to that I need to do some talking right i need to do some talking and I have a lot of stuff on my paper uh some of it I'll write down but most of it I'm just going to talk through it because if I just start writing it's going to be writing and writing and right i don't want that i just want to explain it
1:27:05
to you all right so we have magnetism in matter right when we talk about magnetism mostly what we're talking about is pheromagnetism pharaoh has the prefix pharaoh pherohomagnetism which means iron ferrris means iron right some of the first magnetic materials very easy to magnetize iron and the iron filings we were using as proof of that very easy the most common thing we have to really demonstrate magnetic effects what is ferromagnetism right what it is or what is a
1:27:34
magnet right in general what it is is essentially the electrons that are inside of the atoms in some materials can be aligned in such a way that the magnetic fields that are uh individually contributed by all the different electrons can align up so they can add add together to make a larger magnetic field that can emanate from the bar magnet let me say that again in ferroagnetic materials or permanent magnets like we have talked about here when they are magnetized already what
1:28:07
has happened is on the microscopic domain the electrons have been lined up and I'll talk about more how in a second they've been lined up in such a way that their little in little bitty individual magnetic contributions are adding together and when you have trillions of them aligned in the same direction the magnetic field is additive creating a strong magnetic field which can then emanate from the substance it's kind of like this coil here individually in each little turn of the
1:28:33
coil is generating its own little magnetic field but by aligning them by winding it in a certain way we can force them to add together and give us a high field on the inside and very low field on the outside in ferroagnetic materials that's automatically happening in nature so ferroagnetism refers to sort of two things it's what we typically think of when we think of bar magnets but it also ferroagnetism also applies to materials that are not already
1:28:57
magnetized but can be magnetized very easily for instance when I bring the neodymium magnet close to the iron filings what happens the iron filings start becoming attracted now we're going to talk about the attraction part in a second but what's happening on a microscopic level is the magnetic field from the permanent magnet starts to enter into the vicinity of the iron and that magnetic field causes the electrons in the iron to be aligned so that their magnetic what we call
1:29:25
magnetic moment of the individual iron electrons that are in there can become aligned in the in an overall same direction so essentially what we're doing is we're causing the iron filings to become magnetized when we say become magnetized what it means is we begin to align the magnetic directions of all the atoms in the iron once they're aligned they form sort of their own little magnetic domain
1:29:48
is what we talk about and then the two magnets can be attracted together the iron filings fly forward and then hit the magnet so it's a two-step process the magnetic field permeates the iron aligns the iron's electrons into a common direction and and so then the magnetic fields are additive it make turns it into a magnet at that point and then because you now have two magnets they can be attracted to each other and then we have the attraction effect same thing with the paper clips
1:30:13
same thing with any material that can be uh very easily magnetized we call it ferromagnetic all right when we apply a magnetic mater uh field to a ferroagnetic uh material it gains a a very uh strong magnetic moment is what we say when we remove the magnetic field another characteristic is it it re it begins to retain some of its magnetism and so that's a characteristic of ferroagnetic magnetism as well so if you notice when we magnetize the paper clips even after we
1:30:44
turn the electric current off we still had the paper clip hanging there that's because it's a ferroagnetic material once the alignment happens even after you remove the external stimulus the the atoms are still aligned weekly weakly okay uh they're not strong magnet but they are still aligned and that's why they were still being attracted even after we turned the electric current off or the iron filings were still attracted even after we kind of moved them
1:31:08
uh off to the side and they weren't no longer interacting with a magnetic field so ferroagnetism is a phenomena where matter can be magnetized by microscopically aligning the electrons in a in such a way that I'll talk about in just a second and that creates an external magnetic field and then the two items it can be attracted to a magnet and even after the magnetic field is removed it retains uh some percentage of the magnetic uh magnetic moment that it had
1:31:38
uh and eventually what happens is the material is everything is at a certain temperature at room temperature and different materials behave differently but basically the thermal collisions of the atoms inside slowly begins to destroy the magnetic alignment and that's why they don't stay magnetized forever now some materials if you form a magnet properly and you put it in a very strong magnetic field it can retain its magnetic moment for a long period of time but the paper clips we
1:32:05
were dealing with uh they were weakly magnetic after we turn the electromagnet off but they're not going to maintain their magnetism forever because thermally the atoms are being agitated constantly and they're going to rerandomize the magnetic moments of the material of the electrons that are inside of there all right so I've been dancing around a bunch of things because this is really a quantum mechanical thing and I can't get too far into it without bogging us down in a lot
1:32:32
of theory but in general that is what is basically happening with ferroagnetism any bar magnet that you see that's given to you that's already magnetized it's a ferroagnetic material it's already been aligned with a very strong magnetic field uh in the factory we have materials in the ground we pull them out of the ground they're already magnetic uh magnetic how do you think they're magnetic because the earth is a gigantic magnet we have a magnetic field and it can align
1:32:56
uh the magnetic domains there and it can create permanent magnets in the ground the some of the first uh experiments were magnetism with magnetism were done by pulling rocks out of the ground and figuring out that they can attract things right attract and repel weekly uh if you remove the magnetic stimulus they retain their magnetism for some period of time but thermally they will eventually lose it and if you heat them up beyond a certain point they'll completely lose their
1:33:20
magnetism because the collisions thermally will rerandomize the electrons that were aligned inside of the material all right let me read my notes to make sure uh magnetism all magnetism is purely a quantum mechanical effect you cannot explain it in terms of what we call classical physics quantum mechanics was uh invented in the very early 1900s it explains so many things and enables all of our
1:33:44
modern technology from phones to communications equipment to computers to satellites quantum mechanics is everywhere it also governs magnetism and uh if you uh don't care about that I mean that's fine but all of our power generation comes from magnetism as well so it's kind of important that we understand a little bit of quantum theory it's a but it is a quantum effect all right magnetic materials that we call ferromagnetic iron obviously because of uh pharaoh it means
1:34:09
iron cobalt and there's several others as well that can be uh uh have a strong magnetic field and retain their magnetism after we pull it away all right so now I think what I want to do is I want to talk a little bit more detail without trying to bog us down too much into what it means to align these electrons all right this is going to be a little tricky because it's a quantum effect and
1:34:29
so I'm going to draw pictures that are not true quantum pictures but they can still give us the idea remember that we said that uh basically if you have a coil of electrons that are circulating in this coil what we can do is we can get a concentrated magnetic field inside the coil so if you just consider forget a coil just consider a single electron moving in a circle like if it's just move if you could just grab it with your finger and move it in a circle it should generate
1:34:57
a magnetic field pointed in a certain direction what would that look like right that's what I want to talk about next what would that look like let's say we have uh an electron moving i'm drawing kind of a side view here kind of in this direction like this right and that means at one moment in time the electron is right here it moves this way it moves this way and then the electron later
1:35:17
in time is right there and these arrows are not magnetic fields it's it's the direction i guess I'll shade them so that we don't get them confused with magnetic fields right it's it's circulating like this in other words imagine it just kind of going around in a circle like this and we know that moving electrons generate magnetic fields how in what direction would it be uh uh would it be generated in well first of all I want to talk about something called angular momentum right or
1:35:43
spin right so the spin axis of this thing you would you could think of the spin axis of this thing call it s or the angular momentum in the direction of travel you have an angular momentum pointed uh perpendicular to however the thing is rotating we call that spin or you can also think of it as angular momentum right if I wanted to figure out how the magnetic field was pointed here I would use the right-h hand rule but remember the right-h hand rule deals with positive
1:36:08
currents everything has to be reversed when you're talking about electrons so if I put my finger into the board if if the thing is going this way right here that would be uh uh positive current flow but the electron is really going in that direction so what I would do is I would turn my finger around and say the positive current would be going the opposite direction of the electron remember the
1:36:28
right-hand rule thumb points in the positive current flow so if this thing is is going like this it's going into the board here but then I have to turn it around because the positive would be going in the exact opposite way that would mean that I would have a magnetic field circulating uh kind of like this uh around it would basically be going down and then kind of like back up through
1:36:51
here right at this point in time if I again it's coming out of the board which means I go into the board here then I'm going to have a a circulation and a magnetic uh field that's going to be going down like this and then this way it's going to be going the opposite way it's like one little loop of the coil that we had just talked about right here and notice that these are kind of additive
1:37:11
so we get a strong magnetic field in the middle and a kind of a weak magnetic field uh everywhere else now if you can this is why I said I'm lying to you a little bit because electrons are not little balls okay electrons obey wave mechanics from quantum mechanics but you can still think of them classically as little balls and it helps us visualize it but just know that I'm lying to you a little bit they're not little balls but classically we can envision them like this okay
1:37:36
so don't get too mad at me i'm just trying to make it easy for you to understand if we make the radius of this thing smaller and smaller but keep orbiting this electron then what's going to happen is we're going to get a very concentrated magnetic field on the inside as we get it smaller and smaller and smaller what happens if we make the radius of the thing so small that really it's
1:37:56
not orbiting it's just like a ball rotating would the electron have a magnetic field associated with it the answer is yes every school child learns that electrons and protons have charges and they repel electric repulsion either they repel if they're the same charge or they attract if they're opposites opposites attract right but most school children are not taught that electrons also have a
1:38:20
magnetic field associated with them we can measure it very very accurately it's called the magnetic moment of an electron and even though we know electrons are not balls that spin we can still envision it in this thought experiment an orbiting electron getting smaller and smaller and smaller eventually what it is is just a a single electron that is kind of like rotating even though it's not
1:38:43
rotating but if you had the radius of it getting smaller and smaller eventually it rotates then it there should be a magnetic field associated with this and the magnetic field that we measure for electrons is a fact that and it behaves kind of as you can think of it as an electron spinning so we say that electrons have spin now it doesn't really mean that electrons are balls that spin what it
1:39:08
really means is electron is this thing that nobody can really visualize but it obeys wave mechanics and they have angular momentum which means they have a spin axis and they have a magnetic field oriented in a certain direction somewhere along the the line of that spin axis right so if we do the right-hand rule and figure out that these things are essentially if it's if it's kind of going this this direction the magnetic field is pointing uh down in the center here if you
1:39:34
shrink the radius of this thing then what you I'm going to turn I'm going to take the little arrow away and I'm going to put the uh I'm going to take the uh I guess I'll put it here this is an electron right uh here then what we can say is that electrons behave as if they are spinning and they have a sort of a magnetic field that emanates from this or from them and uh as you might guess
1:39:55
looks something like this right now this is not an exact uh uh exact picture or anything like this but essentially they behave like this so they're you have uh pointing like this like this pointed like this right so if you look at it it's almost like like down and then up but if you shrink it down it's like along the spin axis it should be pointing down and so the along the spin axis it's
1:40:20
pointed down and so they're coming down out like this right and they kind of go back into the other side so it's sort of like just shrinking down this concept right here so there's a lot of things going on inside of an atom we have electrons surrounding the atoms those electrons we say are orbiting but that picture of a solar system of orbiting like planets is not really true but it's
1:40:44
still good for us to visualize that general idea there is an angular momentum of the electron cloud around an atom that's what we can say is true and that contributes to some magnetic effects but more dominant than that is that the electron even just by itself spins all the time now it's not really a ball spinning but it has angular momentum right it has angular momentum and so it has a spin axis
1:41:07
we can label here and then it has what we call a magnetic moment which is going to point down this magnetic moment of the electron points down we call it mu subs this is the magnetic moment of a single electron by itself not near an atom not near anything it appears as if it's a spinning ball it's not a spinning ball but that's a good way to think of it and has a magnetic field oriented opposite to the spin axis the reason it's oriented opposite is because the right-h
1:41:33
hand rule is for positive charges but electrons are negative and so the axis is flipped opposite exactly why I spent time on the um right-hand rule earlier so in ferroagnetic materials what we say or what the theory is is that the electrons that are in all of the atoms in a ferroagnetic material are very easily or much more easily able to be aligned what it me means is the spin axis of
1:42:00
all of these electrons are able to be aligned and that means the magnetic moments and the magnetic fields are all able to be aligned so if you can imagine trillions of these electrons everywhere in the material and they're all lined up like this then the magnetic fields will be additive just like they're additive inside of the coil and then they're eventually exit the whole thing and come back around and enter into the other side and this is why if you break a magnet in half
1:42:24
there's a north and a south pole so you think okay I'll just break it in half what will happen well then you have a new north and a south pole on each piece because there's not just a north and a south pole there's almost an infinite number of north and south poles all the little electrons are forming kind of a tiny little north and south pole bar magnet you can almost think of each electron
1:42:42
almost being like a little bitty bar magnet inside so if you break it in half all that's going to happen is the field lines are going to connect to wherever it broke off so you can never get down to a single uh you'll always have closed loops I guess is what I'm trying to say even if you break the bar magnet in half all right so the picture that we often draw is in a ferroagnetic material
1:43:05
right uh like a bar magnet or something like this then uh uh below a certain temperature or if it's not magnetized already the spins of the electrons are basically in in all the material they're just randomly lined up in different directions right but if you apply a magnetic field to this material or if the earth does it because the earth is a permanent magnet right then what you can end
1:43:29
doing is you can end up aligning them in the same direction now in reality they're not all lined up in the same direction because remember everything is at a certain temperature everything's being agitated so thermally there's collisions happening and there things are being knocked out but still there's an overall alignment happening in aggregate across the material and that makes the magnetic field emanate from one side to the other and it's because of the quantum mechanical
1:43:53
nature of electron behavior so there's a tiny contribution from the orbiting of the atom we call it the orbital angular momentum but there's a larger contribution to the spin angular momentum of how electrons behave so that's what effectively ferroagnetism is any bar magnet has already been aligned and it retains that magnetism uh but if you heat it up too much thermally it'll start to be unaligned again and you can demagnetize a magnet that way all right um now let's talk about
1:44:21
let's see I talked about that talked about that let's talk about another kind of magnetism you may have heard of called paramagnetism so the prefix parah I looked it up it can mean lots of things like 10 different things but it can mean beside it can mean near beyond or abnormal so think of paranormal as like abnormal so paramagnetism is sort of like abnormal magnetism or you can think of it as near magnetism there's many different meanings for the word parah paramagnetism is
1:44:48
simply induced magnetism just like we can take ferroagnetis magnetic substance and line them up and they'll retain their alignment because of of the I I've kind of skipped over a lot the reason iron can do that the reason iron can be aligned that way is because of the way the electrons are paired up in the material at the at the quantum at the quantum structure of the of the electrons orbiting the atoms are paired up in such a way that allow them to be aligned like this most
1:45:14
materials cannot be lined up like this and so most materials are not magnetic at all well at least they're not ferroag magnetic many materials can be what we call paramag magnetic which means that if you apply a magnetic field to them they can be aligned but only weakly right and when you remove the magnetic field they immediately go back to their random state and they're unmagnetized many
1:45:36
materials are like this um examples are tungsten aluminum lithium typically if you put a magnet next to an aluminum can it won't be magnetically attracted but aluminum is weakly paramagnetic so you if you put it in a strong enough magnetic field it will align and turn magnetic but only weekly again the electronic structure of the electrons orbiting the atoms govern this behavior it's beyond the scope of this lesson and you study quantum mechanics and chemistry we'll
1:46:05
learn exactly in the electron configuration why some materials are magnetic and some aren't but it has to do with how the electrons are in the orbitals of the atoms and how they're paired up so paramagnetism alignment of the magnetic moments of the electrons when an external magnetic field is applied but again it's a weak alignment and when you turn off the external magnetic field the effect goes away uh and so then you uh it just loses all of its uh magnetism all
1:46:30
right we could talk about paramagnetism and ferroagnetism forever um but I think I want to be done with that for now i want to tackle the concept of why do magnets attract and repel i'm going to say right now that no matter what I tell you someone is going to email me and say it's wrong and that's because there's multiple ways of thinking about why this effect happens ultimately magnetic attraction is purely a quantum mechanical effect and we don't have everyday experience with
1:46:55
that so everything at the quantum level seems seems like it's unnatural but in fact it is natural because everything is made of quantum objects ultimately right but the way I'm going to teach you about it I think is a good way to think about it but just know that there are other ways to think about magnetic attraction you can even use uh Einstein's theory of relativity believe it or not to describe magnetism and I'll do that maybe another day but for now I want you to have
1:47:22
an intuitive understanding why magnets attract each other and how they can repel each other all right before I do that I need you to understand something the magnetic energy density i promise uh it looks complicated but it's actually very very easy to understand magnetic fields store energy right uh they store energy and when when you you can extract some of that energy and some of our modern devices like generators and things like that but they extract they they contain potential
1:47:54
energy electric fields also store potential energy so the equation that governs that is the following the uh the magnetic energy density is equal to the magnetic field strength squared divided by two times this constant the permeability which I mentioned several times applies to magnetism only thing I care about you knowing and I don't even care about the units although I'll tell you that the units is basically going to be jewels per some unit volume right it's an energy density
1:48:23
so the magnetic field you square it and then you divide by two numbers this is a number and this is a number so basically the energy density is just related to the magnetic field strength squared the higher the magnetic field the more energy it stores right we can build electronic devices coils of wire that store lots of energy and magnetic fields that can be released in uh you know in other um in other situations right in circuits for instance the best way to think
1:48:49
about stored energy is a rubber band if I pull a rubber band I'm storing energy in that rubber band how is it stored in the electric attraction between the atoms which are now being stretched apart it's wanting to pull them back together so there's energy stored in the electric field between atoms and electrons and there's energy stored in the magnetic field that exists in space and that how where the magnetic field is strongest then the energy is going to be
1:49:14
higher so if you think about it around this wire out here far away the the energy stored in the magnetic field is small but the energy density is very high very close to the wire the magnetic energy density is very high inside of the coil but very weak outside for the same reason now I need you to understand that in order to understand why magnets attract and repel each other so here we go
1:49:37
it's going to be easy to understand I promise here is a bar magnet right here is another bar magnet all bar magnets have some north and south pole i'm going to draw this one north south i'm going to draw this one north south now how are these things going to behave same uh same poles are going to repel each other we know that to be the case let's draw the magnetic field not the whole field we'll
1:49:59
just draw kind of a little portion of it comes out of the north goes into the south so this way this way this way it goes out of the north into the south right this one is going to go this way and it's going to connect again to its south pole out of the north like this and in to the south right now what's going to happen as we push these things closer together notice that the direction of these
1:50:26
arrows are kind of pointed uh at odds with each other but the closer I get them what's going to happen is they're going to be sort of additive yes you can think of it as a vector you can think of it some of it pointed this way and some of it pointed up so you are going to have a cancellation in the portions that are pointed at each other but you are going to have a portion pointed up and as
1:50:45
you get them closer together that's going to get bigger and bigger and bigger so they're going to be additive inside they're in general pointed in the same direction so you're going to have strong uh field inside of here as you push them together because you can see they're sort of pointed not exactly in the same direction but as they get closer together they're going to be more and more
1:51:04
if you can think about uh the ones coming this way they're going to be aligned up more and more and it's going to get very very strong magnetic field in the center but the stronger the magnetic field the more energy is stored so you have to think about how does the the universe operate the universe operates by going from high energy to low energy this marker has potential energy from the gravitational field of Earth here it is at a high potential energy when I let it go it's
1:51:31
going to move down to a lower potential energy because it's closer to the ground everything in general wants to travel towards lower energy if you start asking me questions like well why does everything try to go to lower energy i am sorry i can't help you but that is how our universe works the rules that are in place are that things tend to wind down towards lower energy when you drop things they go from high energy to low energy when you have temperature a a very hot cup
1:51:58
of water it tends to cool off because it's going from high energy high movement of the atoms to low energy low movement of the atoms when you stretch a rubber band that's high energy you let it go it goes to low energy state and I if you try to push these magnets together it's going to be trying to make a stronger and stronger magnetic field in the center which is going to raise the energy of
1:52:19
the magnetic of the of the energy stored there and the universe never wants to go to a higher energy state that goes against the laws of nature so when you put two magnets together because the magnetic field is trying to get stronger in the middle storing more energy it's going to resist that in other words I have to put work in to store the energy there let me say that again i have to put work in from my chemical reactions in my muscles I have to do work on the magnets
1:52:44
to store the energy that is now higher between the magnets because when I put them together and force them together and hold them there then I've now stored energy in the field where did the energy come from it came from my muscles where did that energy come from it came from the food I ate where did that energy come from the chemical bonds of the food I had so the energy came from somewhere
1:53:05
the food and into the magnetic field when I let it go they tend to push apart because the energy is then released and uh everything the universe tries to move towards lower energy states just like the marker goes from high to low the child on the slide goes from high to low the rubber band goes from high to low the cup of coffee goes from hot to cold high energy to low energy that's why they repel because as you push them together you're trying to make the field stronger there
1:53:32
which means more energy there it's like trying to go uphill on a slide you're going to have to fight and do energy and and work on yourself to climb a flight of stairs you this that's just the way the the universe works now let us talk about the opposite situation let's talk about the situation where now I have two bar magnets and instead of this I put this uh as the north pole here and I put this as the south pole here you already know what's going to happen opposites attract so
1:54:06
they're going to come together let's see if we can understand it the magnetic field exits and enters here exits and enters here it comes out here and enters here it comes out here and it enters here it goes out of the north pole always into the south pole so out of the north pole always into the south pole and then it goes out of the north pole here out of the north pole here and this direction and into the south pole here into the south pole here now I'm going to
1:54:34
erase this one because I think this is just makes it confusing but you can see the arrow uh actually let me erase this one as well i think it's going to be a little clearer if I put Yeah like this like that so like this notice the direction of the arrows when I bring these things closer together notice that this one is going up but this one at the same location is going down they're fighting
1:54:54
each other and as I bring them closer and closer together I messed up my drawing i'm sorry about that as I bring them closer and closer together what is going to happen this magnetic field is going to tend to cancel with that one and make the magnetic field strength lower this one is going to be going opposite direction of this one and it's going to tend to make the magnetic field strength lower in the center here so as I bring these guys together I'm going to
1:55:19
write down weaker as I bring them closer together the field gets weaker in strength but weaker in strength means weaker in energy storage and remember the universe likes to go towards lower and lower energy storage so two magnets attracting can be explained because when we bring those two poles of the magnet together we are cancelling the magnetic field making the magnetic field lower between them which is a lower energy state lower energy it's like releasing energy
1:55:47
from the rubber band the same way the rubber band comes together the magnets come together because as soon as that energy starts to get lowered it is just going to fly together to make the energy lower forces in nature generally always push things in the direction of lower energy gravity pushes you down the slide to lower energy the electric forces pull us to lower energy from the rubber band and the magnets pull each other together or push each other together into a lower
1:56:11
energy state together where the field is weaker you feel a repulsive force because as we try to do this the field is stronger and we're raising the energy here and so it wants to resist that okay that is about all I want to say about it i can talk about magnetic attraction and repulsive in other ways you can use relativity theory to talk about relativistic effects to explain why magnets work and I probably will do that one day because I think it's a neat way to look at it but
1:56:38
it's just another way of looking at it right an alternative way of looking at it you can also look at the magnetic force on a charged particle the deflection of a charged particle from the mag from the magnetic force itself to explain why magnets attract each other that's another fine way of doing it i thought about presenting all of those but ultimately I think that this is the most clear and uh elucidating to use a big word way to explain it the universe likes to go from high
1:57:06
energy to low energy when you push two magnets together with the same pole either both north or both south the same exact thing will happen if you take this if you can imagine the south pole over here they're both going to be pointed in the same direction and the two south poles are going to make a strong field and it resists that but if you flip it around they're going to attract to make the field and the energy stored lower now if you ask another question well why why does the
1:57:30
the energy of the universe like to get lower well I don't know and nobody knows all right or you might say back to the electron spinning you might say okay that's a neat theory about the electron spinning and how it explains magnetism but why do electrons spin i don't know okay and also is it a ball no we know it's not a ball quantum mechanics is a wave theory we know electrons are waves but they have some kind of angular momentum and nobody has a really good picture to describe
1:57:56
how a wavy thing has an angular momentum which we usually associate with spinning objects in the macroscopic level ultimately one of my favorite people that I've ever studied is a famous scientist named Richard Feman probably knew more about quantum mechanics than most people will ever learn right way more than me and somebody asked him "Hey explain to me why magnets work." and he thought about it and he gave about a 20-minute answer and ultimately concluded I
1:58:22
can't explain it to you because once you continue asking questions you get down to the point beyond which anyone has any answers to anything so all we do in science is we have models of nature right do magnetic field lines exist not sure they're a great calculational tool to calculate how things will behave though do electrons really spin not sure probably not but it's a great calculational
1:58:46
tool it's a good model of how the universe works maybe everything is string theory maybe everything is waving strings maybe angular momentum is something totally different than I can conceive of but that doesn't make the theories and the ideas worthless we come up with better and better models to describe the world this is how I chose to describe how magnetism is attracts and repel objects to you when you bring a magnet next to the paperclip it aligns the magnetic domains as we
1:59:13
drew in the paperclip and then now we've explained how magnets can attract and repel and then of course they attract each other so you're inducing a magnet to form and then they attract each other and then of course we uh talked about this if that doesn't satisfy you well join the club it doesn't totally satisfy me either but I think it's the best humanity can do with just making better and better models to describe our world i hope you've enjoyed this i know it was a bit long
1:59:36
i thought about cutting several things out but ultimately I thought you know what I'll just put it out there and see what people think so please drop me a line let me know what you think and if you made it to the end thank you very much drop me your thoughts and I'll see you in the next one
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