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Magnetic Flux & Faraday's Law · Acedra
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Magnetic Flux & Faraday's Law
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0:03
hi guys happy Monday how's everybody feeling today got a case of the Mondays office space anyone office space it's a great movie you got to see office space um all right welcome back hopefully that weekend wasn't uh Too Short seemed a little short to me um but we had a good time we went down to Comic Con and walked around a bit didn't anybody go down to ComiCon yeah it was kind of I we didn't go into the convention center we just walked around near the convention center
0:36
and lots of interesting characters down there yeah fun place my boy is like three and a half so he was walking around in an outfit because that's what you do right when you're three and a half or 35 or however old you want to be but he had a Superman hat on he had a Batman shirt on and he had a cape that said shooterman so he was looking good and confusing everybody all right we uh have actually quite a bit to cover uh today and we in fact might not finish up this chapter
1:12
today uh we might work on it a little bit more tomorrow so uh the first thing that you might notice is that the homework that was due tonight is no longer due tonight it is due tomorrow night okay I see a sigh of relief over there several people just looked up to the heavens so that's good um so let's get going on this we'll talk for about 45 minutes we'll take a break and then we'll talk for another uh three or four hours okay so just get comfortable and let's have a discussion
1:46
uh let's talk a little bit more about this idea of flux okay magnetic flux through a surface and let's ask uh let's ask this question let's say I have lines of B that are pointing to the right and now I have a surface like that okay so it's a plain parallel surface that is perpendicular to those lines of B and we want to ask what is the flux through that surface and remember flux is lines of B through a surface all right well here comes one line goes through the surface here comes another
2:38
line goes through the surface here comes another line and it goes through the surface and so we would say what's the flux it's three okay we know that it's B times the area a but whatever units you end up with we can just say that is three three lines of B are going through that area but now let's do the following let's say we're going to take our lines of B still pointing to the right and but we are going to tip the area sideways okay so this is supposed to represent a vertical plane but now it
3:22
is a horizontal plane and it's still area a what is the flux in this case what do you guys think sitting here in my studio on what's the flux through this surface Z zero right the Top Line skims right on pass the middle line skims right on pass the bottom line skims right on pass none of them actually go through this infinitely thin surface and so the flux is zero okay so there is some relationship between B and the area which is important and let's look at the intermediate
4:10
case so let's say my lines of B are pointing to the right and now I'm going to draw this area but it's tilted okay and this is the surface normal to the area and hat and let's say that this thing is tilted down at an angle Theta relative to the horizontal it's still area a but now what is the flux it's not the full three it's not zero it's something in between okay and so flux in this case remember we write flux with a capital V is the following it's B time the area time the coine of that angle
5:06
Theta okay when Theta is zero you're back to this case okay and therefore the flux 3 is just B * a * the cosine of 0 de which is just B * a in this case it would be B * a * the cosine of what well the surface normal would be pointing up and so the angle between B and the surface normal is 90° and we know that 90° when you take the coine of it you get zero and so for some angle in between like we have here it's just B * a * cosine of that angle right cosine of
6:01
theta all right so let's try this for um an example and let's try the following situation
6:36
so let's say we draw an XYZ coordinate system right-handed XYZ and now let's have our B field pointing up at an angle of 35° and this is in the YZ plane okay so it's in the plane of the glass here and now let's draw two different areas let's draw this one okay and we will call this one area a XZ because it's in the XZ plane and then we'll draw this
7:25
one and that's area a XY because it's in the XY plane okay and we want to find the flux through the XZ plane and we want to fly we want to find the flux through that XY area okay how do we do this well we go back to our definition right flux is going to be B * a Time the cosine of the angle between two all right so for f
8:17
XZ what do we have well we've got B we have some area a and we're going to say that both these areas are equal so axz is equal to axy and we're just going to call that capital A and now we have the angle between this area and this B field okay and now we have to be a little bit careful right because the area has a surface normal to it and that's the relevant angle here so the surface normal to axz is in fact directly to the right let me make a little space here it is directly to the
9:14
right okay that is the normal to that surface so if that's pointing in the Y AIS and B is pointing up in this direction what is the angle between those two well the other angle is 35 so this one has to be 90 minus 35 90 - 35 is 55 so this is 55° so that's the relevant number that you want to put right there b * a * the cosine of 55° what about uh the other one f x y well axy is pointing straight up right that's the normal to it and so that is along the Z and we
10:14
already know that the angle between z and b is 35° so that one becomes B * a * the cosine of 35°
10:30
okay so this is how you attack flux problems when you're dealing with B fields in areas that are not necessarily at right angles to each other or parallel to each other it's somewhere in between the two if you guys have questions as we go just shout them out it's going to be a little hard for me to see your hand but and what was your name again over here d d d is monitoring the uh chat room online hopefully for this class not some other chat room so if you have questions
11:05
out there at home fire them up
11:19
hi I should just have a a whole bunch of like stick on things right so I could just do my little emoticon right there Hi
11:35
okay yeah let's go back to um let's go back to Faraday's law for a second okay the reason that you care about flux is because when you have a current Loop when you have a loop that can generate current in it it depends on how much flux is going through it but it also depends on how quickly that happens so Faraday's law law tells
12:04
us that the EMF generated remember EMF is like a voltage it's electromotive Force it's how hard is that thing going to get pushed those charges how hard are they going to get pushed it is negative Delta V over delta T okay so this is kind of cool because if I just take a b field and I just have it pointed in One Direction and now I take a current Loop and I spin it at some frequency Omega what happens in this Loop okay what happens is when it's facing one way
12:53
there is current generated one way and when it flips around and goes the other way there is current generated the other way and so this will actually generate an AC current in this little Loop okay current's going to go one way and then later on it's going to switch and go back the other way and it will keep sloshing back and forth between those two and we can understand that from this idea of flux flux was positive in One Direction and then the loop flipped around and so now it was negative and
13:29
then it keeps going it flips back to positive and so forth but let's say we do this with more than one loop I don't want just one coil I want a whole bunch of coils in that case we just add up the EMF which is kind of like adding up the voltages you throw an n in there to tell you that you're going to get n times the EMF that you would have with just one coil okay so if we have a whole coil here let's see if we can draw
14:12
this okay there's a whole stack of coils and now as it rotates in this B field it's going to generate an AC current and we know that it's going to generate it sinusoidally because it's rotating around at Omega all right so let's take a look at an example problem of this
14:57
okay okay so so we're going to start um with our coil pointing down and our B field pointing to the right okay and this is our coil right here and there's a few different loops on
15:19
it and it's pointing down so we have our surface normal n hat pointing down and let's give you the following information when we start this experiment at tals 0 this angle is of course 90° but this thing is going to rotate into a new position and at some later time it's sitting right
15:52
here okay n hat is now in this direction and this angle between those two is Theta 1 and Theta 1 = 45° and it does this at a time T1 of a 100th of a second okay so this thing is rotating pretty quickly it rotates into this position in a 100th of a second and let's give you a little bit more information the number of turns on this coil is is 950 uh the coil has a radius so this is information about the coil the radius of the coil R is 6 cm so 0.06 M and let's also tell you that the EMF
16:50
generated is 0.065 Vols okay and this is is all the information that we're given and let's say that we are looking for B what is the strength of the B field that's going to generate these results okay so we go back to our definition for EMF okay let's make a little room
17:33
so the EMF we said was n Delta V over delta T all right and we're only really worried about the magnitude here so we'll just put some magnitude bars on it not worry about the negative sign it's Delta V over delta T but what is Delta V well F we said was B * a * cosine of theta so a Delta Fe is just going to be Fe in the first case which is B * a * cosine of some Theta
18:22
1 and then we're going to subtract F KN okay so this is B * a * cosine of we just called it Theta that's what we get on the top on the bottom we have delta T and now we have some common factors and so we can factor out some stuff we've got n * B * a we have the cosine of theta 1 the cosine of theta and we're all dividing this by delta T and so now we can solve this thing for B what do we get well I've got to multiply across by delta T so I get EMF Epsilon time delta T and then I have to
19:13
divide by nide a and divide by cosine Theta 1us cosine of theta and now we should have just about all those numbers except it's a circular Loop right so we need to put in for the area a so this is pi r SAR for our area a cine Theta 1us cine of theta okay and now we can solve this
20:05
all right so we've got b equals Epsilon we said was 0.065 volts delta T was 0.01 seconds down on the bottom we've got n which we said was 950 we've got Pi which is pi we've got r which is 0.06 squared and then we have cosine of theta 1 which we said was 45° Theta was 0° okay and if somebody punches in this stuff into your calculator tell me what you get so we've got 6.5 * 10 the - 2 we've got another 10us 2 right there we've got 950 we've got a pi we've got 6 * 10 - 2^
21:11
2ar cosine of 45 is 1 over < tk2 cosine of 0 is what yeah oh was it okay let's sneak in nine right there there cosine of 90 okay good yeah that's right because the surface normal is pointing down yeah thank you so cosine of 90 we know that cosine of 90 is zero okay so this is what we end up with and let's approximate it here while you guys punch it into your calculator so we've got 6.5 * 10us 4 up top we've got 9.5 * 10 2 we've got a pi we have 36 * 10-4 and then we have a 1 over <
22:05
tk2 and let's see what this becomes 10us 4 drops out with that uh we've got 6.5 over this stuff which is 9.5 * < * 36 this is a lot of numbers here but let's let's keep going we're going to say this is 10 so this becomes a 10 the 3 and then we've got Pi * 36 that's got to be really close to 100 right so that's 10 3 * a 10 2 so that's a 10 5 and then we got a 1 over < tk2 and that's the same as multiplying by < TK of two up at the top which has to be really close to 10 up in the top
22:56
and so I'm going to say my guess is 10 - 4 that's what I'm guessing anybody punch it into your calculator and get an answer 86 8.56 * 105 good so that was a decent guess right because 10 * 105 would be 10-4 okay so that is the strength of the B field what are the units on B field Tesla right so we put a capital T right
23:38
there okay questions about that
23:45
one okay
24:08
Dave how you doing do you have a good weekend oh great weekend did you go down to Comic-Con no I enjoyed gardening in the rain we uh checked out the there was a truck down there from the movie Into The Storm oh yeah and uh my was looking at this truck and saying wow what does that do what does that do what does that do and the lady was giving him the whole Spiel and then finally she leans over and she goes it's not real it's a fake truck for a fake storm and he was like you're so
24:46
bummed I said yeah I got a car that goes into the storm but it's in San Diego goes into the light Breeze the sprink okay so let's talk a little bit more about uh lens's law for a second we introduced this last time but let's just review what lens's law says lens's law is solely for determining the direction of the current okay farad Faraday's law tells us about the EMF the voltage that develops okay but lens's law tells us which way that current is going to get pushed and it's
25:23
very simple right we said nature abhors a a change in
25:35
flux nature abor a change in flux so let's say I do the following let's say I have a magnet that is approaching a current Loop like so North and South okay and we want to figure out what direction the current is going to go well the magnetic field is pointing up out of this thing okay so the magnetic field from the bar magnet is up and we know it's spreading out and some of it is poking through our
26:26
Loop like so so the flux is increasing in that Loop and it doesn't like that it doesn't like an increase in flux and so it wants to make a b field that is going to point down okay the loop wants to generate a current such that the B field is pointing down which means it's going to develop in this direction if I use my right hand rule what I said was if you put your fingers in the direction of the current then your thumb will be the direction of the B field so for this one we've got a B
27:14
field that is going down because the current Loop is coming around like this right this is the direction of the current and so the B field is in fact pointing down
27:35
okay and this is B due to the loop okay I I drew it without the magnet here for Simplicity but the idea is that nature of wh is a change in flux and so if flux is increasing from some other source it's going to do whatever it can to make it decrease okay so what happens now if instead of doing something like this we just take our Loop and we move it through a region of magnetic
28:13
field so let's do the following we're going to draw a region of magnetic field here B where it's everywhere pointing out of the page okay when it's pointing out of the screen and we take a ring and we start to move it
28:40
through something's going to happen there's going to be current that develops in the ring now before it gets to the magnetic field region what's the current in the ring no current right current zero okay when it is in the center of this region and it's still moving to the right what is the current in the
29:23
ring what do you guys think what is it 90% of the time when I ask you zero the current zero why because the flux is not changing in this region it's moving through a constant magnetic field a uniform magnetic field so the only time something interesting happens is right here where it crosses and right here where it crosses okay and when it crosses there and it crosses there the current is no longer zero and now we have to think about the flux okay so the flux is out of the
30:07
page which means that the ring wants to make a current that is going into the page right and this helps if you look over there at the computer monitor instead of looking at me okay so B is coming out of the screen but my ring wants to make something wants to make a field that's going into the screen okay so how does it do that it does it like this if you take your right hand and you put your fingers in the direction of the current right I'm going to wrap my fingers around in the direction of the
30:45
current my thumb is telling me that that will make a b field going into the screen okay so current is going to develop in the ring in that direction and now you know exactly what's going to happen on this side the exact opposite is going to happen so over here current in fact generates is generated in that direction because the B field that it was in is decreasing the B field coming out of the screen is decreasing but it wants to keep that going it doesn't want to
31:21
change and so by putting a b field in this direction take your right hand wrap your fingers around around now we got our thumb coming out of the screen okay and so it's making a current in that direction and then finally when it gets back out here and it's still moving along at V then current goes back to zero so the only time current develops is at these boundaries
32:01
anywhere it's uniform or zero then there is no current that develops in the
32:20
loop okay any questions about that did I get the right hand rule right did everybody agree with what I was doing okay I wrapping around this way gives me a b that's pointing into the screen I wrapping around this way gives me a b that's pointing out of the screen
33:02
okay let's say we do the following experiment let's take a big bar magnet okay bar magnet has a north and a South Pole and now let's take a voltage source
33:22
here and let's make a little solenoid right here
33:32
okay and let's run some wires around this
33:40
solenoid and eventually coming back to our voltage
33:47
source so if I run current through this thing it's going to create a magnetic field if the North Pole of that magnetic field is facing this North Pole they're going to get pushed apart if the South Pole of that magnetic field that I generate is facing the North Pole they're going to get pulled together and so if I alternate it right if I have a voltage source here that is oscillating what's going to happen to the solenoid it's going to go up it's going to go down it's going to go up and
34:27
then it's going to go go down okay and if I attach
34:35
that to a big cone and I turn this thing on what have I just produced what is this
34:50
device anybody this is a speaker okay this is your speaker or loudspeaker however you like to say it okay this is your speaker cone in your stereo if you open up that front cover you can see the cone there's usually a sort of round shape on the inside and you can look in there and you can see where the wires attach to the cone and then on the back side there's a very powerful magnet and you know this because if you take the speaker cone out and you stick it up on the fridge it
35:25
just sticks it right that magnet is very powerful so when I run current through this thing back and forth it flips the direction of the B field in this solenoid back and forth and The Cone goes up and down and it emits sound
35:45
waves okay so this is exactly how your speaker works but let's say we reverse the process let's say we do the whole thing
36:01
again okay here's our
36:07
solenoid anybody try my solenoid joke on your ta
36:17
no try it it's good for a hearty chuckle how's your lab going I'm so
36:26
annoyed let's say we do it again but we're not going to drive the circuit okay we are actually going to blast it with sound waves coming
36:43
in okay instead of sound waves going out we're going to blast it with sound waves coming in if the sound wave hits this speaker cone what happens it pushes the speaker cone up and down just a little bit okay just like this one over here and if that speaker cone gets pushed up and down a little bit this coil is now closer or further from the magnetic field due to this bar magnet and if there is a changing flux through the coil then there is an EMF that is generated here and so let's not
37:27
label this V Let's label this EMF Epsilon okay and we know what that is EMF Epsilon is n Delta V over delta T so now if you put a device here that can measure that EMF that voltage all of a sudden you can in fact record sound waves anybody know what this device is called
38:00
what have we created here maybe not the most efficient creation but this is a
38:12
microphone okay but wait a minute I just drew the exact same pictures right am I saying that you could use this thing as a speaker but you could also use it as a microphone yes that's exactly what I'm saying and that's kind of weird to think about right but if you just grab hold of your speaker and you start yelling into your speaker and you measure the voltage coming out it will mimic your sound waves going in okay it's not going to be the best right real microphones like the
38:46
lapel mic that I'm wearing right here are designed differently but the idea is exactly the same if you turn sound waves into voltages it's a microphone if you turn voltages into sound waves it's a speaker it's all the same reversible physics which I think is pretty cool so when you're stuck out there in the wilderness you don't have a microphone just grab your speaker it'll work can you hear me now can you hear me now can you guys hear me now okay good speaking
39:28
yeah um Sarah asked a question about a couple of the uh uh the misconceptual questions on the homework so let's take a look at a couple of those um and the first one says a loop rests in the plane of a page of a textbook while a magnetic field is directed into the page a clockwise current is induced check all that apply okay so we got to figure out when the clockwise current is induced and let's see if we can draw the picture so this is related to what we just
40:02
talked about a second ago uh a loop rest in the in the plane of a page of a textbook while a magnetic field is directed into the page so B is everywhere going into the page or if you look at the computer monitor it's into the screen and it says that a clockwise current is induced okay so clock wise current means it's going around like that all right clockwise current going around like that in the loop will generate a b field in the loop that is
40:47
pointing out towards you right take your right hand and put it in the direction of the current let's see if we did this right I think I I got it wrong I think it's going into the screen right because I put my fingers around in the direction of the current and my thumb is coming back into the computer monitor okay so how would it possibly do that the way it would do that is if this B field was getting weaker then it would try to keep the B field in the same direction so one of
41:27
the options is when the magnetic field gets stronger that doesn't sound right okay one of the options is when the loop is moved sideways across the page maybe let's come back to that one in a second it says when the magnetic field is tilted so it is no longer perpendicular to the page so if I took this whole B field that was pointing into the page and suddenly I pointed it parallel to the screen then the flux would drop in that Loop and it would therefore make a b field that
42:10
would try to keep the flux going in the same direction so that one sounds good all right I'm going to click that one the other one the last one says when the size of the loop decreases right remember flux is equal to B * a * the cosine of the angle so if the area decreases then the flux through it is starting to decrease it doesn't like that and so it's going to make a b field that is stronger to compensate for it and it would do it in this particular direction so I like that one as well so
42:52
I have two answers right now and let's go back to the first one it says when the Loop is moved sideways across the page so if I move this Loop in this uniform B field is that going to generate a current no right it's only when you get to the edge of the page that it would generate a current so when it crosses this Edge or it crosses that edge then it will generate a current but if it's moving all in the page AG in the uniform B field then there won't be a current so I
43:31
would say that there are two answers I would say that when the B field is
43:39
tilted that sounds like a good one to me and I would say when the area decreases so I'm going to answer those two and click in and see if I got it right and it says correct hey cool
44:00
okay questions about that one
44:11
yeah yeah so when you have um current in a loop you can do this if you curl your fingers that's in the direction of I and then your thumb will tell you the direction of B this is a caveat to the right- hand rule that we talked about last time okay an alternative form of the right hand rule so if I curl my fingers around in the direction of the current then my thumb is going into the screen okay so if you hold up your right hand and try that looking at the computer monitor if you hold up your
44:57
right hand and you curl your fingers around in the direction of the loop then your thumb should be going into the screen okay into the screen is drawn with an X does that is that working for everybody okay so the only reason we drew I in this direction is because in the problem they told us that that is the current that's induced in the loop okay they gave us that little bit of information okay any other questions on that one
45:36
yeah it's zero inside if B doesn't change a doesn't change or Theta doesn't change so the two that they gave us where it did change was this one B changed and this one area changed oh I'm sorry this first one is not B changing it's Theta changing right it's tilted Theta was changing in that one okay so if it's moving across in a uniform B and the area of the loop doesn't change and the B field doesn't change and nothing is tilted then there's no current that develops but if
46:18
something here changes then there is a current that develops okay did that answer your question okay
46:42
yeah uh so what this square area represents is a uniform B there and then outside b equals z yeah so certainly if you move this Loop all the way to the edge then B would be changing okay and so you would develop a current yeah okay let's take a look at the next misconceptual
47:29
okay so the next one uh it has a little figure and let's draw it right here we've got a ring and then there is B field which is pointing out of this ring okay and it says the following a non-conducting plastic hoop is held in a magnetic field that points out of the figure as the strength of the field increases so B field is coming out towards you and it's increasing we need to figure out what's going to happen to the EMF in this Loop and here are some choices an
48:12
induced EMF will be produced that causes a clockwise current no induced EMF will be produced an induced EMF will be produced that causes a counterclockwise current and induced EMF will be produced but no current H what do you guys think do you like the last one why do you like the last one okay EMF is Delta V over delta T and we know what Delta V is right it can change change B it can change a or it can change Theta so is something changing yes they tell us that b increases so B increasing
49:11
means that this is non zero okay so EMF is
49:24
produced now what we said was EMF being produced means that there will be a current generated in this Loop but you can think of this loop as composed of metal and a resistor and what they tell us is that it is a non-conducting plastic hoop so if it's plastic what is r
49:59
approximately or we should say approaching it's approaching Infinity right what is the current that develops I is equal to v/ R which is EMF Epsilon over R the Epsilon was not zero of course but the resistance is basically infinite so you do produce an EMF but you produce no current I like the last one as well let's click that and submit it and that is indeed correct okay EMF is produced but no current flows because the resistance is
50:51
infinite Sarah is that okay all right
51:19
okay one thing that we just talked about was uh the following let's say that I have a coil and I'm going to take a bar magnet and I'm going to push it towards the coil when I do that I can
51:42
generate an Epsilon in the
51:48
coil okay but pushing the bar magnet towards the coil is really like increasing the strength of the magnetic field in the coil so let's replace the bar magnet
52:05
with a solenoid okay so let's take a solenoid right here and we're going to run some current through the
52:20
solenoid okay and if I run current I through that solenoid I know what it's going to do it's going to produce a b field that is pointing up just like the B field was pointing up over there and if I increase the current going through this thing I'm going to increase the strength of the B field and that is also going to generate an EMF in the
52:51
coil okay and in fact we know what direction it is if B is increasing going up then the coil is going to want to oppose that and so it's going to have a current in the opposite direction and now here's the cool thing right let's call this current in the solenoid the primary and let's call this one the secondary
53:26
okay but is there any reason that I just need to have one coil there no not not at all I can do many coils up
53:42
there but let's think about the following instead of doing that right let's do just one coil to simplify everything so I'm going to make one coil like so and it's going to come back around and we're going to call that our secondary
54:05
coil and then down here I'm going to have a primary coil wraps around and we're going to run current through these things if I run current I'm going to intercept some flux and the amount of flux that I intercept in the secondary depends on how much current I run through the primary and so this is equal to M * i p this is IP there's some current is which develops in the top one how much current depends how much current in the bottom one dictates how much magnetic
54:48
field is going to go through the top one and so you get this Factor m in there where m is something called the mutual
55:05
inductance okay and now we're going to go back to this case where we add many turns to
55:18
it so in my secondary if I put many turns then the amount of flux just increases like n okay so with NS
55:37
turns then the flux goes like n but that is still just equal to M * IP okay and so you can write down what m is m is equal to N Subs V Subs / I sub p
56:00
okay but Faraday told us that if you're intercepting flux and it's changing in time then you develop an EMF the EMF we said was minus n Delta V over delta T and so in the secondary the EMF which develops is minus N Subs Delta V Subs over delta T but we know what N Subs V Subs is and so this becomes minus Delta m i subp divid by delta T
57:01
and we get an equation for the EMF in the secondary it is minus M change in the primary current Delta IP divided by delta
57:21
T okay so coils can in fact talk to each other run current through the low lower coil there is current that is generated in the upper coil how much well this is the EMF that defines
57:39
it so there's something else very interesting going on here
57:50
though and this is something called self inductance
58:02
if I take a coil okay let's just do one Loop for Simplicity here's my coil and I run some current through it I I know that I generate a b
58:20
field okay but the coil itself says wait a minute there's a b field being generated that is changing the flux that I see and I don't like that lens's law says I should not like a change in flux and so there is an EMF that is developed to oppose that okay so the changing B the changing B field through itself through the same
59:04
coil produces an EMF and this is in fact what we call the back
59:14
EMF because it's trying to oppose that okay what is that quantity well the EMF is l Delta I over delta T where L is something called self
59:38
inductance okay and so here's the catch any coil is an inductor inductors are something that you've probably played around with already in the lab any coil Loop is an inductor meaning if you try to run current through it it's going to generate a b field the loop itself doesn't like that changing B field and so it's going to fight back against you with this back EMF and this is the strength of that back EMF so we don't have to do it with just one Loop we can do it with a bunch of loops
1:00:29
and that is our
1:00:37
solenoid solenoid is just a bunch of Loops stacked up on top of each other okay and when I start to drive current through this thing we know that there is a b field that is produced but that changing B field says I I don't like that I don't like that change and flux through the solenoid itself and it's going to fight back against you okay this thing is an inductor okay we call it a solenoid but it's also known as an inductor and it fights
1:01:20
against changing current
1:01:28
it doesn't like it when you change
1:01:34
current so let me give you an example of this sort of thing in action and this is something that you can all try at home okay and I want you to do the following I want you to turn on your
1:01:54
toaster and okay and let it run for a little bit turn off all the lights in your
1:02:05
house and I want you to unplug it from the
1:02:14
wall if you do that what do You observe has anybody done this experiment you might have done this by accident right toaster is running instead of turning it off you walk over to the wall and you unplug it from the wall what do you see you see a spark okay it will spark why is that well let's think about the toaster okay here's our toaster and there's some wires that are coming into the toaster and then it goes to a wall plug which has two big metal prongs on
1:03:00
it but inside the toaster what is there there's a bunch of heating elements and those heating elements look like a big
1:03:16
coil so when you run current through this thing the toaster looks just like an inductor
1:03:27
okay and now when you unplug it from the wall here's the wall socket when you unplug it from the wall you in fact see a spark there is a little tiny lightning bolt that goes from the wall to your
1:03:52
toaster to that plug so don't do this at home if you have a gas leak in your house that would be bad okay but if you have a normal house plug in your toaster for a while turn off all the lights and unplug it from the wall real quick and you should be able to see a spark so now the question is why why does this happen yes
1:04:48
okay so I don't know if you guys heard him at home but that was basically the perfect answer what he said was there is current running from the wall through the toaster and now there is an electromagnetic field there's a magnetic field specifically that develops in this inductor in those coils in the toaster itself okay and everybody's happy there's a big strong magnetic field but then you unplug it from the wall and suddenly that magnetic field drops to zero but the coil doesn't like that
1:05:28
right the coil wants to keep it going and so the coil pushes current through the wires to try and do that to try and keep that magnetic field going inductors fight against changing current when you unplug it from the wall you suddenly change the current and so the inductor is going to fight to keep it going in the same direction and in fact so much current is generated that there is a spark between the plug and the wall the electrons are trying so hard to keep that current going that
1:06:05
they jump across that little Gap okay and the gap's going to be small it's going to be like a millimeter or 2 millimet but you will be able to see a little tiny spark in that region which is kind of
1:06:19
cool and then you can enjoy your toast so it's you know it's a bonus
1:06:49
okay is there some energy that we can store in an inductor right it's hard to push current through this inductor that means that we've done some work to do it there must be some way to store that energy in the inductor
1:07:08
itself remember when we charged up a capacitor we of course had energy in that capacitor how does this work with an inductor well remember work W was equal to QV okay but V is really in this case like
1:07:32
EMF what is the electromotive force that's going to drive these charges around so if I think about Delta W how much work do I Do by moving a Delta Q through the system it's that there's a little bit of a technical point you got to have a negative sign on there okay don't worry too much about the negative sign but we know what Epsilon is for an inductor right it is self-inductance L which is a value times Delta I over delta T okay L is the value of the inductor and it's
1:08:17
measured in Henry's so you might have a Mah Henry inductor look what happens the minus signs cancel out and we get L out in front we get a Delta Q over a delta T and then we still have a Delta I but this is L * Delta Q over delta T is I and then we have a change in I so when you do this properly with integration you can figure out what the energy in the inductor is and it is simply this 12 l i
1:09:12
2 this is similar to what we were talking about with capacitors right remember the capacitor was 1 12 cv^ s similar thing but now we have 12 l i 2 but if you're generating energy in this inductor there really must be energy in those B fields themselves because the B field in the center of the solenoid which is really important for the inductor and so the energy in the B
1:09:46
field itself is a following and we're going to write down the energy density which is energy volume and it is 1 / 2 mu B ^2 remember for the electric field we had 1 12 with an Epsilon KN * e^ 2 now we've got 1 over 2 mu * B ^2
1:10:52
all right let's go back to this idea that coils can talk to each other right if I run current through one coil it's going to generate a magnetic field if I put another coil next to it I can pick up that magnetic field generate an EMF in that secondary coil and let's do it with a particular configuration and if you do it in this configuration it's called a Transformer so it looks a little bit like this you're going to take an iron core
1:11:32
and now you're going to take the coil and wrap it around this side of that iron and that is our primary coil and we run IP through it on the other side you wrap another wire around
1:12:01
and this develops a current in it I sub s and that's our secondary coil okay the purpose of the iron core is to trap the B field lines so B fields that are generated there end up over there and B fields that are generated here end up over there okay so it's just a simple way to sort of trap those B field lines there's another way which is put the coils right on top of each other or wrap them around on top of each other but that gets a little confusing when you're looking at in a
1:12:40
picture so this thing is called a Transformer and let's see if we can write down some properties there is an EMF in the primary side and that EMF is the number of turns of the primary coil times Delta V over delta T there is of course an EMF in the secondary coil which is minus N Subs Delta V over delta T I can divide by n subp and I get Epsilon P Over N Sub P equals minus Delta V over delta T and I can do the same over here Epsilon s Over N Subs equals minus Delta V over delta
1:13:39
T and now here's the thing the iron core traps the B field
1:13:50
lines so the B fields that are coming through this one end up going through the other one okay and so on either side you in fact have the same Delta V over delta T on each side Delta V over delta T on the left side is exactly the same as Delta V over delta T on the right side because all those B field lines go through and they do in the same amount of time delta T so now this whole thing simplifies to what Epsilon p over NP equals Epsilon s over NS and this is typically written like
1:14:42
this Epsilon s over Epsilon P I had to divide by an Epsilon p and so I got to multiply back up by an N Sub s is equal to n n s over NP and once you hook this stuff up to a circuit and there is some resistance in it then these things become voltages voltage of s over voltage of p is just N Subs over n subp and this thing right here is known as the Transformer equation more than meets the eye
1:15:28
Transformers robots in Disguise no you guys were like 5 years old or something right no okay I guess they're still pretty popular right because they're making like those Transformer movies but Transformers was like just this little toy you know a little robot that turns into a car back and forth and it's kind of named appropriately right because what are we doing we're taking one voltage B of s and we're turning it into a different voltage V subp or vice versa
1:15:58
typically you call V subp the primary so by putting a voltage on this side of the Transformer I can get a totally different voltage on the other side of the Transformer and all it depends on is how many coils now if I have the same number of coils then I don't change the voltage that's called a one: one Transformer but if I have twice as many Loops in the second secondary side compared to the primary side then look what happens NS is twice NP and I get twice the voltage on the
1:16:37
secondary side that I would get on the primary side that's called a Step up Transformer because you have stepped up the voltage you come in with one voltage you go out with a bigger voltage okay the opposite is of course true if I come in with a lot of coils and I go out on this side with fewer coils say half as many then it's a Step Down Transformer I've taken some high voltage and I've transformed it down to some low voltage okay Step Up increase of voltage step down decrease the
1:17:12
voltage so where do you see these things where do you see Transformers on the power lines right okay on the power lines you will see Transformers because the high voltage power lines that are going around are too high for your house okay they're kilovolts and you'd obviously don't want kilovolts in your house because then if you accidentally grab hold of that toaster plug while you're pulling it out right you can kill yourself 110 volts 120 volts RMS it'll hurt but it's hard
1:17:47
to kill yourself with your household voltage okay you'll definitely feel it but it's really hard to kill yourself kilovolts can certainly kill you if there's enough current available so the voltages that are running around in the power lines are high voltage and then you want to transform them down to a lower voltage that goes to your house so you see these things all the time they're up on the power lines if you look there's big cans and things up there on the telephone poles and on the
1:18:15
high voltage power lines those are Transformers okay they are transforming the voltage all right let's try an example of this which is very similar to one of your homework problems which is a toy train problem
1:18:55
okay so in this problem it says we have a toy train
1:19:05
transformer and it is a um it has a turn ratio of
1:19:14
8:1 and so it looks like this here's our iron core we've got a whole bunch of turns on this side and then we just have a few on this side okay this is our primary and this is our
1:19:40
secondary so first off the way we drew this is this a Step up Transformer or a step down transformer what do you guys think down right we're going down in voltage why because it's for the toy train and you're going to hand it to your kid and then you don't want them running around with 120 volts you want them running around with you know like 12 volts okay something similar to that so it's a Step Down Transformer there's lots of coils on this side there's very
1:20:13
few coils on that side and let's give you the following we're going to say that the current running through the secondary is 1.6 amps and we need to find IP all right that's probably not too bad right what we said was the voltages step up or step down but voltage is linear with current thanks to Ohm's law and so in fact current is also going to step up and step
1:21:01
down I over IP is NP over NS okay and we're looking for IP so let's just solve this equation for IP we've got IP is equal to uh is times NS over NP and now we have all these numbers is is 1.6 amp NS is 1 n p is 8 we said it was an 8:1 turn ratio and so we just get 1.6 over 8 which is of course 0.2 amps okay so that's the first part and let's think about the second part and the second part is a question how much power does the train
1:22:06
use all right we know that this is coming from the wall right so the voltage over here VP is 120
1:22:21
volts this voltage over here is going to going to be vs and we know what that is now right it's a step down by a factor of eight so it's 120 over 8 120 over 8 is 15 volts so how much power does the train use well the train is on the secondary side and so p s is just secondary current which we knew already times secondary voltage okay and so you can plug this in you've got 1.6 amps times 15 volts and if you do 1.6 * 15 what do you get
1:23:29
hopefully I'm going to guess 24 is that
1:23:35
right it's got to be right because this is the same as 16 * 1.5 that's 1 and a half of 16 which is
1:23:47
24 okay so that's how much current is in the secondary that's how much power is used by the secondary okay questions about Transformers
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