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Maxwell's Laws of Electromagnetism · Acedra
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Maxwell's Laws of Electromagnetism
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0:00
All electric and magnetic fields in the Universe are governed by four laws.
0:08
These are Maxwell’s four laws of electromagnetism.
0:25
Just a single charged particle creates an electric field everywhere throughout the entire Universe.
0:41
Suppose we enclose the charged particle inside an object.
0:48
The number of electric field lines leaving the object is determined by the amount of charge inside.
0:58
Electric fields exert a force on all charged particles.
1:03
The strength of the electric field depends on the number of electric field lines.
1:31
The electric field lines extend to infinity in all directions.
1:41
The electric field is strongest near the charged particle, because this is where the greatest number of electric field lines are close together.
1:53
Maxwell’s first law is that the number of electric field lines leaving an object is determined only by the amount of charge inside.
2:12
Charges outside the object bend the lines, but do not change the number of lines that exit the object.
2:35
The only way to increase the number of lines leaving the object is by increasing the amount of charge inside.
2:44
Since the amount of charge inside the object has now doubled, there are now twice as many electric field lines leaving the object, and the electric field is twice as strong.
2:57
The number of electric field lines leaving the object does not depend on the object’s shape or size.
3:07
Maxwell’s first law says that so long as the amount of charge inside the object does not change, the number of electric field lines leaving the object will stay constant.
3:20
The direction of the lines indicates the direction of the electric fields.
3:34
Electric fields have an opposite effect on negative particles than they do on positive particles.
3:42
Positive particles feel a force in the same direction as the electric field.
3:56
Negative particles feel a force in the opposite direction of the electric field.
4:15
Particles with the same charge repel one another.
4:32
Particles with opposite charges attract one another.
4:49
This is because positive particles cause electric fields to point away from the particle.
5:03
...and negative particles cause electric fields to point towards the particle.
5:22
This means that electric field lines go out of positive particles.
5:33
And electric field lines go into negative particles.
5:47
Negative charges cancel out positive charges.
5:58
The number of electric field lines exiting this object is exactly equal to the number of electric field lines entering the object.
6:14
The net number of electric field lines leaving the object is zero, and the net charge inside the object is also zero.
6:41
Magnetic fields are very different from electric fields.
6:52
Maxwell's second law says that the number of magnetic field lines leaving an object is always zero.
7:05
No matter an object's shape or size, the number of magnetic field lines entering an object will always be exactly equal to the number of magnetic field lines exiting.
7:18
This is true regardless of whether or not there are charges inside.
7:30
Magnetic fields are created by moving charged particles.
7:43
As was the case with electric fields, how close together the magnetic field lines are to one another indicates the strength of the magnetic field.
8:03
Also as was the case with electric fields, the direction of the magnetic field lines indicates the direction of the magnetic fields.
8:22
Maxwell's third law states that the strength of a magnetic field around a loop depends on the amount of charge passing through the loop each second.
8:37
If we increase the amount of charge passing through the loop, the strength of the magnetic field increases.
8:56
Negative particles flowing through a loop create a magnetic field in the opposite direction.
9:14
All moving charged particles create magnetic fields.
9:31
And magnetic fields exert a force on all moving charged particles.
9:49
Negative particles experience a force in the opposite direction of positive particles.
10:08
In the case of electric fields, particles feel a force parallel to the direction of the electric field.
10:23
In the case of magnetic fields, particles feel a force in a direction that is 90 degrees to the magnetic field
10:37
and 90 degrees to the direction of motion.
10:55
There is a rule for using your right hand to remember the direction in which a moving positively charged particle will create a magnetic field.
11:22
There is another rule for using your right hand to remember the direction in which a magnetic field will exert a force on a moving positively charged particle.
11:37
The result is that particles with the same charge moving in the same direction result in a magnetic force attracting them together.
12:01
The opposite is true for particles with the same charge moving in opposite directions.
12:26
Particles with the same charge moving in opposite directions result in a magnetic force pushing them apart.
12:49
A rotating charged particle can be thought of as a loop of charged particles.
13:05
This creates a magnetic field that enters on one side, and exits on the other side.
13:21
Let's call one side the South Pole, and call the other side the North Pole.
13:34
A magnet is a material which has many of its negatively charged particles spinning in the same direction.
13:51
Every rotating charged particle is a miniature magnet. And every magnet can be thought of as a rotating loop of charged particles.
14:06
Suppose we have two magnets aligned in the same direction.
14:17
In this case, since we have particles with the same charge moving in the same direction, there will be a magnetic force attracting them together.
14:37
Now suppose that we have two magnets aligned in opposite directions.
14:48
In this case, since we have particles with the same charge moving in opposite directions, there will be a magnetic force pushing them apart.
15:08
Opposite poles attract one another.
15:25
Similar Poles repel one another.
15:39
Now suppose that we have two magnets aligned in random directions.
15:48
Particles with the same charge moving in the same direction will have a magnetic force pulling them together.
16:12
This will cause the two magnets to align in the same direction, resulting in an attractive force.
16:26
A material doesn’t have to be a magnet to be a magnetic material.
16:36
Magnetic materials have rotating charged particles that can be affected by magnets.
16:47
Normally, these rotations are in random direction.
16:58
In the presence of a magnet, the rotating particles will align in the same direction.
17:23
This is what causes magnets to attract certain objects.
17:42
Instead of using a magnet, we can also use a coil of wire.
17:51
Charged particles moving through a coil create that same forces that magnets do.
18:06
The strength of the force depends on the strength of the magnetic field.
18:19
The strength of the magnetic field around a loop depends on the amount of charge passing through the loop each second.
18:37
We can increase the number of charged particles passing through the loop each second by increasing the number of turns in the coil.
18:53
The number of particles flowing through the loop each second is the number of particles flowing through the wire each second multiplied by the number of turns.
19:08
More turns in the coil results in a stronger field, and in a stronger electromagnet.
19:22
We can also make the coil far stronger by inserting a magnetic material inside.
19:36
The magnetic force from the coil will cause the rotating charged particles in the material to align in the same direction.
20:00
With the charged particles aligned in the same direction, the material behaves like a magnet, greatly strengthening the magnetic field created by the coil.
20:16
For certain materials, the rotation of the charged particles will stay aligned even after the coil is removed.
20:31
In these cases, the material has been magnetized and can now attract all the same objects that a magnet can.
20:48
Coils and magnets create powerful magnetic fields. However, they are electrically neutral.
21:05
This is because magnets and coils have positive particles in equal quantity to the negative particles.
21:19
Positively and negatively charged particles cancel each other out.
21:32
Just as there are materials that are affected by magnetic fields, there are also materials that are affected by electric fields.
21:46
When the molecules inside this material feel an electric field, they orient themselves in a way so as to create an electric field in the opposite direction.
22:13
In the case of magnetic fields, affected materials create a magnetic field in the same direction as the external field, making the total magnetic field inside the material stronger.
22:33
In the case of electric fields, affected materials create an electric field in the opposite direction of the external field, making the total electric field inside the material weaker.
23:01
Electric and Magnetic fields both exert forces on charged particles.
23:13
In the case of electric fields, the strength of a force on a particle is proportional to the amount charge in the particle
23:23
multiplied by the strength of the electric field.
23:33
In the case of magnetic fields, the strength of the force on a particle is proportional to the amount of charge in the particle
23:43
multiplied by the area of the purple rectangle.
23:53
A stronger magnetic field causes the rectangle's area to increase.
24:06
A faster speed also causes the area to increase.
24:18
If we change the direction of motion, the rectangle becomes a parallelogram, and the area changes accordingly.
24:31
The force is greatest if the direction of motion is 90 degrees to the magnetic field.
24:45
The force is zero if the direction of motion is in the same direction as the magnetic field.
25:04
The magnetic field is strongest near the moving charged particles, and we can represent this by the length of the arrows.
25:24
According to Maxwell’s third law, the sum of the arrow lengths around a loop depends on the amount of charge passing through the loop each second.
25:42
In this particular case, the amount of charge passing through the loop is the same, regardless of the loop’s size.
25:59
This means that sum of the arrow lengths around each of these loops will be exactly identical.
26:17
Maxwell’s third law remains true regardless of the loop’s shape or size.
26:34
The amount of charge passing through the loop each second is still the same as before. Therefore, the sum of the arrow lengths around the loop is still the same as before.
26:58
No matter how we bend or twist the loop, Maxwell’s third law will still remain valid.
27:22
Suppose we create a loop that has no charges passing through it.
27:42
Relative to our direction of travel around the loop, different arrows point in opposite directions.
27:59
Arrows pointed in opposite directions cancel each other out.
28:13
The total sum of arrow lengths around this loop is zero, and the amount of charge passing through this loop is also zero.
28:30
Just as magnetic field arrows pointed in opposite directions cancel each other out, charges passing through the loop in opposite directions also cancel each other out.
28:46
The net charge passing through this loop is zero, and the sum of the magnetic field arrows around the loop is also zero.
29:03
If the loop is pointed in a different direction than the magnetic field, each arrow can be thought of as the combination of an arrow pointed 90 degrees to the loop’s path and an arrow parallel to the loop’s path.
29:18
Only the components of the arrows in the direction of the loop’s path get counted for the sum of arrow lengths.
29:33
Now let’s consider the magnetic field created by just a single moving charged particle.
29:43
The magnetic field starts appearing around each loop before the particle arrives, and the magnetic field does not instantly disappear after the particle has passed.
29:58
This means that we can have a magnetic field around a loop even when there is no charged particle passing through it, seeming to violate Maxwell’s third law.
30:12
However, this just means that there is more to Maxwell’s third law than has been discussed so far.
30:20
If the number of electric field lines passing through a loop is changing with time, then this will also create a magnetic field around the loop.
30:34
The sum of the magnetic field arrow lengths around a loop is determined by the amount of charge passing through the loop each second, plus the rate at which the electric field through the loop is changing with time.
31:47
Maxwell’s fourth law is similar to this, but in reverse.
32:00
Just as a changing electric field can create a magnetic field, Maxwell’s fourth law is that a changing magnetic field can create an electric field.
32:14
The sum of the electric field arrow lengths around a loop is determined by the rate at which the magnetic field through the loop is changing with time.
32:34
This is true regardless of the loop’s shape or size, and all the same rules as before for how to add arrow lengths still apply.
32:50
A magnetic field passing through a loop can be created by a rotating ring of charged particles.
33:04
Suppose we have two rings, one which is moving, and one which is stationary.
33:17
If we try to stop the rotating ring, the magnetic field will decrease.
33:32
This change in the magnetic field will create an electric field, causing the second ring to start rotating.
33:45
The rotation of the second ring will create a new magnetic field, in the same direction as the original magnetic field from the first ring.
34:08
The events shown here all happen at the same time, and this is the result.
34:19
Every time we try to change a magnetic field, it forces charged particles to move in a way to keep the magnetic field constant.
34:32
Magnetic fields do not like to change.
34:43
If we try to stop both rings, the magnetic field will decrease very rapidly, creating a very strong electric field.
35:01
If we now try rotating one of the rings, this will cause an increase in the magnetic field.
35:11
The magnetic field does not like to change, so it will react by creating an electric field forcing the other ring to create a magnetic field in the opposite direction.
35:30
The magnetic fields from the two rings cancel each other out, causing the total magnetic field to be close to zero.
35:43
Magnetic fields do not like to change, so if we stop one of the rings, it will cause both rings to stop, so that the total magnetic field will remain close to zero.
35:56
Every time we move one of the rings, this causes the other ring to move in the opposite direction.
36:15
This is the basic principle of how a transformer operates.
36:28
We move the charged particles in the primary coil, and this causes the charged particles in the secondary coil to also move.
36:42
We can make this effect much stronger by wrapping the coils around a magnetic material.
36:56
The rotating charged particles inside the magnetic material behave like miniature magnets.
37:09
The magnets react to the magnetic force from the primary coil, thereby creating a changing magnetic field in the secondary coil.
37:23
We can also create a changing magnetic field in a coil by using a real magnet.
37:36
This is the basic principle of how electric generators operate.
37:47
A rotating magnet creates a rotating magnetic field.
37:56
This causes the magnetic field through a loop to constantly change in strength and direction.
38:21
The changing magnetic field then creates an electric field, causing charged particles to move.
38:46
There is another way to create a rotating magnetic field.
39:05
Suppose we have three coils of moving charged particles, each creating a magnetic field as shown.
39:19
The sum of these three magnetic fields is a rotating magnetic field.
39:35
If we place a magnet inside these coils, it will try to line up with the magnetic field, but never be able to do so because the magnetic field keeps rotating.
39:51
The magnet rotates with its speed synchronized to the speed of the rotating field.
40:01
This is the basic principle of how a three phase synchronous motor operates.
40:12
Suppose we remove the magnet.
40:22
The rotating magnetic field created by the three coils can be thought of as if it is being created by a rotating ring of charged particles.
40:46
Suppose that inside this ring, we place another ring of charged particles which is standing still.
41:03
The changing magnetic field will create an electric field, causing the charged particles in the stationary ring to move.
41:30
The moving charged particles in the rotating ring will exert a magnetic force on the moving charged particles in the stationary ring.
41:45
It will be an attractive force for the particles moving in the same direction, and a repulsive force for the particles moving in the opposite direction.
42:02
This will cause the stationary ring to rotate.
42:34
Therefore, placing a metal ring inside a rotating magnetic field causes the metal ring to rotate.
43:23
If we place many rings together, each of them will feel a force causing it to rotate in the direction of the rotating magnetic field.
43:37
This is the basic principle of how an induction motor operates.
43:54
Suppose we have an electric field that is constantly changing as is shown.
44:07
This changing electric field will create a changing magnetic field, which will then create another changing electric field.
44:21
Each changing electric field will create another changing magnetic field, and each new magnetic field will then create another changing electric field.
44:35
These electric and magnetic fields will therefore keep reproducing each other throughout all of space, and this is how radios and cell phones communicate.
44:51
These electric and magnetic fields that reproduce each other look like this when viewed in one dimension.
45:02
They form a wave that travels through space at the speed of light.
45:13
That is because light is itself an electromagnetic wave.
45:24
Nothing can travel through empty space faster than an electromagnetic wave.
45:36
Electromagnetic waves slow down when they travel through the types of materials discussed in this video.
45:49
But when they travel through empty space, their speed is always constant to all observers.
46:03
All electromagnetic waves traveling through empty space have the same speed, but they can have different frequencies.
46:17
Every color of visible light is an electromagnetic wave with a slightly different frequency.
46:31
Radio waves are electromagnetic waves with frequencies much lower than that of visible light.
46:45
X-rays and gamma rays are electromagnetic waves with frequencies much higher than that of visible light.
46:59
According to Quantum Mechanics, everything in the Universe can behave both as a wave, and as a particle.
47:13
From this perspective, an electromagnetic wave is really composed of particles which we have called photons.
47:28
According to the theory of Quantum Electrodynamics, electric and magnetic fields don’t actually exist, and all the forces attributed to them are really the result of the fact that charged particles exchange photons with one another.
47:44
But that is another story…
47:49
Note: Maxwell’s Laws are not numbered in any particular order. The sequence in which these four laws were presented in this video is arbitrary.
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