In this video, we're going to focus on Faraday's Law of Electromagnetic Induction. So let's take an iron bar, and we're going to wrap some coils of wire around it. So here, we're going to attach this to a voltmeter. And on the other side... We're going to have some coils of wire, and we're going to connect this side to, let's say, a battery.
And we're going to have a resistor so there's not too much current flowing through this circuit. Now, when there's a steady current flowing in this circuit, no EMF, no current is induced in the second coil. Now... Let's say if we have a switch. The moment when we close the switch, for an instant, for a very short period of time, we will get an induced current in that circuit.
The question is why. Why is it that when the current is steady, it induces no current in the second coil? However...
The moment that the current increases for that brief period of time when the current is changing, there is an induced EMF in the second coil. And that's the basis of Faraday's law of electromagnetic induction. A change in magnetic field will give rise to an induced current. Now the equation that is associated with the Faraday's law of electromagnetic induction is this formula.
The induced EMF is equal to negative n times the change in the flux divided by the change in time. So the faster the flux changes, that is the magnetic flux, the greater the induced EMF will be in the second coil. A change in magnetic field leads to a change in the magnetic flux, which will give rise to an induced EMF. The magnetic flux is equal to the magnetic field times the area times cosine theta, where theta is between the normal line perpendicular to the face of the coil and the magnetic field itself. So there's three ways in which you can induce an EMF.
In order to acquire a change in flux, you can either change the magnetic field, you could change the area of the coil, or you could change the angle of the magnetic field with respect to the normal line of the coil. So for example, let's say if we have a square coil of wire, and we want to take a magnet, and we're going to move this magnet into this coil. As we move the magnet into the coil, the magnetic field is increasing. And so this leads to an increase in the flux that's going into the coil.
And that's going to cause an induced EMF. So that's one way in which you could change the flux going into the coil, is by changing the magnetic field, by moving a magnet into or out of the coil. If the magnet is held in place, no induced current flows because there's no change in magnetic flux. But As the magnet moves either into the coil or out of the coil, there is a change in the magnetic field, which leads to a change in the magnetic flux in the coil. And then, therefore, there's going to be an induced EMF that is going to lead to an induced current.
We're not going to focus on the direction of the current in this video, but I just want to give you a basic introduction into Faraday's Law of Induction. So far, we've seen one way. in which we can induce a current in the coil by moving a magnet into or out of the coil.
Now, what are some other ways? How can we change the area? Well, let's say if we have a magnetic field.
Actually, let me draw the coil first. So let's say we have a circular coil of wire, and everywhere we have a magnetic field going into the page. And so this magnetic field is constant, doesn't change.
Now what's going to happen if we basically pull the coil in such a way to increase the area of the coil? If the area goes up, the magnetic flux will increase. And if the magnetic flux changes, this will lead to an induced EMF in the circuit.
So there's going to be an induced current in the circuit. So that's the second way. The third way is to change the angle with respect to, let's say, the magnetic field.
So let's say if we have a square coil of wire. And let's say the magnetic field is directed into the page. If we rotate this coil in this direction, then we're going to change the flux because we're changing the angle. Right now, the angle is 90 degrees. But with respect to the normal line, it's 0 degrees.
It all depends on how you define it. So let's define it with respect to the normal line. So the magnetic field is parallel to the normal line right now.
And let's rotate the coil so it's like this now. And so, this is the normal line. Well, actually, it should be more like that.
And let's say this is the magnetic field. So clearly, the angle is a lot different now. It's no longer 0 degrees. It might be, I'm just going to give a number, 70 degrees or something. And so, because the angle changes, the magnetic flux will change.
In fact, going from 0 degrees to 70, cosine 0 is the one, cosine 70 is a lot less. So the magnetic flux decreased, which means that there's going to be an induced EMF in this coil. So those are the three ways in which you can generate an induced current in the coil.
You can change the magnetic field. You can increase it or decrease it. It doesn't matter.
You can change the area of the coil by stretching it or compressing it. Or, you could change the angle between the magnetic field and the normal line. If you change the angle, then the flux changes, and there's going to be an induced EMF in the coil. Now, let's work on a practice problem. So, we have a square coil of wire, and that wire consists of 50 loops.
And we're given the dimensions of the square. Now, there's a magnetic field that's perpendicular to the face of the coil. So, let's draw a picture.
So let's say this is the coil, and let's say the magnetic field is going straight into it. It's perpendicular to the face of the coil, but it's parallel to the normal line, which means the angle between the normal line and the magnetic field is 0 degrees. Now the magnetic field increases from negative 3 Tesla to 5 Tesla.
Now, this coil is connected across a resistor. How can we calculate the induced EMF in the coil and the current that flows through the resistor? So let's focus on the induced EMF.
So it's going to equal negative n times the change in the magnetic flux divided by the change in time. So the change in magnetic flux in this example... We know flux is going to be BA cosine, but what is changing in this example?
Is it the magnetic field, the area, or the coil? Well, we know based on the problem, the magnetic field is changing. The area is constant, and the angle is constant. So we could say it's delta B, because that's changing, times A, it doesn't need a triangle because that's not changing, times cosine theta, divided by the change in time.
So now let's plug in everything into this formula. So n is 50. The change in the magnetic field, the final value is 5 minus the initial value of negative 3. Now the area is 0.20 times 0.20. 20 centimeters is 0.2 meters. Multiplied by cosine of 0 degrees divided by the change in time.
So the change in time is 0.1 seconds. So 5 minus negative 3, that's the same as 5 plus 3, that's 8. So it's negative 50 times 8, times 0.2 times another 0.2, times cosine 0, which doesn't change anything, divided by 0.1. So in this example, well first I need to make some more space.
The induced EMF. is negative 160 volts. Now for this video I'm not going to worry about the negative sign.
So if we wish to calculate the current, it's going to be the induced EMF divided by the resistance. And we know the resistance. In this example, it's 20 ohms. So 160, let's just make that positive, divided by 20 ohms is equal to 8. So that's the current that flows in this circuit.
It's 8 amps. Now the last thing we need to do is calculate the power dissipated by the resistor. So the power absorbed by the resistor, we can use this formula.
It's I squared times R. So 8 squared times the resistance of 20 ohms. 8 squared is 64. 64 times 20. That's equal to 1280 watts.
And so a lot of power can be generated by a change in magnetic field, or a change in flux in the coil of wire. And the more coils, or rather the more loops that you have, the greater the induced EMF. Because if we had a single loop, the induced voltage won't be this high. It would be 160 divided by 50, and so it would only be 3.2 volts.
But if you increase the number of loops... the induced EMF greatly increases, which is what you want.