In this video, we'll learn two equations to calculate induced EMF.
Just as in the two previous videos, we'll examine a metal rod moving in a magnetic field.
Let's assume that the magnetic field's strength is B, the speed of the rod is V, the length of the rod is L,
and the horizontal distance moved by the rod during time delta T is delta X.
The rod is moving to the right, and after delta T seconds, it ends up here.
As we said, the distance traveled by the rod is delta X.
To deduce the formula for the induced EMF in the rod, we'll combine these four equations from previous stop topics.
A side note here is that you do not have to know this derivation for your IB physics exams.
You just have to be able to use the equation that we derive.
Let's begin here.
F is the force exerted by the magnetic field on the rod, which, if you recall from the previous video,
is the force that opposes the motion of the rod.
Therefore, if the rod is moving at constant speed,
F is also the magnitude of the force that is needed to keep the rod moving at constant speed.
B is the magnetic field strength, I is the induced current in the rod, L is the length of the rod,
and theta is the angle between the direction of the induced current and the direction of the magnetic field.
Since in this example, theta is 90 degrees, sine theta is 1.
So we can write that F is equal to B times I times L.
In the next step, we'll use this equation.
The force that we just expressed does work on the rod.
We can see from the formula from stop topic 2.3 that work done is equal to force multiplied by the distance moved
multiplied by the cosine of the angle between the direction of the force and the direction of the distance moved.
Since in our example, the direction of the force and the direction of the distance moved is the same,
theta is equal to 0, so cosine theta is equal to 1.
Therefore, w, the work done to move the rod by a distance of delta x, is equal to B times I times L times delta x.
Let's continue by using this equation.
This equation tells us that potential difference, v, is equal to the work done per unit charge while moving charge.
As we discussed in the first video of this stop topic,
electromotive force, or EMF, is also equal to work done or energy supplied per unit charge,
therefore it can be expressed as w over q.
Using the equation above for w, we get that EMF is equal to B times I times L times delta x divided by q.
In our example, q is the amount of charge moved as the rod travels a distance of delta x in the magnetic field.
Finally, let's use this equation.
I current is equal to charge over time.
Rearranging this equation gives us that delta q is equal to I times delta t,
so we can substitute I times delta t in the denominator of our fraction for EMF.
This gives us that EMF is equal to B times I times L times delta x divided by I times delta t.
We can cancel I from the numerator and the denominator,
and since delta x over delta t is distance traveled over time, here we get v, the speed of the rod.
Therefore the equation that we get for EMF is B times L times v.
This is how the formula is given in the IB Physics data booklet.
The Greek letter epsilon that you see on the left hand side represents EMF.
There is a slightly different formula in the IB Physics data booklet that looks like this.
It is almost the same as the first one, except that it includes the letter n.
Before discussing what n stands for, let's summarize what these variables represent.
We already mentioned epsilon, B, v and L, and as you can see, n is called the number of turns.
This name comes from the fact that when EMF is induced in a conductor, the conductor often consists of many wires.
For example, if you look inside your computer or phone cable,
you will see that many small wires are twisted together to form the cable.
So n, the number of turns here, simply stands for the number of wires or rods that are combined.
If in our example we would have 2, 3 or 10 rods moving together,
then we would use the second formula to calculate the induced EMF, and simply use 2, 3 or 10 in place of n.
This completes our discussion of the equations that are used to calculate induced EMF.
There is a third equation that you find in the IB Physics data booklet to calculate induced EMF,
and we will discuss this equation in a later video.
In the next video, we'll learn about magnetic flux and magnetic flux density.