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In this video, we'll learn two equations to calculate induced EMF.

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Just as in the two previous videos, we'll examine a metal rod moving in a magnetic field.

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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,

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and the horizontal distance moved by the rod during time delta T is delta X.

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The rod is moving to the right, and after delta T seconds, it ends up here.

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As we said, the distance traveled by the rod is delta X.

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To deduce the formula for the induced EMF in the rod, we'll combine these four equations from previous stop topics.

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A side note here is that you do not have to know this derivation for your IB physics exams.

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You just have to be able to use the equation that we derive.

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Let's begin here.

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F is the force exerted by the magnetic field on the rod, which, if you recall from the previous video,

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is the force that opposes the motion of the rod.

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Therefore, if the rod is moving at constant speed,

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F is also the magnitude of the force that is needed to keep the rod moving at constant speed.

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B is the magnetic field strength, I is the induced current in the rod, L is the length of the rod,

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and theta is the angle between the direction of the induced current and the direction of the magnetic field.

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Since in this example, theta is 90 degrees, sine theta is 1.

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So we can write that F is equal to B times I times L.

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In the next step, we'll use this equation.

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The force that we just expressed does work on the rod.

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We can see from the formula from stop topic 2.3 that work done is equal to force multiplied by the distance moved

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multiplied by the cosine of the angle between the direction of the force and the direction of the distance moved.

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Since in our example, the direction of the force and the direction of the distance moved is the same,

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theta is equal to 0, so cosine theta is equal to 1.

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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.

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Let's continue by using this equation.

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This equation tells us that potential difference, v, is equal to the work done per unit charge while moving charge.

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As we discussed in the first video of this stop topic,

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electromotive force, or EMF, is also equal to work done or energy supplied per unit charge,

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therefore it can be expressed as w over q.

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Using the equation above for w, we get that EMF is equal to B times I times L times delta x divided by q.

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In our example, q is the amount of charge moved as the rod travels a distance of delta x in the magnetic field.

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Finally, let's use this equation.

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I current is equal to charge over time.

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Rearranging this equation gives us that delta q is equal to I times delta t,

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so we can substitute I times delta t in the denominator of our fraction for EMF.

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This gives us that EMF is equal to B times I times L times delta x divided by I times delta t.

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We can cancel I from the numerator and the denominator,

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and since delta x over delta t is distance traveled over time, here we get v, the speed of the rod.

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Therefore the equation that we get for EMF is B times L times v.

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This is how the formula is given in the IB Physics data booklet.

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The Greek letter epsilon that you see on the left hand side represents EMF.

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There is a slightly different formula in the IB Physics data booklet that looks like this.

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It is almost the same as the first one, except that it includes the letter n.

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Before discussing what n stands for, let's summarize what these variables represent.

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We already mentioned epsilon, B, v and L, and as you can see, n is called the number of turns.

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This name comes from the fact that when EMF is induced in a conductor, the conductor often consists of many wires.

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For example, if you look inside your computer or phone cable,

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you will see that many small wires are twisted together to form the cable.

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So n, the number of turns here, simply stands for the number of wires or rods that are combined.

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If in our example we would have 2, 3 or 10 rods moving together,

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then we would use the second formula to calculate the induced EMF, and simply use 2, 3 or 10 in place of n.

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This completes our discussion of the equations that are used to calculate induced EMF.

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There is a third equation that you find in the IB Physics data booklet to calculate induced EMF,

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and we will discuss this equation in a later video.

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In the next video, we'll learn about magnetic flux and magnetic flux density.