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This video is about Faraday's law and magnetic flux linkage.

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Let's return once more to the rod that moves in a magnetic field,

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an example that we've used in previous videos in this subtopic.

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As shown in the diagram, the rod moves a distance of delta x to the right

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in a magnetic field that is pointing out of the screen or page.

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The strength of this magnetic field is b, the rod is travelling at constant speed v,

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the length of the rod is l, and the time it takes for the rod to move the distance of delta x is delta t seconds.

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For this example, let's assume that the number of turns of the rod is n.

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If you need some clarification on what number of turns exactly means,

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feel free to go back and watch video 11.1.3.

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Using the second formula that we did used in video 11.1.3,

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we can write that epsilon, the induced emf in the rod, is equal to b times v times l times n.

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Since the rod moves a distance of delta x in delta t seconds,

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the speed of the rod v is equal to delta x over delta t.

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Therefore, in our equation, we can replace v by delta x over delta t

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and write that epsilon is equal to b times delta x times l times n over delta t.

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Next, let's consider delta x times l.

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Since the distance moved by the rod is delta x and the length of the rod is l,

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the area swept out by the rod during delta t seconds,

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so this area is equal to delta x times l.

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Notice that as the rod moves, the area increases

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and we can write that epsilon is equal to b times delta a times n over delta t.

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In the previous video, we did use the following equation for magnetic flux.

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In our example here, theta is equal to 0,

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so cosine theta is 1, therefore we get that magnetic flux is equal to b times a.

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Rearranging, we get that a is equal to magnetic flux over b.

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Let's replace a in our equation by this expression.

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Therefore, we get that epsilon is equal to b times delta phi,

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so change in flux multiplied by n divided by b times delta t.

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Since we replaced a by phi over b,

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phi ended up in the numerator and b ended up in the denominator.

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Canceling b, we end up with the formula that expresses Faraday's law.

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This is how Faraday's law is given in the IB Physics data booklet

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and here are the variables that are present in the formula.

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The negative sign is added to include Lentz's law,

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in other words to show that the direction of the induced current is such

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as to oppose the change that created the current.

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Before defining Faraday's law in words,

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let's learn about a final quantity in this subtopic.

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Magnetic flux linkage is simply defined as n multiplied by the magnetic flux.

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Therefore Faraday's law can be stated like this.

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The induced EMF in a circuit

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is equal to the rate of change of magnetic flux linkage through the circuit.

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This is what is expressed by the formula that we did used in this video.

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Just a final note, there is no need to learn this derivation for your IB Physics exam

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because you will only be asked to apply this formula when solving questions.

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This wraps up our discussion of Faraday's law and magnetic flux linkage.

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In the next video, we'll learn about coils moving in a magnetic field.