This video is about Faraday's law and magnetic flux linkage.
Let's return once more to the rod that moves in a magnetic field,
an example that we've used in previous videos in this subtopic.
As shown in the diagram, the rod moves a distance of delta x to the right
in a magnetic field that is pointing out of the screen or page.
The strength of this magnetic field is b, the rod is travelling at constant speed v,
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.
For this example, let's assume that the number of turns of the rod is n.
If you need some clarification on what number of turns exactly means,
feel free to go back and watch video 11.1.3.
Using the second formula that we did used in video 11.1.3,
we can write that epsilon, the induced emf in the rod, is equal to b times v times l times n.
Since the rod moves a distance of delta x in delta t seconds,
the speed of the rod v is equal to delta x over delta t.
Therefore, in our equation, we can replace v by delta x over delta t
and write that epsilon is equal to b times delta x times l times n over delta t.
Next, let's consider delta x times l.
Since the distance moved by the rod is delta x and the length of the rod is l,
the area swept out by the rod during delta t seconds,
so this area is equal to delta x times l.
Notice that as the rod moves, the area increases
and we can write that epsilon is equal to b times delta a times n over delta t.
In the previous video, we did use the following equation for magnetic flux.
In our example here, theta is equal to 0,
so cosine theta is 1, therefore we get that magnetic flux is equal to b times a.
Rearranging, we get that a is equal to magnetic flux over b.
Let's replace a in our equation by this expression.
Therefore, we get that epsilon is equal to b times delta phi,
so change in flux multiplied by n divided by b times delta t.
Since we replaced a by phi over b,
phi ended up in the numerator and b ended up in the denominator.
Canceling b, we end up with the formula that expresses Faraday's law.
This is how Faraday's law is given in the IB Physics data booklet
and here are the variables that are present in the formula.
The negative sign is added to include Lentz's law,
in other words to show that the direction of the induced current is such
as to oppose the change that created the current.
Before defining Faraday's law in words,
let's learn about a final quantity in this subtopic.
Magnetic flux linkage is simply defined as n multiplied by the magnetic flux.
Therefore Faraday's law can be stated like this.
The induced EMF in a circuit
is equal to the rate of change of magnetic flux linkage through the circuit.
This is what is expressed by the formula that we did used in this video.
Just a final note, there is no need to learn this derivation for your IB Physics exam
because you will only be asked to apply this formula when solving questions.
This wraps up our discussion of Faraday's law and magnetic flux linkage.
In the next video, we'll learn about coils moving in a magnetic field.