Next, let’s calculate the flux through the square after it’s rotated. Now we have to take
into account the fact that the square is at an angle of 60º:
So the change in magnetic flux is :
The magnetic flux decreases because, as the square is rotated, fewer magnetic field lines
can pass through it.
Faraday’s Law
We have seen earlier that a bar sliding along rails is a source of induced emf. We have
also seen that it is a source of changing magnetic flux: as it moves, it changes the area
bounded by the bar and the rails. The English scientist Michael Faraday discovered that
this is no coincidence: induced emf is a measure of the change in magnetic flux over time.
This formula is called Faraday’s Law.
Equivalence of Faraday’s Law with E = vBl
The earlier example of a metal bar rolling along tracks to induce a current is just a
particular case of the more general Faraday’s Law. If the bar is moving at a constant
velocity v, at which it covers a distance in a time , then:
Because is the same thing as , we get:
Lenz’s Law
Faraday’s Law tells us that a change in magnetic flux induces a current in a loop of
conducting material. However, it doesn’t tell us in what direction that current flows.
According to Lenz’s Law, the current flows so that it opposes the change in magnetic
flux by creating its own magnetic field. Using the right-hand rule, we point our thumb in
the opposite direction of the change in magnetic flux, and the direction in which our
fingers wrap into a fist indicates the direction in which current flows.
Lenz’s Law is included in Faraday’s Law by introducing a minus sign: