Faraday's Law

Faraday’s Law states that a changing Magnetic Field through a coil of wire will “induce” a Current in the wire, called an “induced current”.

The induced current is actually caused by an induced emf . per Ohm’s Law.

The emf is generated by changing the Magnetic Flux, which is done by changing the magnetic field , the area , or the angle between the magnetic field and the area vector.

Faraday’s Law gives the magnitude of the induced emf, while Lenz’s Law gives the direction.

For example: The motional emf for the metal bar on metal rails is:

Example. A rod with no resistance can slide on two frictionless, resistance free rails. The rails are connected by a capacitor, capacitance as shown. There is an infinitely long wire carrying a constant current as shown. The rod is moved by some external force so thaht its velocity along the rails is given by where is a known constant. Ignoring self inductance fund the charge on the capacitor plates as a function of time. What is the direction of the magnetic force exerted on the rod?

First we will note that

Now we use faraday’s law.

The current is counterclockwise through the loop, so it is moving up in the rod. The magnetic field is out of the page. Using,

We find the direction of the magnetic force exerted on the rod is to the left.