## Electromagnetic Induction and Faraday's Law

Faraday found that, when he subjected a closed loop of wire to a changing magnetic field, he could induce a current. To test this theory, he attached a loop of wire to a galvanometer and moved a magnet around inside of the loop of the wire, like so:

Since a current creates a magnetic field, the direction of the current in the loop creates a magnetic field that opposes the change in magnetic field. If there is no change in magnetic field, then there is no electromagnetic induction.

Another way to induce current is the change the area of the loop.

If the loops gets smaller, then the magnetic field enclosed inside the loop correspondingly gets smaller as well. Thus, there is an induced current that opposes the decreasing magnetic field, which means that the induced current reinforces the magnetic field as the area of the loop decreases. And vice versa.

The following diagram and flash demo is a perfect example of the concepts illustrated above.

Another way to induce current is the change the area of the loop.

If the loops gets smaller, then the magnetic field enclosed inside the loop correspondingly gets smaller as well. Thus, there is an induced current that opposes the decreasing magnetic field, which means that the induced current reinforces the magnetic field as the area of the loop decreases. And vice versa.

The following diagram and flash demo is a perfect example of the concepts illustrated above.

The magnetic flux is determined by the twin variables of magnetic field, and area.

Therefore,

Therefore,

is the equation for magnetic flux

The emf equation is:

The emf equation is:

And with some derivation we get: