Faraday's law describes how an electric field can be induced by a changing magnetic flux.

This can be illustrated by moving a magnet back and forth close to a loop connected to a galvanometer.Note that a similar effect can be observed by moving the coil. It is the relative movement between the coil and the magnet that matters:

When the magnet is moved toward the loop, the meter deflects to the right. But when it is moved away, the meter deflects the other way. This indicates that a current is induced, and that the direction of the current depends on the time rate of change of the field. I.e., if the field is getting stronger or weaker as time progresses.

Faradays law is as follows:

"The emf induced in a circuit is directly proportional to the time rate of change of magnetic flux through the circuit."

For a single turn, this can be expressed by:

Therefore an emf can be produced by changing B(induced emf), or by changing the area, e.g. by moving the wire(motional emf).

We are now going to consider motional emf. Consider a straight conductor moving a velocity through a magnetic field:

An electric field will be induced at either side of the the conductor. This is because the electrons experience a force along the conductor given by:

This is the cross product again.

If the moving bar is part of a closed circuit, we get the situation illustrated in the applet below. If the distance between the rails is l, the velocity of the bar is v and the strength of the magnetic field B, then the EMF is(note that lv=dA/dt):

Try changing the parameters, and see how the lightbulb shines with increased intensity when the strength of the magnetic field is increased.