# Faraday’s Law and Lenz’s Law of Induction

Faraday’s Law of Induction Lenz’s Law
Last semester in EE 381 Electric and Magnetic Fields, you saw that in
. Electrostatics: stationary charges produce `E (and D)
. Magnetostatics: steady currents (charges in constant
motion) produce `B (and H ). These are two distinct theories that were developed from two different experimentally derived laws: Coulomb’s law and Ampère’s force law. Now we are going to consider time-varying fields. While many of the concepts we’ve learned in statics will still apply, two new phenomenon we will observe are:
.Time varying `B produces `E, and
. Time varying `E produces `B!!
The complete electro-magnetic theory uses Coloumb’s and Ampère’s laws as a subset and requires one more experimentally derived law called Faraday’s law of induction. We’ve seen that a steady current in a wire produces a `B:

It may seem possible (by some type of “reciprocity”) that if we had a wire and a magnet, for example, that a current would be “induced” in the wire:

This doesn’t occur, however. If it did, there would be a clear violation of conservation of energy. What Faraday (ca. 1831) and Henry showed was that a timevarying magnetic field would produce (or “induce”) a current I in a closed loop!

In words, Faraday’s law states that the emf generated in a closed loop is equal to the negative time rate of change of the magnetic flux linking the loop.Substituting for the definitions of emf and ym yields an equivalent form of Faraday’s law of induction