Lenz’s Law and Faraday’s Law of Induction

1. With this definition of the flux being , we can now return to Faraday’s

investigations. He found that the magnitude of the emf produced depends on the

rate at which the magnetic flux changes. Faraday found that if the flux through

N loops of wire changes by an amount , during a time delta t, the average

induced emf during this time is

This fundamental result is known as Faraday’s law of induction.

The minus sign is placed there to remind us in which direction the

induced emf acts. Experiment shows that an induced emf always gives rise to a

current whose magnetic field opposes the original change in flux. This is known

a Lenz’s law. Let us apply it to the case of relative motion between a magnet

and a coil. The changing flux induces an emf, which produces a current in the

coil; and this induced current produces its own magnet field. If the distance

between the coil and the magnet decreases; so the magnetic field, and therefore

the flux, through the coil increases. The magnetic field of the magnet points

upward. To oppose this upward increase, the field produced by the induced

current must point downward. Thus Lenz’s law tells us that the current must move

by the use of the use of the right hand rule. If the flux decreases, so the

induced current produces an upward magnetic field that is “trying” to maintain

the status quo.

Let us consider what would happen if Lenz’s law were just the reverse.

The induced current would produce a flux in the same direction as the original

change; this greater change in flux would produce an even larger current,

followed by a still larger change in flux, and so on. The current would continue

to grow indefinitely, producing power (=) even after the original stimulus ended.

This would violate the conservation of energy. Such “perpetual – motion” devices

do not exist.

It is important to note, which I believe was forgotten in the class

lecture, is that Faraday’s investigation, as summarized in Faraday’s law, says

that an emf is induced whenever there is a change in flux. Thus an emf can be

induced in two ways: (1) by changing the magnetic field B; or (2) by changing

the area A of the loop or its orientation theta with respect to the field.

A motor turns and produces mechanical energy when a current is made to

flow in it. You might expect that the armature would accelerate indefinitely as

a result of applied torque. However, as the armature of a motor turns, the

magnetic flux through the coil changes and an emf is generated. This induced emf

acts to oppose the motion (Lenz’s law) and is called the back or counter emf.

The greater the speed of the motor, the greater the back emf. Indeed, as the

motor increases in speed, the back emf increases until a balance is reached

where the speed remains constant. Thus the counter emf controls the speed of a

motor.

For a given coil, the ratio of the electromotive force of induction to

the rate of change in the coil is called the self-inductance of the coil. An

alternative definition of self-inductance is the number of flux linkages per

unit current. Flux linkage is the product of the flux and the number of turns in

the coil. Self-inductance does not affect a circuit in which the current is

unchanging, however, it is of great importance when there is a changing current,

since there is an induced emf during the time that the change takes place.

The mutual inductance of two neighboring circuits is defined as the

ratio of the emf induced in one circuit to the rate of change of current in the

other circuit. ()

The SI unit of mutual inductance is the henry, the same a the unit of

self- inductance. The same value is obtained for a pair of coils, regardless of

which coil is the starting point. ()