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
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. ()