Lenz’s law, like Faraday’s law, describes the phenomenon of electromagnetic induction. The Russian
physicist H.F.E. Lenz formulated his law during the early 1800s, the same period in which Henry and
Faraday conducted their researches of electromagnetic phenomena.
Lenz’s original statement of his law (1833), translated into English, reads
The electrodynamic action of an induced current opposes equally the mechanical action producing it.
What does it mean? Consider the relative motion of a coil and a magnet:
In the figure, the coil enters a magnetic field at constant speed .
Lenz’s law states that the induced current in the coil generates an “electrodynamic action”, a force
of electromagnetic origin, that is equal and opposite to the mechanical force
that your hand
must apply to keep the coil moving at constant speed
By Lorentz’s force law, in the form of the force on a current-carrying wire, the magnitude of the force is
Multiplying through the equation by the coil speed
you must do work) to keep the coil moving
gives the power required of your hand (the rate
Compare this power to the power determined by Faraday’s law
Multiplying through the equation by the induced current gives the power being delivered to the circuit
The two results are equal.
Let’s summarize the effect. Your hand must apply a force of magnitude
in order to keep the
coil moving at constant speed as it enters the field. Your hand does work on the coil; where does the
energy go? It goes into “lifting” the current through the potential . If a light bulb of resistance
placed in the circuit, the bulb will absorb the current’s energy and radiate the energy at the rate
is
There are several ways to measure the induced current:
1) use an ammeter to measure directly;
2) measure the force and solve for
;
3) insert a resistor in the circuit, measure the resistor voltage
then calculate
;
4) use a photocell to measure the power output of a bulb of resistance , then calculate
.
As you can see, Lenz’s original statement describes both the magnitude and direction of the induction
effect, a force. By combining Lenz’s law with the Lorentz force law (in the form of the force on a current
carrying wire), we are able to derive the result found by Faraday’s law.
Compare Lenz’s original statement to the statement given in Y&F page 1004:
The direction of any magnetic induction effect is such as to oppose the cause of the effect.
What, physically, is the effect? What, physically, is the cause?
The modern statement deals with “flux” rather than “force”. If you increase the flux through a loop, a
current is induced in the loop. The current itself creates a magnetic field, which produces a flux through
the loop, and
the induced flux change
“opposes” the applied flux change
.
We emphasize the word “change” here; the flux change, not the flux, is proportional to the induced
current.
The induction effect can also be described in terms of the “motional electromotive force”, which is
calculated using the Lorentz force law. Referring to Y&F figure 29.15, a metal rod of length moves
with speed through a region of uniform magnetic field , where
and are mutually
perpendicular. Each free charge in the rod experiences a force
The work done on this charge by the force acting along the length of the bar is
and the corresponding potential through which the charge is “raised” is nowadays called the
“motional electromotive force”, even though it is a voltage, not a force.
The bar is not a closed loop, so there is no induced current. However, the bar becomes electrically
polarized: charge accumulates at one end of the bar, and charge accumulates at the other end. A
voltmeter whose probes are placed at the ends of the bar measures the potential difference .
The voltage is precisely the emf found using Faraday’s law for a rod that is part of a closed loop (the
the rod may be one side of a rectangular loop, or a sliding bar on conducting rails).
We have two different but equivalent ways of describing electromagnetic induction:
one first requires a rod to be moving so that its free charges experience the Lorentz force;
the other requires a rate of change of magnetic flux through a loop (the loop may be stationary).
The theory of relativity provides a unified view, showing that the two descriptions are two ways of
looking at the same physical process, electromagnetic induction.
Let’s review methods of determining the direction of the induced current in a coil. As we said before,
when using Faraday’s law, point your left thumb in the direction of the flux increase; then your fingers
will curl in the direction of the induced current.
What if the flux is decreasing?
A decreasing upward flux is the same as an increasing downward flux; point your left thumb down.
A decreasing downward flux is the same as an increasing upward flux; point your left thumb up.
Y&F figure 29.6 gives four cases involving the direction of
You can likewise sketch cases involving the direction of
You can likewise sketch cases involving the rotation
.
.
.
Consider two solenoids, A and B. Solenoid A carries current . For the cases below, find the direction
of the induced flux change and current in solenoid B, and compare to the applied flux change:
a) solenoid A approaches solenoid B. The flux through B increases.
b) solenoid A moves away from solenoid B. The flux through B decreases.
c) solenoid A flips over near solenoid B. The flux through B reverses direction, which happens in two
stages: first the flux decreases to zero, then the flux increases in the opposite direction.
d) current
increases. The flux through B increases.
e) current
decreases. The flux through B decreases.