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 result to the determination based on 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 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
√
.
Lenz’s original statement describes both the magnitude and direction of the induction effect. 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 same result found by using 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 statement is vague.
Here are a few versions plucked from the web via a Google search on “Lenz’s law”:
An induced electromotive force generates a current that induces a counter magnetic field that opposes
the magnetic field generating the current.
Ahem: a magnetic field does not generate the current! A “changing” field does.
An induced electric current flows in a direction such that the current opposes the change that induced it.
What, physically, is the change? How does the current oppose it?
As you can see, these modern statements vary from the original
The electrodynamic action of an induced current opposes equally the mechanical action producing it.
The modern versions are variously ambiguous and imprecise, and make use of concepts (electromotive
force and magnetic field) that do not appear in Lenz’s original statement. Lenz speaks only of an
induced current and of actions, namely forces; a mechanical force and an electromagnetic force.
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 called the motional
electromotive force. Notice that is precisely the emf found using Faraday’s law (for which we
picture the rod as one end of a rectangular loop of wire, or as a sliding bar on conducting rails).
We have two different but equivalent ways of describing electromagnetic induction:
the first way is based on the Lorentz force experienced by a free charge in a rod (the leading edge of a
coil) as the rod moves through a magnetic field;
the second way is based on the change of magnetic flux through a loop (which can be effected by a
change in the magnetic field passing through a stationary coil, or a change in the area of field enclosed
by the coil, due to the relative motion of the coil and magnet).
In both cases, the relative motion of the coil and magnet produces the induction effect.
If you continue your studies in physics, you will eventually encounter the theory of relativity, which
provides a simple viewpoint that unifies the above two descriptions into one, and you will see clearly
that the two descriptions are simply different ways of looking at the same physical process,
electromagnetic induction.
Let’s review methods of determining the direction of the induced current. 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.
You may ask: 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 ⃗ relative to , and the direction of ⃗ .
You can likewise sketch cases involving direction of
relative to ⃗ , and the direction of
.
How many stinking cases does this make, eight?
Here is my first suggestion: review each case and work exercises until you develop a “feel” for direction
of increasing flux.