I am doing some research in electromagnetic induction,
and found the following letter from Faraday that appears to contradict
Lenz's law. I doubt very much that Faraday made a mistake here, but I
have been unable to find a plausible explanation for this incongruity.
Could you please help me elucidate this conundrum?
Michael Faraday wrote to R. Phillips on Nov. 29, 1831:
"When an electric current is passed through one of two parallel wires it
causes at first a current in the same direction through the other, but
this induced current does not last a moment, notwithstanding the inducing
current (from the Voltaic battery) is continued all seems unchanged except
that the principal current continues its course, but when the current is
stopped then a return current occurs in the wire under induction of about
the same intensity and momentary duration but in the opposite direction to
that first found. Electricity in currents therefore exerts an inductive
action like ordinary electricity but subject to peculiar laws: the
effects are a current in the same
direction when the induction is established: a reverse current when the
induction ceases and a peculiar state in the interim..."
I don't see a problem here. The induced emf in the undriven wire is
proportional to the rate of change of the flux, so it's nonzero only
while the current in the driven wire is changing.
Faraday's letter refers to two separate wires, not wire loops. As a result,
it can be difficult to relate to Lenz'z Law.
When current begins to flow in the primary wire, the magnetic field around
that wire begins to increase. As the magnetic field increases, it produces
a current in the secondary wire. Because the field is stronger between the
wires than beyond the secondary wire, the secondary current's magnetic field
will oppose the magnetic field between the wires. To do this, both currents
must be in the same direction. This agrees with Lenz's Law.
After the primary current is constant, there is no more change of magnetic
field and no more induced current.
After the primary current is turned off, the primary magnetic field
decreases. The change is opposite the change when turned on. To counter
the decrease of magnetic field between the wires, the induced secondary
current must be opposite what it was at the beginning. Thus, all of
Faraday's letter agrees with Lenz's Law.
I don't think this contradicts Lenz's Law. Basically what Faraday is saying
is that a changing electric current in the first wire induces currents in
the second. As I recall it, Lenz's Law prohibits an induced current in a
conductor (such as the second wire here) from reinforcing the magnetic field
that does the inducing. Recall that the magnetic field from a current
flowing in a straight line is a right-handed circle centered on the wire.
The magnetic field from a current flowing in the same direction along a
parallel path will also be a right-handed circle, opposing the first field
in the regions of greatest overlap.
Bear in mind, though, that it's been a LONG time since I took Physics...
Richard E. Barrans Jr., Ph.D.
PG Research Foundation, Darien, Illinois
Rather than dealing with written arguments and disagreements, be a true
scientist: find out for yourself. There are several ways to try it.
Set up two fairly long adjacent wires, very close but not touching. Have
the "primary wire" connected to an ammeter, resistor (to avoid too much
current), and a power source. Connect the "secondary wire" to just an
ammeter. Make both of them series circuits.
If you have a computer system that with sensors that can measure and record
current as a function of time, have the sensors be the ammeters. Be sure
"positive" current is in the same direction for both wires. After the
computer system is recording, turn on the power source, wait a few seconds,
and then turn off the power source. See what direction the secondary
current flows with respect to the primary current.
If you prefer to use an oscilloscope and square wave function generator, you
can. Use a square wave that is positive, then zero, then positive,.... The
function generator powers the primary wire. Use one oscilloscope channel to
read the current of the primary wire. Use another channel to read the
current of the secondary coil. How you attach the oscilloscope depends on
the individual equipment. Trigger of the primary coil. See how the
secondary current relates to the primary current.
One thing to note. If you only have devices that read voltage, you can
create an ammeter with a small resistor. Put the small resistor in series
with the circuit. Read the voltage across that small resistor.
Click here to return to the Physics Archives
Update: June 2012