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Re: Lenz's Law



At 09:40 AM 3/22/00 -0500, Stuart Leinoff wrote:

Given: a long straight wire lying on a horizontal table carrying conventional
current north. Next to the wire, on the right, is a metal ring lying flat on
the table.

If the current in the wire is increased, there will be a growing B-field
inside
the metal ring directed down into the table. This should (I'm pretty sure)
induce a counter-clockwise current in the ring which will cause a B-field
up out
of the table in opposition to the change in field that induced the current in
the first place (Lenz's Law?)

Right. Also, in the limit that the ring is a very good conductor (e.g.
superconductor) you can replace the indicative "will be a growing B-field"
with the subjunctive "would be a growing B-field" because the induced
current will 100% oppose the entry of flux into the ring.

What bothers me is that (by my understanding is that by Lenz's law) this
induced
current in the ring should somehow oppose the increasing current in the wire,

Your understanding is correct...

and I don't see the mechanism for that.

Let's continue to concentrate on the case of a very good conductor.

The mechanism in question is simply that the induced current in the loop
creates a field which wouldn't otherwise have been there. This field
induces a voltage in the long wire. This alters the I/V relationship of
the wire.

To say the same thing another way: The loop is by no means 100% effective
in preventing an increase in current in the wire. The wire just has to put
its flux somewhere else. This means the wire has to expend more energy per
unit flux than it would in the no-loop case.

======

In the situation you described, the self-inductance of the wire is large
compared to the wire-to-loop mutual inductance.

In another situation, such as a well-engineered transformer, the mutual
inductance would dominate, and it would be very difficult indeed to change
the current in the transformer primary if the secondary were shorted.

If the ring was part of a circuit with
resistance, the induce current would do work, which would mean that it would
take more work to increase the current in the straight wire when the loop was
present than without the loop.

That's also true, but it's not the easiest way to approach your original
question.