Re: simple magnets question

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Thu, 24 Jun 1999, William Beaty wrote:

> Here's another thought-experiment which illustrates some of the problems
> which arise when thinking about Faraday's Disk.
>
> Suppose a copper ring is moving through a uniform magnetic field.  Since
> the flux within the ring is unchanging, there should be zero EMF around
> the ring, and zero induced current.  I think we all agree on this.
>
> However, what do the individual electrons in the copper ring do?  Well,
> since they are moving through a magnetic field, they should experience a
> perpendicular e-field.

Right but to be clear, it's not simply that they "experience" an E-field;
in their frame there *is* a background E-field.  You are apparently
assuming that there is no E-field in the frame of "the observer" (who
claims the ring is "moving"), so the E-field in the reference frame of the
ring will be the velocity of the ring relative to the observer's frame
crossed with the magnetic field in the observer's frame.

It could just as easily (if not more easily) be the case that there *is*
an E-field in the observer's frame.  Then, the ring would be polarized
even if it were "at rest."  But as long as the B-field is perpendicular
to the E-field and large enough in magnitude, we could eliminate the
polarization by a judicious choice of ring velocity. Specifically, we
would choose its velocity to be (E_vec cross B_vec)/B^2.  There is
nothing magical going on here.  All we have done is to find that very
special reference frame in which E = 0 -- the one we usually
implicitly assume we are in at the start.

> ... To think about:
>
>   If the ring was accelerated in a straight line back and forth through
>   the uniform magnetic field, there would still be zero current around the
>   ring.  However, wouldn't we see an alternating current as the electrons
>   all rush from one side of the ring to the other?  Will a hunk of metal
>   get hot if we wiggle it in a straight-line motion in a uniform magnetic
>   field?

Yes, because it "sees" an alternating E-field.

John
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