Re: Induced EMF on loop

["John S. Denker" <jsd@MONMOUTH.COM>]

I wrote:

> Geometry matters
...
> In many cases your best bet would be to run an
> "auxiliary" cut loop in parallel with the uncut
> loop, and measure the voltage in the auxiliary
> in the usual way.

The best geometry for the auxiliary loop is _inside_
the uncut loop.  You can use a piece of coax cable
for this.  Short the ends of the shield to form the
uncut loop.  Use your scope to measure the voltage
drop across the ends of the loop formed by the inner
conductor. Using a piece of coax 3 feet long you get
a loop with a 15 cm radius, for which the shield has
an L/R time on the order of 50 microseconds I figure.
So if the applied field is at 1MHz the shield will
be virtually 100% effective at shielding the inner,
as you can verify by unshorting and re-shorting
the shield.  At 1kHz and below, the shield will be
essentially unable to stop the applied magnetic field.
You can explore the intermediate cases by varying
the frequency of the applied field.

===================================

I wrote:
> | there is no potential, so the concept of "same"
> | potential does not apply for the same reason that
> | "difference" of potential does not apply. . . .

Maybe I should have written no _uniquely-defined_
potential.  But I wasn't expecting any disagreement.

Bob Sciamanda wrote:

> Except for the special case where the original induced electric field
> happens to follow the same contour as the loop, charges will accumulate on
> the conductor to "properly" direct the current.  There will be electric
> fields and potential differences associated with these separated charges.

There will be a contribution to the field from the
separated charges.  There will be a contribution to
the field from the original applied field.  The
overall field will be the superposition of all
contributions.

The overall field will not be a potential, so
IMHO talking about differences in potential is
confusing at best.

There is not in general a unique way to decompose
the overall field into a "potential piece" and an
"everything else piece".  Any such decomposition
depends on choice of gauge.  Choose whatever you
like, but be explicit about it, and don't complain
if others choose differently.

See e.g. Jackson, _Classical Electrodynamics_,
equation 6.41.

All physical consequences depend on the overall
field, not the alleged "potential piece", so I
don't see why attempting to define a "potential
piece" is worth the trouble.