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Re: Induced EMF on loop



Savinainen Antti asked about what happens if

> the circular loop is *not* cut.

OK. This may be different from the question that
started this thread, but it's a question in its
own right, so here goes....

> When the loop is
> moving into a magnetic field a changing magnetic flux induces an emf.
> This is a standard high school physics problem:

I assume we are temporarily returning to the _cut_ loop.

> the shape of the loop is rectangular, the magnetic
> field is uniform, velocity
> of the loop is kept constant etc.

OK...

> Of course the concept of potential difference does
> not apply in the case of induced emf;

Right.

> the loop is in the same potential at all points.

No, there is no potential, so the concept of "same"
potential does not apply for the same reason that
"difference" of potential does not apply.

> The problem as I see it, is how to measure the induced
> emf if the loop is not cut.

The usual questions apply: what are you trying to measure,
and why?

In the limit of a highly-conducting uncut loop, or
more generally in the limit where the L/R time of
the loop is small compared to other timescales in
the problem, there will be _no_ induced voltage.
Lenz's law and all that. Measuring this non-existent
voltage will be tricky. If this is what you want to
measure, please say so; null measurements have a
long and glorious history. But they are tricky.
The devil is in the details.

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.

> Does it matter where the voltmeter leads are
> connected in the loop
> (close or far away from each other)?

Yes, because anything that is inducing a voltage
or current in the loop will induce a voltage in
the meter leads.

Geometry matters here. This is in contrast with
Kirchhoff's "laws" which are not laws, just
approximations that apply in limit where geometry
doesn't matter.

> Would a voltmeter measure differently in
> cases of uncut and cut loops
> which are otherwise similar?

Since the phenomenon to be measured is radically
different in the two cases (because of the induced
current in the uncut loop) one would hope that the
measurement would give different results in the two
cases.