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Re: Faraday induction



At 05:38 PM 5/30/01 -0500, Lemmerhirt, Fred wrote:
It is tempting to speculate that by symmetry the "emf" (a term not allowed
by some PHYS-L participants) induced in a circular arc of central angle A
should be just A/(2 pi) times that induced around the corresponding complete
circle. By the same reasoning, the emf induced in a straight segment would
be just one-fourth of that induced around a square of side equal to the
length of the segment.


This hypothesis is either true or not, depending on what additional
assumptions are made. Consider three cases:

1) The induced field is induced by the changing flux in a solenoid that is
centered in the square. The square is demarcated by small bits of inert
insulator. Result: the induced voltage on each of the four straight
segments is the same. This is obvious by symmetry, and can be verified by
direct calculation.

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2) Suppose the solenoid is moved off-center. Then the four segments will
not have equal induced voltages.

3) Return to the case where the solenoid is centered in the square, but
this time three legs of the square are made of metal, while the fourth is
made of wood. The metal will "short out" the induced field in its
vicinity. The total voltage drop around the loop will be the same, but it
will all be concentrated on the non-conducting segment. Wolfgang's
original question is in this category.

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

The term "EMF" carries the following unfortunate baggage:
1) The quantity it represents is an energy per unit charge,
so why call it a force?
2) Sometimes people use the term as synonymous with voltage, while
other people use it to refer to the non-potential part of the
voltage, to the exclusion of the potential-type voltage.
a) I don't like the concept of such a distinction. Test charges
don't know the difference between one type of electrical field
and another. Such a distinction is inadvisable in elementary
situations (slowly-varying fields) and physically untenable in
more general situations.
b) This is a non-standard use of the word. I don't object to non-
standard usages if people define their terms as they go along,
but it's a real problem if authors throw around non-standard terms
without defining them, and expect readers to divine the meaning.

My recommended solution: I just talk about "voltage". It's easy. It
removes any temptation to talk about "EMF".

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Tangentially related point: One should be careful not to talk about the
"electric potential" in situations such as the present one. The voltage in
question is not a potential.