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Re: Faraday induction



What does work is the more careful statement that the line integral of
E(r) around any closed path is equal to the rate of change of the magnetic
flux through any chosen surface bounded by that closed path. This follows
from Stokes' theorem applied to Curl(E) = -dB/dt.

Whether this results in an "EMF" driving a current depends upon the
presence of an appropriate distribution of conducting matter.

An interesting aside: Feynman is intriqued that two such disparate
effects (the motional vxB force and the dB/dt E field "source") can be
included in a single calculational rule. He expects this to come from
some "single deep underlying principle" but finds none. He says this is
unique in all of Physics. I might reply that such a grouping of disparate
phenomena with a common effect occurs in the first law of thermodynamics,
or anytime we group together the effects of different energy forms.

Bob Sciamanda
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor
----- Original Message -----
From: "Wolfgang Rueckner" <rueckner@FAS.HARVARD.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Wednesday, May 30, 2001 02:39 PM
Subject: Re: Faraday induction


Thank you -- I should have thought of going to Feynman in the first place.
But now, how to explain this to an introductory physics student in an
algebra-based course .... I guess the only answer is again, "the flux rule
does not work in this case!" Wolfgang


The "flux rule" is a calculational help in many circumstances, but it is
not "fundamental" and can lead to confusion. I refer you to Feynman
Lectures II; 17-1 and 17-2. A sample extract:
" . . . The 'flux rule' does not work in this case. . . The correct
physics is always given by the two basic laws:
F = q(E + vxB), and CURL(E) = -dB/dt.


Bob Sciamanda
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor
----- Original Message -----
From: "Wolfgang Rueckner" <rueckner@FAS.HARVARD.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Wednesday, May 30, 2001 09:51 AM
Subject: Faraday induction


A student asked me a question that I couldn't satisfactorily answer and
could use your help. It concerns Faraday induction. Suppose we have a
single loop of wire lying in the plane of the page (or monitor screen)
and
the loop is split -- that is to say, it's not a complete circuit. Also
imagine an increasing magnetic field into the page (monitor).
Faraday's/Lenz's law tells us that an emf will be induced such as to
produce a CCW current which generates a magnetic field out of the page.
If
you envision the split in the loop being at the top of the page, then the
end of the loop to the left of the split would be at a positive potential
w.r.t. the other end.

Now here's the question. How large can this "split" become? For
example,
suppose we open up the split so that it's as large as the diameter of the
loop -- what area does one use to calculate the magnetic flux? Does one
just imagine a "short" between the two open ends of the loop so that one
has a quasi enclosed area? Or suppose it's opened up even more so that
the
loop becomes just a curved wire? At what point does the loop of wire no
longer enclose an area so that the problem can't be solved in this
manner?
I look forward to your insights. Thanks, Wolfgang