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induced emf and eddy currents



In a recent message Carl Mungan asked:

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A more basic issue. What exactly is an "emf"? Given
that, "The (nonconservative) electric fields produced by induction cannot
be described by an electric potential" (bottom of p. 791), what is emf, if
not a potential?
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Two individuals responded

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"First an emf is just the line integral of the electric field
around some closed path."

and

"An emf is, by definition, the
integral of the tangential component of the electric field around
a *closed* (but not necessarily physical) loop."
********************

It seems to me that both of these "definitions" are inadequate in that
they are restricted to emfs that are associated with time varying magnetic
fluxes. They do not apply to motional emfs, chemical cells, and the
thermocouple.

Arriving at general definition of emf is, at least for me, a daunting
challenge. For example, motional emf is given by the line integral of v x
B around a closed path, where v is the velocity of the conductor. At
first glance, this line integral appears to represent work done by the
magnetic field. However, a magnetic force never does work as it is always
perpendicular to the velocity of the particle it acts on. Therefore,
motional emf is not work done on the conduction electrons by magnetic
forces. The question is, what force is doing work on a conduction
electron? The answer is, it is an electric force associated with the Hall
effect electric field. This electric force cancels out one of the
components of the magnetic force leaving the net electromagnetic force
equal to v x B. So motion emf is the work done on the charge carriers by
the Hall-effect electric field, a field both sourced and sinked by
charges.

Gene