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inductive cooktops

I'm relaying this note from Jim James:

The frequency of the oscillators for the Westinghouse unit was about 40 kHz,
chosen to get above the audio range because the noise is intense at lower
frequencies. We ran experiments from 60 Hz all the way up, using square
wave generators, coverting ac to do then to sq. wave.

Ihave been looking for some time for an analysis of an inductive circuit in
which the only variable is the number of turns, N. In case A, a coil is
wound on a mandrel rotating at a constant angular velocity so the turns are
linearly increasing. The magnetic field in the coil is constant and the
crosssectional area is constant. The only variable is N. What is the
induced voltage? If the mandrel is rotated back and forth, can you generate
a square-wave output? Case B is a coil arranged with a tap at each coil and
a sliding contact that engages the taps to produce a stepwise linear change
of turns as the sliders is moved with constant velocity, either increasing
or decreasing. How is this different from Case A? I vaguely remember a
series of short essays by Joseph Slepian in the IEEE magazine covering
circuits like this. And my flawed memeory of these essays was that changing
the turns in this manner would NOT produce an induced voltage, but why? Can
some one help?
Homer B. (Jim) James Home: 1636 Jamestown Place
Adjunct Professor of Physics Pittsburgh, PA 15235-4922
Community College of Allegheny County (412) 731-3239 (voice)
Allegheny Campus