On Fri, 1 Jan 2010, Stephen A. Lawrence wrote:
So the problem I had is failure to properly picture a non-uniform
magnetic field.
Or, from practical experience with inductors, I could imagine noticing the
effects of saturation, but ascribing the cause to nonuniform fields! :)
First, let me explain that I see why an ideal toroidal coil has no
external field -- symmetry and simple arguments regarding the curl of
the B field show that it's got to be null outside the torus. In
particular, any loop around the outside of the torus must have zero net
Yep, that's exactly it.
But I see one extra source of confusion: any nonuniform e-field threading
the donut hole of the torus, if it's fast-changing, constitutes a
significant displacement current having a circular b-field in the core,
and will induce a small current in the toroid coil.
For example, if we place capacitor plates above and below the plane of the
toroid coil and adjacent to the coil, then apply AC, we've essentially
passed a single-wire primary coil through the donut hole, and the toroid
acts as a transformer secondary.
But those capacitor plates will measure a couple of picofarads. Moving
magnets produce effects in tens of mSec, 10Hz - 100Hz, so the capacitive
reactance will be ~billion ohms. My gut-level impression is that, for
this effect to even be detectable, the fast-changing external e-field has
to be damn fast, like tens of MHz. It may be a major effect when
high-power RF is involved. But waving a magnet near a toroid won't do it.
(Waving a magnet past the leads of an AC digital voltmeter won't produce a
reading, even though in theory the changing b-fields in space are
producing EM waves, and the meter leads must act as a dipole radio
antenna!)
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William J. Beaty SCIENCE HOBBYIST website
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