At 03:38 PM 10/4/99 -0400, Chuck Britton asserted:
Flux, measured in Maxwells HAS a quantized minimum value.
Really? Let's explore the consequences of such an idea. Here are some
questions:
1) What might that minimum value be?
2) We know voltage = flux dot. That is, voltage = d(flux)/d(t). Consider
the voltage across a loop of wire. When the flux in the loop changes from
one value to another, how does the voltage change? Is the voltage zero
except during changes, with infinite spikes when the flux suddenly changes
from one quantized voltage to another?
3) We know flux = inductance times current. For a fixed inductor, does
that mean that the current is quantized? In an LR circuit, does that mean
that the voltage across the resistor is quantized?
4) Consider a region of space, shielded from all external fields, and with
no internal sources except for a single electron which has been measured to
be in the spin=+1/2 state along the Z axis. We agree that the magnetic
field (as measured in Teslas) is not quantized, so it falls off smoothly
with distance. It goes like 1/R cubed. Now suppose I go one meter away
from the electron along the X axis and set up a square loop of aluminum
wire. The loop is 10 microns on a side, lying in the XY plane. We know
the field. We know the area. Therefore we can calculate the flux through
the loop. I get
flux in loop = 9.28e-41 Wb
This is about 25 orders of magnitude smaller than the answer that is
typically given to question (1) above. But it is a perfectly real flux,
and in principle could be measured e.g. by flipping the loop end-over-end
rapidly and observing the AC voltage.
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Just because you saw a table of numbers somewhere that gave a value for
"the quantum of flux" it doesn't mean that flux is quantized in ordinary
real-world situations.
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copyright (C) 1999 John S. Denker jsd@monmouth.com