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Re: non-potential voltage



I wrote:
> There will be innumerably many z values for each (x,y)
> position. An ant crawling around on the model can
> follow a path which when
> viewed from above projects onto a closed loop in the (x,y) plane; this is
> analogous to close-loop motion of a test charge in the presence of a
> changing magnetic field. In so doing, the ant can climb up the
> helix; this is analogous to the increase in the test particle's
> energy. Emphasize that x and y represent real space, while z abstractly
> represents energy value, which is a nonfunction of x and y.

Then at 04:26 PM 4/17/00 -0500, Paul O. Johnson wrote:

I'm having a hard time visualizing your ant-on-the-helix analogy. The
closed-loop view of the ant's motion is only a projection of its actual
motion along the helix. Your implication seems to be that the ant can
independently move in a planar closed loop (analogous to closed-loop motion
of a test charge in the presence of a changing magnetic field) and up and
down the helix (analogous to the increase in the test particle's energy).
How can it do one without the other?


Please re-read the sentence
> Emphasize that x and y represent real space, while z abstractly
> represents energy value, which is a nonfunction of x and y.

The ant and the test-charge are not identical, they are only
analogous. Here is the analogy, spelled out in more detail. Differences
are flagged. Unflagged lines are verbatim identical.

ant test charge
===== =============
X-position X-position
independent variable independent variable

Y-position Y-position
independent variable independent variable

Z-position V-energy per unit charge <<<<<<
dependent variable dependent variable
nonfunction of (X,Y) nonfunction of (X,Y)

no other variables Z implicitly constant <<<<<<

(X,Y,Z1) is a different (X,Y,Z,V1) is the same <<<<<<
position from (X,Y,Z2) position as (X,Y,Z,V2) <<<<<<