Re: non-potential voltage

["Paul O. Johnson" <pojhome@SWBELL.NET>]

----- Original Message -----
From: "John Denker" <jsd@MONMOUTH.COM>
Sent: Monday, April 17, 2000 1:36 PM
Subject: Re: non-potential voltage

> In this case, an even more apropos example is z = arctangent(x/y).  This
is
> easily modelled using popsicle sticks;  drill a hole in the middle of
each,
> stack them on a string or rod, and then arrange them in a nice multi-turn
> helix.  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.

John, 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?

> (Fanatics note: This isn't my favorite representation of arctangent;  I
> much prefer the two-argument form z = atan2(x,y) which involves drilling a
> hole at the _end_ of each stick... slope is the same but the z-axis period
> is twice as large... alas this is harder to build.)

Why is this model harder to build? I made one years ago of cypress sticks
(1/2 x 1/4 x 8 inches) clamped together by a 20-inch threaded rod through
holes in one end and hanging on a string from a tree in the back yard. It
rotates like a barber pole in even a slight breeze.

Paul