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Re: visualizing a non-potential



It looks like there is a height change if one takes a step radially. In the
betatron E field, moving at right angles to the circular field lines involves no
work. Perhaps you need steps in the form of radial strips, rather than small
circles.

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor
----- Original Message -----
From: "John S. Denker" <jsd@MONMOUTH.COM>
To: <PHYS-L@lists.nau.edu>
Sent: Saturday, April 26, 2003 8:16 PM
Subject: visualizing a non-potential


| Hi --
|
| I cobbled up an improved scheme for systematically
| portraying non-potentials, i.e. things that have a
| slope but no well-defined height.
|
| Here's an example. Clockwise = down, everywhere.
| http://www.monmouth.com/~jsd/physics/img48/nonpot.png
|
| This particular example is meant to depict the
| electric field in a cyclotron, i.e. the electric
| field induced by a magnetic field that is uniform
| in space and steadily increasing as a function of
| time.
|
| Non-experts tend to think that everything that is
| a function of position has to be a potential, but
| it's just not true.
|
| Pick two points A and B and count how many steps
| you go down along a path from A to B. The answer
| depends on your choice of path. For a potential,
| the answer would be independent of path.
|
| I'm moderately pleased with how this looks. This
| is the tenth scheme I tried. The first nine looked
| awful.
|
| My next agenda item is to extend the technique to
| handle cases where the magnitude (not just direction)
| of the one-form depends strongly on position. This
| is needed for e.g. thermodynamics, where PdV is an
| important non-potential.
|
| A more aesthetic non-potential is seen at
| http://www.monmouth.com/~jsd/physics/img48/escher-waterfall.jpg
| but it isn't quite as precise or generalizable.