Re: visualizing a non-potential

[Jack Uretsky <jlu@HEP.ANL.GOV>]

Hi all-
        That seems to be the problem, that one keeps coming back to the
same circle (when traversing at constant radius).  What seems to be needed
is a 3-d representation involving spirals rather than circles.  So I'd say
to John, "Nice try!"
                                Regards,
                                        Jack

On Sat, 26 Apr 2003, Bob LaMontagne wrote:

> "John S. Denker" wrote:
>
> > The force vector acting on the electron has components
> > proportional to
> >         Fx =  y/sqrt(x^2+y^2)
> >         Fy = -x/sqrt(x^2+y^2)
> >         Fz =  0
> >
> > Note that the magnitude of F is constant everywhere,
> > and that F points clockwise everywhere.
>
> Yes - this is a great example of a function of position not being a potential.
> Since the magnitude of this F is 1, and it always points counterclockwise,
> integrating the dot product of F and ds around a complete circle of unit
> radius in the xy plane centered about the origin gives 2 PI - going around
> twice gives 4 Pi, etc. - definitely not a potential.
>
> But your depiction always comes back to the same value regardless of how many
> times you pass through the same point. What I was curious about is how one
> creates a function which seems to constantly increase along a closed path but
> gives the same value when one returns to any point on the closed path. I love
> the Escher _local_ vs _global_ paradoxes, but unfortunately have not had the
> time to explore the literature on the underlying mathematics.
>
> Bob at PC

--
        "What did Barrow's lectures contain?  Bourbaki writes with some
scorn that in his book in a hundred pages of the text there are about 180
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worse.)"
                                        V. I. Arnol'd in
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