Re: visualizing a non-potential

[Bob LaMontagne <rlamont@POSTOFFICE.PROVIDENCE.EDU>]

"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