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Hi --
Here's an example. Clockwise = down, everywhere.
http://www.monmouth.com/~jsd/physics/img48/nonpot.png
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.