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VectorPlot on a Circle


I'm trying to do a vector plot but confine the vectors to a unit circle.

If[Abs[x^2 + y^2 - 1] == 0, {x, y}, {0, 0}], {x, -1, 1}, {y, -1, 1}]
only plots a couple of vectors, not the dense set of vectors that I want.

If[Abs[x^2 + y^2 - 1] <.1, {x, y}, {0, 0}], {x, -1, 1}, {y, -1, 1}]
plots lots of vectors but they're on an annulus rather than a circle.

Is there any way to do this?

Or more generally is there any way to confine the vectors to a curve.
Or, kicking the dimension up by 1, can VectorPlot3D confine the vectors
to a surface?

Dave Snead

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