Vector calculus

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Hi, I having some issues with vector fields and picturing how they look on a x-y plane. The field is defined by

$F = (\frac{-y}{x^2 + y^2},\frac{x}{x^2 + y^2},0)$

The question is simply, Sketch F, in the x-y plane. Thanks for the help in advance!

BillyK Feb 28, 2016

heureka · Answer 1 · 2016-02-28T12:54:32

circle inversion (unit circle (R=1) ) and axis-rotation 90 degrees.

circle inversion: $x' = \frac{R^2\cdot x}{x^2+y^2}\\ y' = \frac{R^2\cdot y}{x^2+y^2}\\ r'\cdot r = R^2$