curl_3 - PHY2061 R. D. Field The Curl of a Radial Function...

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PHY2061 R. D. Field Department of Physics curl_3.doc Univesity of Florida The Curl of a Radial Function Suppose ) , , ( z y x F is a radial ( or central ) function of r. Namely, r r f r F ) ( ) ( = , it points radially outward (or inward) along the radius vector z z y y x x r ˆ ˆ ˆ + + = and has a magnitude rf(r) that depends only on the distance 2 2 2 z y x r + + = from the origin. Theorem: The curl of a radial function is zero. 0 = × F if f F ( = Proof: r f r f r f F × + × = ×
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