PHY2061 R. D. Field Department of Physics curl_3.doc Univesity of Florida The Curl of a Radial FunctionSuppose),,(zyxF!is a radial (or central) function of r. Namely, rrfrF!!)()(=, it points radially outward (or inward) along the radius vector zzyyxxrˆˆˆ++=!and has a magnitude rf(r) that depends only on the distance 222zyxr++=from the origin. Theorem: The curl of a radial function is zero. 0=×∇F!!if rrfF!!)(=Proof: rfrfrfF!!!!!!!!×∇+×∇=×∇=×∇
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