Chapter4_4

# Chapter4_4 - PHY4604 R D Field Spherical Coordinates...

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PHY4604 R. D. Field Department of Physics Chapter4_4.doc University of Florida Spherical Coordinates Spherical Coordinates: We must express the operators in spherical coordinates where θ φ θ φ θ cos sin sin cos sin r z r y r x = = = x y z y x z r z z y x r / tan / / cos 2 2 2 2 2 2 = + + = = + + = φ θ Hence, 0 sin cos 1 sin sin 1 sin 1 sin cos 1 cos cos 1 cos sin sin cos sin = = = = = = = = = z r y r x r z r y r x z r y r x r φ θ φ φ θ φ φ θ θ φ θ θ φ θ θ θ φ θ φ θ . Chain Rule: Use the chain rule. For example, x f x f x r r f x f + + = φ φ θ θ . and thus = = + + = = + = = θ θ θ φ θ φ θ φ θ φ θ φ θ φ θ φ θ φ θ sin 1 cos ) ( sin cos 1 sin cos 1 sin sin ) ( sin sin 1 cos cos 1 cos sin ) ( r r i x i p r r r
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