## Question

###### B. Consider now the vector field F() = (22 + yP)i + 2k _ where 2 = ci +yj + zk. Express F(E) in a spherical coordinate system: Namely: F() = F(r,0 ,o)7 (z) + Folr,9,0)0 () + Fo(r,9,0)o(w). You may use only the following definitions: x = r sin 0 cos $ y = r sin 0 sin $ 2 = r COS 0and:r(z) = sin 0 COS $ & + sin 0 sin $ j + cos 0 k 0 (2) cos 0 COS 0 i + cos 0 sin $ j sin 0 k $(z) = _ sin $ i + COS 0 j

B. Consider now the vector field F() = (22 + yP)i + 2k _ where 2 = ci +yj + zk. Express F(E) in a spherical coordinate system: Namely: F() = F(r,0 ,o)7 (z) + Folr,9,0)0 () + Fo(r,9,0)o(w). You may use only the following definitions: x = r sin 0 cos $ y = r sin 0 sin $ 2 = r COS 0 and: r(z) = sin 0 COS $ & + sin 0 sin $ j + cos 0 k 0 (2) cos 0 COS 0 i + cos 0 sin $ j sin 0 k $(z) = _ sin $ i + COS 0 j

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