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A vector field is described in Cartesian components but the problem has spherical symmetry. The sensible course is to

  • A.transform to spherical coordinates before proceeding
  • B.work in Cartesian coordinates throughout
  • C.use whichever system gives the smaller number of components in the field
  • D.abandon the vector treatment and work with the scalar potential alone

Answer: A

Matching the coordinate system to the symmetry reduces the number of variables the field depends on, often from three to one, and that saving far outweighs the extra complexity of the curvilinear operators. The transformation itself is a routine substitution.

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