Physics I / Polar, Cylindrical, and Spherical Coordinates
Practice question · Multiple choice

A sphere is awkward in Cartesian coordinates and simple in spherical ones. What does that coordinate change actually buy?

Hints
  1. Write the limits for a sphere in xx, yy, zz, then in ρ\rho, φ\varphi, θ\theta.
  2. Compare which set contains square roots.
Show the answer

A. Constant limits: the curved boundary becomes ρ=a\rho = a

Why

Substitution is chosen for the LIMITS. The Jacobian ρ2sinφ\rho^{2}\sin\varphi is the price, and it is worth paying because a box is easy and a variable-limit region is not.

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