Practice question · Multiple choice
Spherical coordinates carry a volume element of while Cartesian coordinates carry none. Why does the factor vary with position?
Hints
- Compare the patch swept by one degree of longitude at the equator and near a pole.
- Ask whether a Cartesian grid cell changes size anywhere.
Show the answer
A. Because the coordinate grid stretches away from the origin
Why
A Cartesian grid is uniform and a spherical one is not. The Jacobian records how much real volume each coordinate cell occupies, which is why it is needed at all.
Practise Polar, Cylindrical, and Spherical Coordinates
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