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So I was told that any kind of $3$ space Cartesian coordinate volume question can be solved using rectangular coordinate, cylindrical coordinate and spherical coordinate. Here is the thing, by using one of the coordinate systems you can solve the question easily compare to the other coordinate system. My question is only about cylindrical coordinate and spherical coordinate, what kind of geometry or how do we know which coordinate system we should use to easily solve a geometry problem.

Thanks.

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Basically it makes things easier if your coordinates look like the problem. If you have a problem with spherical symmetry, like the gravity of a planet or a hydrogen atom, spherical coordinates can be helpful. If you have a problem with cylindrical symmetry, like the magnetic field of a wire, use those coordinates. There are many other systems possible. It is not required that the axes be orthogonal, though you get some new terms in your equations. If you are studying certain crystals, you might want to align your axes with the crystal axes, even if they are not orthogonal.

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  • $\begingroup$ thanks for the explanation. $\endgroup$
    – Yuvin Ng
    Apr 16, 2013 at 0:13

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