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Why do we use cylindrical coordinates for infinite line charge? And why can't we use rectangular or spherical coordinates?

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2 Answers 2

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You very well can. But the coordinates are used with the required symmetries in mind. In a line charge, the system is cylindrically symmetric about the axis of the line. This makes the vector equations to solve for the fields way easier.

Plus, you can also invoke physical arguments to determine the direction of the fields. If you still have any doubt, just covert your solutions in terms of cylindrical coordinates to spherical coordinates. You will understand the solutions and the complexity that is involved in it.

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We use cylindrical coordinates because they're convenient and because they allow us to solve the problem cleanly and effectively. You could attempt to use rectangular or spherical coordinates to formulate the problem (which will be doable enough) and to attempt to solve it (which will be much harder), but generally speaking, if your problem has a definite symmetry, there's very rarely anything to be gained by studying it in a coordinate system that's not well adjusted to it.

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