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Coulomb's law is applied to point charges because there are "problems" applying it to a charge that has "dimension" to it. A charge is surrounded by an electric field. If we cannot treat it as a point, then the charge has to be "distributed" through the "body" of the charge. It will change the way we have to do the math. If we view charges as non-point sources, then we can't apply the mathematics to the charges in quite the same way as we do when we work things out with point sources. Take a charge that isn't a point source and one that is. If the charge that isn't a point source has "dimension" to it, then the charge on that charge (if that makes sense) is not eminating from a point but from the "body" of the charge as a whole. The electric field will be "distributed" over the volume of the body of the charge, and its effect on a point source will have to be worked out differently than it would if it was point source-to-point source.

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15y ago
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11y ago

Because otherwise, parts of the charge will exert their force at different distances,

or in different directions. Let's just say that calculations are simpler for a point charge.

If the charge is distributed, you have to imagine the charge spread out over many

small "point charges" (that is, each piece is small enough so that, for practical

purposes, it can be considered a point charge), and the individual contributions

must be added. This is called "integration".

None of this means that Coulomb's law is not 'valid' for a distributed charge.

It certainly is, just as surely as Newton's law of universal gravitation is valid for a

distributed mass. Smeared out charge behaves exactly as if all the charge were

concentrated at the "center of charge", in the same way that smeared out mass

behaves exactly as if all the mass were concentrated at the "center of mass".

If the concentrated version and the distributed version are in identical sealed

cartons, you can't tell the difference from the outside.

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Q: Why is Coulomb's law valid only for a point charge?
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