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Two large conducting sphere carrying charges `Q_(1)` and `Q_(2)` are brought close to each other. Is the magnitude of the electrostatic force between them exactly given by `Q_(1) Q_(2) //4pi in_(0) r^(2)`, where r is the distance between their centres ?

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No, because Coulomb's law is applicable only for point charges. For large conductors, if the distance between the conductors becomes very large, then only their size may be neglected. Further the charges reside only on the surface of the conductor, so the charge distribution is not uniform.
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