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arXiv · 1609.04248

On the electrostatic equilibrium of charges and cavities in a conductor

Aritro Pathak
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Abstract

We consider a charged conductor of arbitrary shape, in electrostatic equilibrium, with one or more cavities inside it, and with fixed charges placed outside the conductors and inside the cavities. The field inside a particular cavity is then only due to charges within that cavity itself and to the surface charge induced on the surface of the same cavity. A similar statement holds for the exterior of the conductor. Although this is an elementary property of conductors, it is not a trivial statement, as explained in this article. Undergraduate texts in electrodynamics do not discuss at length or provide a complete argument for an important problem such as this. Two simple and complete proofs are provided in this note with the help of the standard electrostatic uniqueness theorems.

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Aritro Pathak. 2016-09-11. On the electrostatic equilibrium of charges and cavities in a conductor. https://doi.org/10.1088/0143-0807%2F37%2F6%2F065203

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