DIELECTRIC SPHERE-SPHERE AND SPHERE-PLANE PROBLEMS IN ELECTROSTATICS

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Abstract
Exact analytical solutions are derived in bispherical coordinates for the fields due to (i) two equal dielectric spheres, and (ii) a single dielectric sphere and a plane, when either system is inclined at an arbitrary angle to a uniform electrostatic field. The dipole moment of each system is evaluated as a function of separation. In the limit of infinite separation the results for single spheres are recovered, and in the conducting-sphere limit agreement is found with existing results.

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