Electrostatics of the conducting double sphere

General solutions to the electrostatic problem of a pair of intersecting, c onducting spheres of arbitrary radii (a double sphere) placed in an arbitra ry potential field are derived. The method is based on Kelvin's transformat ion combined with reflection and translation properties for harmonic functi ons. The basic idea is described in detail for orthogonally intersecting sp heres. A theorem is offered for finding the image system for the two-sphere assembly placed in a given electrostatic potential. From the general formu la, the image systems for various applied potentials are obtained in a stra ightforward fashion. The earlier special solutions for equal-sized spheres are recovered from our results. The fundamental quantities of interest in e lectrostatics such as capacity and polarization (dipole moment) are compute d. The polarizability tensor is found to be diagonal with different compone nts for the directions parallel and perpendicular to the line of centers. T he general solutions to the problem of a pair of spheres, intersecting at a n angle pi/n (n an integer), immersed in an arbitrary imposed potential fie ld are also presented. (C) 1999 American Institute of Physics. [S0021-8979( 99)01918-0].