Variational principles of electrostatics and higher polarizabilities of conductors

Based on variational principles, new concepts of higher polarizability of an isolated conductor are introduced that generalize well-known concepts of capacity and polarizability. It is shown that the lth-order polarizability in a spherical coordinate system is represented by a (2l + 1) × (2l + 1) matrix. The corresponding (2l+1) potentials can be considered as a system of lth-order multipoles typical of a conductor and more general than systems of spherical multipoles known in electrodynamics. It is exemplified what new results can be obtained using the higher polarizability technique for solving problems in electrostatics. © 1999 Kluwer Academic/Plenum Publisher.