Van Siclen (1988 Am. J. Phys. 56 1142) reported a curious property of a dielectric sphere in the field of an external point charge: the field outside the sphere generated by the combination of the original charge exterior and the Kelvin image charge interior to the sphere is independent of the permittivity of the sphere. In this paper, we simplify and correct the original derivation and give a detailed analysis of the sources of the field. We also present various checks for the theory, providing instructive exercises for advanced undergraduates.

Abstract-The Kelvin image theory for a conducting sphere is extended to the case of a conducting oblate spheroid in uniform motion along its axis of revolution (a Heaviside ellipsoid) using the well-known method provided by Special Relativity. The results derived are checked in various ways.

This paper presents a study of two commercial hollow-cathode lamps (HCLs) with the intention of demonstrating different phenomena in gas discharges. The optogalvanic effect in both HCLs is produced by a laser diode radiated at the wavelength that corresponds to neon transition 1s2–2p2 at 659.89 nm. The voltage–current characteristics of the lamps are explained using a classical theory of hollow-cathode discharge, while the optogalvanic signal is treated as a small perturbation of the discharge current. For certain values of voltage self-sustained current oscillations are observed in one of the HCLs. In the same HCL laser-induced optogalvanic dumped oscillations are detected. A phenomenological model that includes the effective circuit parameters of the discharge is used to explain the oscillation characteristics.