Open AccessThe electrostatic problem of a conducting sphere in a spherical cavity
Author(s) -
Alexander Russell
Publication year - 1918
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1918.0007
Subject(s) - spheres , conductor , connection (principal bundle) , physics , classical mechanics , spherical geometry , electrical conductor , theoretical physics , mathematics , geometry , quantum mechanics , astronomy
The mathematical problems which arise in connection with spherical electrodes have often been discussed. Arésumé of them is given in Chap. VIII, Vol. I, of the second edition of the author’s treatise on ‘Alternating Current Theory.’ The problem, however, of a sphere in a spherical cavity has barely been considered. Sir W. Thomson (Lord Kelvin) gives numerical results which he says were calculated for application to the theory of conducting spheres “in the interior of a hollow insulated and electrified conductor.” As a matter of fact, however, the numerical results given apply only to two equal conducting spheres external to one another. Solutions for the capacity between two spheres have been given for the case when the centre of the sphere is close to the centre of the cavity. These solutions are either incorrect, or approximately correct only in special cases. It will be useful, therefore, to show how the complete numerical solution can be readily found in all cases.