Charged line segments and ellipsoidal equipotentials
Abstract
This is a survey of the electrostatic potentials produced by charged straight-line segments, in various numbers of spatial dimensions, with comparisons between uniformly charged segments and those having non-uniform linear charge distributions that give rise to ellipsoidal equipotentials surrounding the segments. A uniform linear distribution of charge is compatible with ellipsoidal equipotentials only for three dimensions. In higher dimensions, the linear charge density giving rise to ellipsoidal equipotentials is counter-intuitive --- the charge distribution has a maximum at the center of the segment and vanishes at the ends of the segment. Only in two dimensions is the continuous charge distribution intuitive --- for that one case of ellipsoidal equipotentials, the charge is peaked at the ends of the segment and minimized at the center.
Keywords
Cite
@article{arxiv.1601.04047,
title = {Charged line segments and ellipsoidal equipotentials},
author = {T L Curtright and N M Aden and X Chen and M J Haddad and S Karayev and D B Khadka and J Li},
journal= {arXiv preprint arXiv:1601.04047},
year = {2016}
}