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arXiv · 1601.04047

Charged line segments and ellipsoidal equipotentials

T L Curtright·N M Aden·X Chen·M J Haddad·S Karayev·D B Khadka·J Li
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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.

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T L Curtright, N M Aden, X Chen, M J Haddad, S Karayev, D B Khadka, J Li. 2016-01-15. Charged line segments and ellipsoidal equipotentials. https://doi.org/10.1088/0143-0807/37/3/035201

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