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This is a survey of the electrostatic potentials produced by chargedstraight-line segments, in various numbers of spatial dimensions, withcomparisons between uniformly charged segments and those having non-uniformlinear charge distributions that give rise to ellipsoidal equipotentialssurrounding the segments. A uniform linear distribution of charge is compatiblewith ellipsoidal equipotentials only for three dimensions. In higherdimensions, the linear charge density giving rise to ellipsoidal equipotentialsis counter-intuitive --- the charge distribution has a maximum at the center ofthe segment and vanishes at the ends of the segment. Only in two dimensions isthe continuous charge distribution intuitive --- for that one case ofellipsoidal equipotentials, the charge is peaked at the ends of the segment andminimized at the center.

Charged line segments and ellipsoidal equipotentials