The question of the equilibrium linear charge density on a charged straight conducting “wire” of finite length as its cross-sectional dimension becomes vanishingly small relative to the length is revisited in our didactic presentation. We first consider the wire as the limit of a prolate spheroidal conductor with semi-minor axis a and semi-major axis c when a/c >1 the linear charge density becomes essentially uniform, but that the tiny nonuniformity (of order 1/Λ) is sufficient to produce a tangential electric field (of order Λ0) that cancels the zeroth-order field that naively seems to belie equilibrium. We specialize to a right circular cylind...

Charge density on thin straight wire, revisited

The electrostatic charge distribution on a conducting cylindrical wire exactly satisfies an integral equation Many textbooks discuss an approximate form of this equation and solve it using the method of moments (MoM) This approximate electrostatics equation admits MoM solutions that are unphysical, and we will explain why such solutions occur and propose several remedies We include a rigorous theorem pertinent to the solvability of the equation Our approach has parallels in recent works on Hall&#x000E9;n's and Pocklington's equations (HE/PE), in particular, because we use the wire of infinite length as a means of deducing information about the actual (finite-length) wire Our analysis of the infinite wire has particular difficulties that are not present in the works on HE/PE

P. Wang

Papers

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