Document Type

Journal Article

Role

Author

Published In

Journal of Mathematical Physics

Volume

55

Issue

12

Publication Date

2014

Abstract

While there is no general relationship between the electric charge density on a conductingsurface and its curvature, the two quantities can be functionally related in special circumstances. This paper presents a complete classification of two-dimensional conductors for which charge density is a function of boundary curvature. Whenever the curvature function is non-injective, the conductor must transform under one of the planar symmetry groups. In particular, for the charge density on a closed conductor with smooth boundary to be a function of its curvature, the conductor must possess dihedral symmetry with a mirror line running through each curvature extremum. Several examples are presented along with explicit charge-curvature functions. Both increasing and decreasing functions were found.

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