Characterization of the electric field concentration between two adjacent spherical perfect conductors

TL;DR

This paper derives an asymptotic formula describing how the electric field concentrates and becomes singular between two closely spaced spherical perfect conductors in three dimensions.

Contribution

It provides a precise asymptotic characterization of electric field concentration between identical spherical conductors as their separation approaches zero.

Findings

Asymptotic formula for electric field concentration derived

Singular behavior characterized for spherical inclusions in 3D

Field intensity becomes arbitrarily large as distance shrinks

Abstract

When two perfectly conducting inclusions are located closely to each other, the electric field concentrates in a narrow region in between two inclusions, and becomes arbitrarily large as the distance between two inclusions tends to zero. The purpose of this paper is to derive an asymptotic formula of the concentration which completely characterizes the singular behavior of the electric field, when inclusions are balls of the same radii in three dimensions.