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We consider the enhancement of electric field in the presence of twoperfectly conducting spheres. When the two spheres get closer, the electricfield have a much larger magnitude compared to the external field in the smallgap region between the two spheres. The enhanced field can be arbitrary largewith the generic blow-up rate $|\epsilon\ln\epsilon|^{-1}$ in three dimensionalspace, where $\epsilon$ is the distance between the spheres. In this paper wederive rigorously an asymptotic formula of the electric field consisting ofelementary functions. The asymptotic formula explicitly characterizessuperfocusing of the electric field in terms of the spheres radii, the distancebetween the spheres, and the external field. We illustrate our results withnumerical calculations.

Asymptotic analysis for superfocusing of the electric field in between two nearly touching metallic spheres