Near approach of two conducting spheres: Enhancement of external electric field

An external electric field applied to two uncharged conducting spheres in close approach is amplified (by charge separation on the spheres) in the region between the spheres. This enhancement increases without limit as the separation between the spheres decreases. We calculate the enhancement factor analytically, for spheres of radii a and b. A compact formula is given for the case where the separation s between the spheres is small compared to both a and b.