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.

► An external electric field is amplified in the region between two conducting spheres.
► Approximate analytical expressions are obtained when the spheres are close together.
► These expressions become more accurate as distance between the spheres gets small.