Comment on "Point charge in a three-dielectric medium with planar interfaces"

Abstract

In a recent paper that appeared in this journal,1 there is a serious error. The statement is made that since the voltage is maintained by the battery, the electric field is constant everywhere. Rather, it is the path integral of the electric field between the plates via any path that is constant. The two statements are equivalent in the usual approximation in which the fringing of the electric field is neglected. However, when the fringing field is explicitly included, as was the case in Ref. 1, then there are discontinuities in the electric field on all surfaces of the dielectric. Because the calculation specifically uses the electric field present before the dielectric is inserted, the calculation is not correct. At best it is a more accurate approximation than the one in which the fringing field is neglected.