Reply to “Comment on ‘Resistance of a square lamina by the method of images,’ ” by B. E. Pieters [Am. J. Phys. 78 (6), 647–647 (2010)]

I would like to thank B. E. Pieters for his comment.¹ While the purely electrostatic boundary conditions are satisfied by charges whose fields are radial in either two or three dimensions (just vector addition), the correct mapping of the electrostatic problem back to the original current problem requires adopting Eq. (1) in Pieters’ comment for the field in a plane. There, $r$ is the cylindrical radius vector. Using that field, whose divergence vanishes, we have the additional constraint that the current must be independent of the radius of the arc enclosing the contact, which is a somewhat subtle point that I missed in my original paper.²