Hey. I am trying to solve the following problem: Given a spherical shell with radius a and charge density sigma. If a very small patch of this surface were removed, leaving a small hole, what is the electric field just above and just below this hole? For the electric field below the hole, I think the answer is zero, by gauss' law. Since the charge enclosed would be zero (same as if the hole were not present). However, I'm not sure how I would go about solving for the electric field above the hole. I initially thought that I could simply calculate what the field would be if the hole was not there, and then take this result and subtract the electric field of a small disk of radius a (that would represent the hole) but I don't seem to get the right answer. And help would be appreciated! Thanks!