Why does the charge on a conductor accumulate at sharp points? I've read one or two explanations, but I don't follow them, and when I try to think about it I reach the opposite conclusion. Halliday and Resnick has an example where a large conducting sphere and a small conducting sphere are attached by a long wire (which we neglect the effects of). Since the spheres are a long way away if we charge the system both the spheres become positively charged, the larger sphere has more charge (proportional to radius) but a lower electric field at the surface (inversely proportional to radius). To my this implies that having a smaller radius of curvature can cause something to have less charge. Why doesn't it? (Incidentally in Griffiths I found a formula for the charge density of an ellipsoid, but I found it difficult to integrate to find the charge on a part of the ellipsoid with small/large radius of curvature - in this case there is more charge density near points of small radius of curvature, but since they have a smaller area I think it could be like the Halliday and Resnick case where there is less actual charge).