Consider a nonconducting hemisphere of inner radius R, that has a uniform charge distribution of magnitude Q on its interior surface. Find the magnitude of the electric field at C (the centre of curvature of the hemisphere).
we haven't learned GauB's law yet. That is the next chapter.
What i have so far:
Centre of curvature: isn't a circle a special case of ellipse where the distance between the two foci is zero? so C = R?
as far as what to do, i have nothing. first i was going to consider a spherical shell distribution then devide by 2, but E in the centre of a sphere is 0. because this is a PROBLEM and not an EXCERCISE, i'm guessing it should be alot harder than this. the best i could come up with was to consider a bunch of stacked rings a distance d from C, where r increases as d -> 0, and then sum the field strengths at d. now i'm a victim of mathematical ineptitude. i know that this is done as an integral, but i don't know how. and if the integral turns out to be zero, i'm going to be choked.