# Charge at a distance from a non-conducting hemisphere

1. Apr 24, 2013

1. The problem statement, all variables and given/known data
A non-conducting hemisphere of radius R centered at the origin has a total charge Q spread uniformly over its surface. The hemisphere is oriented such that its base is in the (y,z) plane. Find the electric field anywhere along the x axis for x > 0. Give explicitly the value of the electric field at x = 0.
Here is an image of the problem as it was given to me:
http://i.imgur.com/GZ5Edcc.jpg

2. Relevant equations
ERing = (1/4∏ε0)*Qx/(x2+R2)3/2
Q = 2ρ∏r2

3. The attempt at a solution
I attempted to sub-divide the hemisphere in to separate rings and integrate the sum, but the integral I ended up with was pretty ugly and I'm not even sure it's correct. I added a variable r, representing the radius of each individual ring and integrated with respect to it.
My integral:
(R2ρ/2∏ε0)*∫(x+(R-r))dr/((x+(R-r))2+r2)3/2
From 0 → R
I could probably solve this integral given enough time, but I'm pretty sure I will be expected to do this on a test and was hoping there was a less complicated solution.

Thank you

2. Apr 24, 2013