# Finding Potential due to hemispherical charge distribution.

1. Oct 13, 2012

### cat_facts

1. The problem statement, all variables and given/known data
Given that the hemisphere has a uniform charge density σ distributed through its inner surface with radius a. Find the electric potential at the base of the hemisphere and the top of the hemisphere (that point where the radius is the largest).

2. Relevant equations

V = ∫ (kσ / [r-r'])*da (Surface Integral)

3. The attempt at a solution

I tried seperating this hemisphere into rings integrating from of the bottom of the hemisphere to the top, but that isn't working. I was trying to then solve it for all z along z(hat), then plugging in 0 and the height of the hemisphere, but wasn't sure how to proceed.

I tried V = ∫ (kσ / [r-r'])*da = kσ∫ (1/ [r-r'])*da = kσ∫ (1/ [h^2 + a^2])*2pi*radius*dh = 2*pi*kσ∫ (a/ [h^2 + a^2])dh

but know I'm not proceeding correctly. What should I do?

Last edited: Oct 13, 2012