What is the electric field at the center of a hemisphere bounded by r=a, 0<θ<pi/2 / and 0<∅< 2pi with a uniform surface charge density?
(1/4piε0) ∫ p(r') ((r-r')/[r-r']^3) dr'
The Attempt at a Solution
Forgive my formatting
ds= (r^2)sinθdθd∅ (In direction of r)
p(r')=constant = σ
r=r (in the direction of r)
r'= 0 (I have trouble with understanding r and r')
E= (σ/4piε0) ∫(0 to 2pi) ∫(0 to /2pi) (r^3)sinθdθd∅ / (r^3)
E= (σ/4piε0) (2pi)(1)
Everywhere I look I see the answer to this problem is (σ/4ε0) and I cannot figure out where I am going wrong. I feel as though I am missing to include something in my equation but I am stumped, help would be appreciated.