- #1
Avatrin
- 245
- 6
Homework Statement
Find the E produced by a spherical charge distribution with uniform charge density at a point inside the sphere, using triple integration.
Homework Equations
E = 1/4πε ∫f(x,y,z)/r^2 dV
The Attempt at a Solution
f(x,y,z) = p
Radius of sphere = R
Position of point = d = (a,b,c)
E = p/4πε ∫∫∫1/r^2 dxdydz
I tried several things. Among them:
I change to spherical coordinates.
0≤θ≤pi
0≤φ≤2pi
r ≤ R
E = 1/4πε ∫∫∫p/r^2 *r^2sinθdrdθdφ = p/4πε ∫∫∫sinθdrdθdφ = pR/ε
I tried setting (r-d)^2≤R^2, but didn't get anywhere.
Anyhow... The answer I get is not pr/3ε (I don't even know if the r in this answer is supposed to be the radius of the sphere or the distance from origin to what I called d)