A non-uniformly charged sphere of radius R has a charge density p = p_o(r/R) where p_o is constant and r is the distrance from the center of the spere.
a) find the total charge inside the sphere
b) find the electric field everywhere (inside & outside sphere)
c) find the electric potential difference between teh center of the sphere and a distance r away from the center for both r<R and r>R.
d)Graph the potential as afunction of r
The Attempt at a Solution
a) Find the total charge in sphere.
p = dQ/dV
Q = integral p dV where dV = 4(pi)R^2dR and it is integrated from 0 to R
Q = integral from 0 to R p_o*(r/R)*4*pi*(R^2)*dR = 2*pi*p_o*r*(R^2)
b) Find electric Field inside & out of sphere
Q = 2*pi*p_o*r*(R^2)
[tex]\oint[/tex]EdA = Q_encl / E_o = E(4*pi*(R^2)) = (2*pi*p_o*r*(R^2))/E_o
E = (p_o*r)/2E_o
If the rest is correct, can i get a hint on finding the inside as to the outside. this confuses me. it seems the only difference is r<R, but how would that effect the equation.