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## Homework Statement

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

## Homework Equations

## 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

Outisde r>R

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

Inside... r<R

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.