Electric Field of a Charged Sphere?

[ronk]

Homework Statement

A sphere of radius R has total charge Q. The volume charge density (C/m^3) within the sphere is ρ = ρ_0 (1 - r/R).

This charge density decreases linearly from ρ_0 at the center to zero at the edge of sphere.

a. Show that ρ_0 = 3Q/πR^3.
b. Show that the electric field inside the sphere points radially outward with magnitude E = (Qr/4πε_0 R^3) (4 - 3 r/R).
c. Find the electric field outside the sphere (r > R).

Homework Equations

Volume of a Sphere: V = 4/3 πR^3.

The Attempt at a Solution

I knew that ρ = Q/V and could make this equal to our given value of ρ to find ρ_0, but I was unable to get rid of the 4 in the denominator to find ρ_0.

 

[Orodruin]

I knew that ρ = Q/V

This is incorrect. The sphere does not have uniform charge. You need to integrate the charge density to relate it to the total charge.