# Homework Help: Calculate the total charge on a sphere

1. Feb 6, 2012

### nosmas

1. The problem statement, all variables and given/known data
Using integration calculate the total charge on the sphere

Volume charge density at the surface of the sphere p0

p = p0r/R

I started with dq = 4*pi*r^2*dr*(p0r/R)

but i am not sure how to integrate (in terms of what variable I would assume r=0 to r=R) but i am not sure i set up the question right

Last edited: Feb 6, 2012
2. Feb 6, 2012

### SammyS

Staff Emeritus
I presume that you mean ρ = ρ0(r/R) is the volume charge density for a sphere of radius, R, where ρ0 is the volume charge density at the surface of the sphere.

The volume element is dV = 4πr2dr.

So that dq = 4πr2(ρ)dr = 4πr20/R)r dr .

4, π, ρ0, and R are all constants.

Integrate that over the entire sphere. → r goes from 0 to R .

3. Feb 7, 2012

### nosmas

That makes sense so if I was asked to find the E field using gauss's law for r<=R would I just use E=q/(area*epsilon) but how would I know what q enclosed is???

4. Feb 7, 2012

### SammyS

Staff Emeritus
To find the charge enclosed in a sphere of radius, r, integrate from 0 to r .