# Concentric Spheres and Flux

1. Oct 1, 2015

### SarahAlbert

1. The problem statement, all variables and given/known data
A sphere of radius a has its center at the origin and a charge density given by p=Ar^2 where A=constant. Another sphere of radius 2a is concentric with the first. Find the flux through the larger sphere.

2. Relevant equations
Flux=E*da

3. The attempt at a solution
According to my textbook, flux is independent of the radius. It depends on the charge enclosed by the sphere. So regardless, the flux is the same for both. We know flux is determined by the field magnitude and area. The area is 4piR^2 and the field magnitude is given by (1/4pi(eo))(q/R^2)
Multiplying the two gives us that flux is the charge divided by eo.
The flux should then be Ar^2/eo r being a Aa^2/eo

I feel like I'm missing an important concept.

2. Oct 1, 2015

### lep11

That's not correct. What is the net charge enclosed by the larger sphere?

3. Oct 1, 2015

### J Hann

You need to find the total charge on the inner sphere (integrating the the charge density).
Then this also the charge enclosed by the outer sphere and Gauss' Law will immediately
give you the total flux.(you don't need to use the electric field E)