Concentric Spheres and Flux

  • #1

Homework Statement


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.

Homework Equations


Flux=E*da

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.
 

Answers and Replies

  • #2
380
7
The flux should then be Ar^2/eo r being a Aa^2/eo
That's not correct. What is the net charge enclosed by the larger sphere?
 
  • #3
264
26
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)
 

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