Problem on Gauss's Law

1. Oct 13, 2008

Minakami

1. The problem statement, all variables and given/known data
The spherical region a < r < b carries a charge per unit volume of $$\rho$$ = A/r, where A is a constant. At the center (r = 0) of the enclosed cavity is a point charge q. What should be the value of A so that the electric field in the region a< r < b has constant magnitude?

The answer says A = q/(2pi a2)

2. The attempt at a solution
I drew a sphere with radius r as a Gaussian surface.
My work is in the attachment.

I got stuck from that point. I need help :!!)

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2. Oct 13, 2008

borgwal

You go wrong in the second line, the right-hand side: the volume element is NOT $2\pi r dr$, but....

Otherwise, you got the right idea.