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**A solid sphere of radius [tex]R[/tex] has a non-uniform volume charge density [tex]\rho(r)[/tex] and a constant surface charge density [tex]\sigma[/tex]. If the field inside the sphere is uniform and radially atuned, and the field a distance [tex]2R[/tex] away from the center is zero, find [tex]\rho[/tex] and [tex]\sigma[/tex] in terms of [tex]R[/tex], [tex]r[/tex] (distance from the center of the sphere), and [tex]Q_\text{volume}[/tex] (the charge associated with [tex]\rho[/tex], but not with [tex]\sigma[/tex]).**

## Homework Equations

Gauss's Law

## The Attempt at a Solution

I'm not sure how to proceed, but I think the solution should begin by find the total charge on the sphere (ie., adding the integral of the charge calculable from the surface charge density with the integral of the charge calculable from the volume charge density). Am I on the right track?