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## Homework Statement

A uniformly charged ball of radius a and a total charge -Q is at the center of a hollow metal shell with inner radius b and outer radius c. The hollow sphere has a net charge +2Q. Find the magnitude of the electric field in the regions: [tex]r_1 < a[/tex],[tex] a < r_2 < b[/tex],[tex] b < r_3 < c[/tex], and [tex]r_4 > c.[/tex]

## Homework Equations

[tex]V = \frac{4}{3} \pi R^3[/tex]

[tex]S = 4 \pi R^2[/tex]

[tex]\oint E(x)dA = \frac{q_{in}}{\epsilon_o}[/tex]

## The Attempt at a Solution

For E(r1 < a):

[tex]\rho = \frac{Q_{tot}}{\epsilon_o}[/tex]

[tex]Q_{in,tot} = \rho*\frac{4}{3} \pi r_1^3[/tex]

[tex]\oint_0^rE(x)dA = \frac{q_{in}}{\epsilon_o}[/tex]

[tex]E(r_1) = \frac{\rho\frac{4}{3} \pi r_1^3}{\epsilon*4 \pi r_1^2}[/tex]

[tex]E(r_1) = \frac{\rho*r_1}{3\epsilon_o}[/tex]

This is actually where I am stuck, I got everything else. Am I supposed to get rid of that volume charge density, [tex]\rho[/tex]?

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