(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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]

2. Relevant 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]

3. 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]?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Gauss's law problem

**Physics Forums | Science Articles, Homework Help, Discussion**