# Gauss' Law question

1. Jun 4, 2013

1. The problem statement, all variables and given/known data
a spherical shell has an outer radius R and a inner radius R/2 and carries a total charge -q, distributed with uniform charge density. A point charge +q is at the centre of the sphere. Calculate the electric field strength for R/2<r<R

2. Relevant equations

Gauss' Law

3. The attempt at a solution

I figured out the charge density in the shell ρ = $\frac{-6q}{7πR^3}$, so the charge enclosed by a gaussian sphere is q(1-$\frac{8r^3}{7R^3}$)

Then using gauss' law I get E = $\frac{q}{4πε_0r^2}$(1-$\frac{8r^3}{7R^3}$)

But my book says E = $\frac{q}{4πε_0r^2}$$\frac{8}{7}$(1-$\frac{r^3}{R^3}$)

Also does anyone know why the latex things aren't working? I'm new to all this stuff.

Edit: cheers guys

Last edited: Jun 4, 2013
2. Jun 4, 2013

### MisterX

Don't use the BB code tags like inside the LaTeX code. If you want to do superscripts in the LaTex math code, use ^ .

3. Jun 4, 2013

### Staff: Mentor

Could be that you're combining Latex with non-Latex stuff. Stick to pure Latex and it should work.

4. Jun 4, 2013

### Staff: Mentor

Good.

Redo that one.

(FYI: I agree with the book's answer.)

5. Oct 10, 2014

### jilia

how do you get

6. Oct 10, 2014

### Staff: Mentor

What's the definition of charge density?

7. Oct 10, 2014

### jilia

i dont really understand charge density. all i know is that it have 3 charge densities, volume, area, and linear.
i just learned this today and i get ρ = −6q/πR3 not ρ = −6q/7πR3.
can you help me solve this step by step?

8. Oct 10, 2014

### Staff: Mentor

Here we are talking about ρ, which is a volume density.