Solving Gauss' Law for Electric Field Around Spherical Shell

[radiator0505]

Homework Statement

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

Homework Equations

Gauss' Law

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

 

[MisterX]

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

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

 

[Doc Al]

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

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

 

[Doc Al]

I figured out the charge density in the shell ρ = \frac{-6q}{7πR^3},

Good.

so the charge enclosed by a gaussian sphere is q(1-\frac{8r^3}{7R^3})

Redo that one.

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

 

[jilia]

how do you get

ρ = −6q7πR3

 

[Doc Al]

how do you get

What's the definition of charge density?

 

[jilia]

What's the definition of charge density?

i don't 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?

 

[Doc Al]

i don't really understand charge density. all i know is that it have 3 charge densities, volume, area, and linear.

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

i just learned this today and i get ρ = −6q/πR3 not ρ = −6q/7πR3.
can you help me solve this step by step?

Why don't you show how you arrived at your answer?