# More Gauss' Law

1. Feb 2, 2006

### Punchlinegirl

Consider a solid insulating sphere of radius b with nonuniform charge density $$\sigma = ar$$ where a is a constant. Find the charge Q_r contained within the radius r, when r < b. Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to $$4\pi r^2$$.
I got this part, the answer was Q_r = $$\pi ar^4$$.
The second part says if a = 2 x 10^-6 C/m^4 and b= 1 m, find E at r= 0.6 m. Answer in units of N/C.
I used the equation $$E= Qr/4\pi E_0 R^3$$
Plugging in the previous answer for Q gave me $$E= (\pi ar^4)r/ 4\pi E_0 R^3$$
so $$\pi ar^5/4\pi E_0 B^3$$ since R=B in this problem.
then $$\pi (2 x 10^-6)(.6)^5/ 4\pi (8.85 x 10^-12)$$
This gave me 4378 N/C... which is wrong.

2. Feb 2, 2006

### Gamma

$$E= Qr/4\pi E_0 R^3$$

Did you mean Q_r?

3. Feb 2, 2006

### Punchlinegirl

Yes, sorry I meant Q_r * r.