# Gauss's Law and a conducting sphere

1. Mar 23, 2005

### Alem2000

"A solid conducting sphere with radius $$R$$ carries a posative total charge $$Q$$. The sphere is surrounded by an insulating shell with inner radius $$R$$ and outer radius $$2R$$. The insulating shell has a uniform charge density $$\rho$$ a) find the value of $$\rho$$ so that the net charge of the entire system is zero b) if $$\rho$$ has the value found in part (a), fnd the electric field (magnitude and direction) in each of the regions
$$0<r<R$$ $$R<r<2R$$ and $$r>2R$$"

Calculating charge in terms of $$\rho$$ i got
$$\sum Q=\frac{-28\pi\rho R^3}{3}$$

now my problem is trying to fine the $$\vec{E}$$ below is my work
$$\oint\vec{E}d\vec{A}=\frac{Q_inc}{\epsilon_0}$$
there is an electric field only between
$$R<r<2R$$
$$\vec{E}=\frac{Q}{4\pi R^2 \epsilon_0}$$
and after solving my above value for
$$\rho$$ in terms of $$Q$$
I got

$$\vec{E}=\frac{7R\rho}{3}$$

which is soo wrong, im sure I did some of this problem correctly..the part I dont understand is how I would find the electric field? Can anyone please help?

Last edited: Mar 23, 2005
2. Mar 23, 2005

### Dr Transport

You had the charge density in the shell correct but forgot that

$$Q_{inc} = Q - 4\pi \int_{R} ^{R'} \rho r^{2} dr$$

not just the charge of the spherical shell.....