Gauss Law Problem With A Spherical Conductive Shell

1. Oct 2, 2011

Lancelot59

You are a hollow metallic sphere of inner radius r1, and outer radius r2. Inside is a charge of magnitude Q and a distance d<r1 from the centre.

First I need to draw the electric field lines for regions r<r1, r1<r<r2, and r2<r

Since the sphere is a conductor the only place where there is not an electric field is inside the shell. The point charge induces a charge on the conducting sphere, making it in turn create an electric field outside the sphere.

I then need to use Gauss's law to find the electric field where possible. I think this is correct:

$$\int \vec{E}\cdot d\vec{A}=\frac{Q_{enclosed}}{\epsilon_{0}}$$
$$E\int d\vec{A}=\frac{Q}{\epsilon_{0}}$$
$$E(4\pi r^{2})=\frac{Q}{\epsilon_{0}}$$
$$E=\frac{Q}{4\pi r^{2}\epsilon_{0}}$$

For all locations that are not inside the shell. Am I correct?

Last edited: Oct 2, 2011
2. Oct 2, 2011

G01

Looks fine to me.

3. Oct 2, 2011

Lancelot59

Thanks for the confirmation.