Gauss Law Problem With A Spherical Conductive Shell

[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?

 

[G01]

Looks fine to me.

 

[Lancelot59]

Thanks for the confirmation.