# Charged Cavity in conductor

Problem:

Suppose we have an isolated spherical conductor and a cavity that is not concentric. Then, a charge is placed at the center of the cavity.

• What can we say about the distribution of negative charge on the inner surface of the cavity?

• How do we calculate the potential of the sphere?

• Will the potential of the sphere be independent of the position of the cavity?

Pardon my naivety, but I was taught that the field pattern outside the conductor will be independent of the the field inside the cavity and the potential of the charge as well as the negatively charged inner surface will cancel out, outside of the conductor. Is there a law or reason behind this?

If $+q$ charge is placed at the cavity center, an equal and opposite charge $-q$ is induced on the inner surface of cavity.
If $+q$ charge is at center then negative charge distribution will be symmetric else the density of negative charge will be more in the side closer to the $+q$ charge.