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I have a doubt that , suppose we have a spherical conductor (isolated ) and a cavity that is not concentric, and then a charged is placed at the center of the cavity , then what can we say about the distribution of negetive charge on the inner surface of the cavity and how do we calculate the potential of the sphere , will it be independent of the position of the cavity or if not then what? 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 negetively charged innner surface will cancel out  , outside of the conductor , Is there a law or reason behind this?

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?