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## Main Question or Discussion Point

it states that in a given volume V surrounded by conductors or for that matter infinity if the charge density [tex]\rho[/tex] and the charge on each conductor is fixed then the electric field is uniquely determined in that volume V

Can someone use this find the field in certain situations.

For Example consider this classical situation where in an uncharged conductor has a cavity of arbitrary shape inside it which has a point charge q inside it .The question is to find the net field

Ofcourse the answer is shielding by the metallic sphere ?

Can someone prove this using the uniqueness theorem .I have a proof in mind but i am unsure of it?

Can someone use this find the field in certain situations.

For Example consider this classical situation where in an uncharged conductor has a cavity of arbitrary shape inside it which has a point charge q inside it .The question is to find the net field

**outside**it .Ofcourse the answer is shielding by the metallic sphere ?

Can someone prove this using the uniqueness theorem .I have a proof in mind but i am unsure of it?