Problem 5P

Prove that the field is uniquely determined when the charge density ρ is given and either V or the normal derivative ∂V/∂n is specified on each boundary surface. Do not assume the boundaries are conductors, or that V is constant over any given surface.

Step 1 of 3

The unique determination of an electric field can be done from the second uniqueness theorem. We are required to know the total charge of each conductor if a given volume is surrounded by several conductors.