Problem 38P

Prove the following uniqueness theorem: A volume V contains a specified free charge distribution, and various pieces of linear dielectric material, with the susceptibility of each one given. If the potential is specified on the boundaries S of V (V = 0 at infinity would be suitable) then the potential throughout V is uniquely determined. [Hint: Integrate ∇ · (V3D3) over V.]

Solution 38P:

Step 1 of 5:-

Here we need to prove the uniqueness theorem for the given system.

The volume contains a specified free charge distribution and various pieces of linear dielectric materials, with the susceptibility of each one given.

The potential is given at the boundaries.