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Get Full Access to Introduction To Electrodynamics - 4 Edition - Chapter 4 - Problem 38p
Get Full Access to Introduction To Electrodynamics - 4 Edition - Chapter 4 - Problem 38p

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# Prove the following uniqueness theorem: A volume V ISBN: 9780321856562 45

## Solution for problem 38P Chapter 4

Introduction to Electrodynamics | 4th Edition

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Problem 38P

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.]

Step-by-Step Solution:

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.

Step 2 of 5

Step 3 of 5

##### ISBN: 9780321856562

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