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Physics / Introduction to Electrodynamics 4 / Chapter 4 / Problem 38P

Introduction to Electrodynamics | 4th Edition | ISBN: 9780321856562 | Authors: David J. Griffiths

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Prove the following uniqueness theorem: A volume V

Chapter 4, Problem 38P

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QUESTION:

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.]

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QUESTION:

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.]

ANSWER:

Solution 38P:

Step 1 of 5:-

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

The volume $v$ 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.

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