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Which of the potentials in Ex. 10.1, Prob. 10.3, and Prob.

Introduction to Electrodynamics | 4th Edition | ISBN: 9780321856562 | Authors: David J. Griffiths ISBN: 9780321856562 45

Solution for problem 5P Chapter 10

Introduction to Electrodynamics | 4th Edition

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

Introduction to Electrodynamics | 4th Edition

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Problem 5P

Problem 5P

Which of the potentials in Ex. 10.1, Prob. 10.3, and Prob. 10.4 are in the Coulomb gauge? Which are in the Lorenz gauge? (Notice that these gauges are not mutually exclusive.)

Reference prob.10.3

(a) Find the fields, and the charge and current distributions, corresponding to

(b) Use the gauge function  to transform the potentials, and comment on the result.

Reference prob.10.4

Suppose V = 0 andwhere A0, ω, and k are constants. Find E and B, and check that they satisfy Maxwell’s equations in vacuum. What condition must you impose on ω and k?

Step-by-Step Solution:

Solution 5P:

Step 1 of 4:-

Here we need to show that, which of the potentials in example 10.1, problem 10.3 and problem 10.4 are in Coulomb gauge and which are in Lorentz gauge.

The condition for Coulomb gauge is:

And the condition for Lorentz gauge is:

Step 2 of 4

Chapter 10, Problem 5P is Solved
Step 3 of 4

Textbook: Introduction to Electrodynamics
Edition: 4
Author: David J. Griffiths
ISBN: 9780321856562

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Which of the potentials in Ex. 10.1, Prob. 10.3, and Prob.