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?

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: