Question

Field Sources:

Consider the following electric field (where ? and ? are constants):

?(?, ?) = ? cos[? (? − ??)] ̂?

(a) What is the charge density ?(?, ?) associated with this E-field? By unit analysis, what must be the units of the parameters ? and ??

(b) Given this electric field, come up with the simplest possible magnetic field ?(?, ?) that satisfies Faraday’s law. (What is the required magnitude of the B-field?)

(c) Show that the remaining Maxwell equations in vacuum are satisfied if you make a specific choice for the parameter ?. What is that choice? (Assume that there is no current causing the magnetic field.)

Answer 1