A Radiated Electromagnetic Pulse

We will solve Equations (1) the same way we have been solving all equations involving derivatives or integrals—by guessing and checking. The rules of the game are as follows. Guess a solution, then apply Equations (1) to your guess in every possible way you can think of. If you cannot find an inconsistency, your guess may be correct.
In order to guess a solution, we want to pick an example that we know as much as possible about and use every insight we can to improve our chances of getting the right answer. Since we are already familiar with the fields associated with a current in a wire, we will focus on that situation. Explicitly, we will consider what happens, what kind of fields we get, when we first turn on a current in a wire. We will see that a structure of magnetic and electric fields travels out from the wire, in what will be an example of a radiated electromagnetic pulse or wave.

..........(1)