Given Ez, with Bz = 0, how to find other components?

[carlosbgois]

Hey there, I have a quick question, and it can be answered with a reference to a book chapter of article.

If I'm given the z component of the electric field inside a resonant cavity, and furthermore, if it's set that Bz = 0, how do I determine the other components for both E and B?

 

[stedwards]

I don't know if you can. Picture loops of B field about the Z axis in a conductive box. As the B field builds and collapses there is an electric field E_Z , through each B field loop.

In the simplest case (the fundamental frequency), you have a soup can cavity with only one B field loop. You can think of the top and bottom of the cavity as the plates of a capacitor delivering charge, alternately over time, to top or bottom. The sides of the can (chicken noodle soup concentrate) are the vertical conductors. As the Z-electric field changes there must necessarily be loops of B field circling the changing electric field. One of maxwell's equations.

 

[carlosbgois]

Thank you for your answer. I was wondering this because of the following excerpt, from a textbook example on solving Helmholtz equation for a cylindrical cavity:

"Once a solution (with Bz = 0) has been found for Ez , then the remaining components of B and E have definite values. For further details, see J. D. Jackson, Electrodynamics in Additional Readings."
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But in the additional readings they don't specify any chapter or part of the book to look at.