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

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1. May 23, 2015

### 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?

2. May 23, 2015

### 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 EZ , 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.

3. May 24, 2015

### 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."
But in the additional readings they don't specify any chapter or part of the book to look at.