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

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To determine the other components of the electric (E) and magnetic (B) fields in a resonant cavity when given the z component of the electric field (Ez) and with Bz set to zero, one can reference Maxwell's equations. The discussion highlights that as the electric field changes, it induces loops of the magnetic field around it, consistent with the principles of electromagnetic theory. The fundamental frequency scenario is illustrated using a soup can cavity model, where the top and bottom act as capacitor plates. The excerpt from a textbook suggests that once a solution for Ez is found, the remaining components of E and B can be determined. For detailed guidance, the textbook "Electrodynamics" by J. D. Jackson is recommended, though it lacks specific chapter references.
carlosbgois
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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?
 
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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.
 
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.
 
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