Interpreting ##\hat{e}_z## in Maxwell's equations

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Homework Help Overview

The discussion revolves around interpreting a specific form of Maxwell's equations, particularly focusing on the term $\hat{e}_z$ within the context of electromagnetic wave propagation.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to understand the origin of the term $\hat{e}_z$ in the equation and are questioning the assumptions related to plane wave field dependence. There is also a request for clarification regarding the notation used in the equation.

Discussion Status

Some participants have provided insights regarding the interpretation of the equation, suggesting that it relates to the curl of the magnetic field in the context of plane waves. However, there is a noted concern about the correctness of the equation, indicating that the discussion is ongoing and exploring various interpretations.

Contextual Notes

There is a mention of needing more background on the source of the equation, which suggests that certain information may be missing or unclear in the current context.

flintbox
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Hi, I'm trying to interpret a form of Maxwell's equations, but I can't seem to figure out where the term $\^{e}_z$ comes from in the following equation:
##
\frac{\partial{\vec{E}_t}}{\partial{z}}+i\frac{\omega}{c}\hat{e}_z\times \vec{B}_t=\vec{\nabla}_tE_z
##
 
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This is a guess because more background on the source of this equation is needed. My guess is that the problem being worked is assuming a plane wave field dependence?
 
Will you please clarify the notations? What does ##t## stand for?
 
flintbox said:
Hi, I'm trying to interpret a form of Maxwell's equations, but I can't seem to figure out where the term $\^{e}_z$ comes from in the following equation:
##
\frac{\partial{\vec{E}_t}}{\partial{z}}+i\frac{\omega}{c}\hat{e}_z\times \vec{B}_t=\vec{\nabla}_tE_z
##
It comes from taking the curl of the B field (here they are assuming a plane wave). But the equation is not completely correct, the term on the rhs does not make any sense.
 

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