What is this version of the wave equation?

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Discussion Overview

The discussion revolves around a specific expression of the wave equation, particularly in the context of electromagnetic waves in a conducting medium. Participants explore the implications of the equation and its components, including the refractive index and conductivity.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant presents a version of the wave equation and inquires about the medium it describes.
  • Another participant asserts that the equation pertains to electromagnetic waves in a conducting medium and notes a potential error in the expression regarding the second derivative of the electric field.
  • A further inquiry is made about the origin of the refractive index in this context.
  • Another participant confirms that the medium has both a refractive index and a conductivity.

Areas of Agreement / Disagreement

There is some agreement on the nature of the wave equation relating to electromagnetic waves in a conducting medium, but there is disagreement regarding the correctness of the expression provided and the specifics of the refractive index.

Contextual Notes

The discussion includes potential errors in the mathematical expression and assumptions about the definitions of the terms involved, which remain unresolved.

girlinphysics
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I came across this expression for the wave equation:

\nabla^2E + \mu\sigma\frac{\partial{E}}{\partial{t}} - \frac{n^2}{c^2}\frac{\partial{E}}{\partial{t^2}} = 0

My question is what kind of medium is it for/where did it come from?
 
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That is the equation of an electromagnetic wave passing through a conducting medium. You wrote the last term wrong. It should be the second derivative of the electric field. You will see it in any book on classical electrodynamics.
 
Chandra Prayaga said:
That is the equation of an electromagnetic wave passing through a conducting medium. You wrote the last term wrong. It should be the second derivative of the electric field. You will see it in any book on classical electrodynamics.
Where does the refractive index come from?
 
The medium has a refractive index and a conductivity.
 

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