Solve EM Wave Vacuum Homework: Prove Relation, Find B, Reflect Wave Form

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Homework Help Overview

The discussion revolves around electromagnetic (EM) waves propagating through a vacuum towards a conducting surface. The original poster presents a multi-part problem involving boundary conditions for electric (E) and magnetic (B) fields, the relationship between E and B, and the characteristics of reflected waves at a conducting surface.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • The original poster attempts to establish boundary conditions for E and B fields in the presence of charge and current densities on the surface. They express confusion regarding the assumptions of zero free charge and current for a perfect conductor while the problem suggests otherwise. There is also a mention of deriving the reflected E-field and the challenges faced in doing so.

Discussion Status

The discussion appears to be ongoing, with participants exploring various interpretations of the problem. The original poster has raised specific concerns about their assumptions and the implications for their calculations, indicating a productive inquiry into the topic.

Contextual Notes

There is a noted tension between the assumptions of a perfect conductor (implying no free charge or currents) and the problem's stipulation of existing charge and current densities. This discrepancy may be influencing the original poster's reasoning and calculations.

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Homework Statement


EM Waves propagating through vacuum towards the x-direction approaches a conducting surface at x = 0.

Part (a): Prove the following relations. Find the boundary conditions for E and B if charge density σ and current density s exists on the surface.

Part (b): Find B in terms of E_0

Part (c): Show the reflected wave has the following form:

Part (d) Find magnetic field of reflected wave and s

Homework Equations


The Attempt at a Solution



Part(a)
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Part(b)
migps3.png


Part(c)

This is the part that disturbs me. I assumed the free current s = 0 and σ = 0. Usually k would be perpendicular to the surface, making derivations easier.

I actually got perpendicular reflected E-field = 0, which is wrong..
But, I got parallel reflected E-field = - incoming parallel E-field, which is right

rms6rn.png


I'm confused - If it's a perfect conductor it should have no free charge or currents, but the question says it does. Then again, in order to derive the reflected e-field, we need to assume they are 0.
 
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Edit: Question here
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