Radiation Pressure: Proving Magnetic Field Reflection on Perfect Conductor

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Discussion Overview

The discussion revolves around proving that during the reflection of an electromagnetic wave on a perfect conductor, the magnetic field \(\vec{b}\) acting on a surface element \(ds\) is half the total magnetic field \(\vec{B}\). Participants explore the justification for the factor of one half in the expression for the force acting on \(ds\) using Ampère's Law and other potential methods.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant asks how to prove that \(\vec{b} = \frac{1}{2}\vec{B}\) using Ampère's Law, seeking clarification on the derivation of the force expression \(d\vec{f} = \frac{1}{2}\vec{j_{s}} \times \vec{B} \cdot ds\).
  • Another participant suggests there may be alternative justifications for the \(\frac{1}{2}\) factor that do not rely on Ampère's Law, referencing a textbook explanation that they found difficult to understand.
  • A participant describes a scenario involving a sheet of surface current \(K\) with an incident electromagnetic wave, explaining that the total magnetic field outside the surface is twice the field \(B_W\) due to the contributions from both the wave and the current.
  • A later reply confirms understanding of the previous explanation regarding the magnetic field contributions and acknowledges the assistance received.

Areas of Agreement / Disagreement

Participants express differing views on the justification of the \(\frac{1}{2}\) factor, with some seeking clarification on Ampère's Law while others propose alternative methods. The discussion remains unresolved regarding the best approach to prove the claim.

Contextual Notes

Some participants mention difficulties in understanding the justification methods, indicating potential limitations in the clarity of the explanations provided.

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Hi everyone ! This is my first post!

How can we prove that during the reflection of an electromagnetic wave on the surface of a perfect conductor, the magnetic field \vec{b} acting on a surface element ds is worth half the total magnetic field \vec{B} using Ampere's Law. That is \vec{b}=\frac{1}{2}\vec{B}.
This in order to justify the one half factor in the expression of the force acting on ds which is d\vec{f}=\frac{1}{2}\vec{j_{s}}\times \vec{B} \cdot ds, where \vec{j_{s}} is the surface current density on the conductor.
A drawing would be welcome.

Thanks in advance for your answersPS: Why does it automatically go to a new line when i insert a Latex equation?
 
Last edited:
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When you want an equation to appear "in line", use "itex" in the opening and closing tags, not "tex".
 
jtbell said:
When you want an equation to appear "in line", use "itex" in the opening and closing tags, not "tex".

Thank you.
And what about the subject ?
 
There's maybe another way to justify the \frac{1}{2} factor without using Ampère's law ? It's how it was justified in my textbook but I couldn't understand it.
Anyone ?
 
Consider a sheet of surface current K: KKKKKKKKKKKKKKKKKKKKKKKKKK
with the EM wave incident from above. The B field comes from two sources
1) the wave B_W, and 2)the current, B_K. Below the surface (in the metal) B is zero.
That mean the two components of B cancel so B_W=B_K in magnitude and opposite in sign.
Above the surface, B_K changes sign, but B_W doesn't, so the total B field outside is twice the field B_W which acts on the surface current.
 
Meir Achuz said:
Consider a sheet of surface current K: KKKKKKKKKKKKKKKKKKKKKKKKKK
with the EM wave incident from above. The B field comes from two sources
1) the wave B_W, and 2)the current, B_K. Below the surface (in the metal) B is zero.
That mean the two components of B cancel so B_W=B_K in magnitude and opposite in sign.
Above the surface, B_K changes sign, but B_W doesn't, so the total B field outside is twice the field B_W which acts on the surface current.

Yep I figured this out.
Thank you for you answer.
 

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