What does this boundary condition mean?

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Discussion Overview

The discussion revolves around the physical interpretation of a specific boundary condition for a homogeneous uniform waveguide, specifically the condition \(\frac{\partial H_z}{\partial n}=0\). Participants explore its implications and derivations, particularly in the context of cylindrical and rectangular waveguides.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant asks about the physical meaning of the boundary condition \(\frac{\partial H_z}{\partial n}=0\) for waveguides.
  • Another participant clarifies that \(d/dn\) refers to the derivative in the direction perpendicular to the wall.
  • A different participant connects the boundary condition to the equation \(n \cdot B = 0\) but expresses uncertainty about its derivation from a cylindrical waveguide perspective.
  • A later reply corrects the reference to the equation, suggesting it is Eq. (8.30) and explains how it follows from Eq. (8.24) by applying the dot product with \(n\), leading to the boundary condition on \(B_z\) and a proposed form for \(H_z\) in a rectangular guide.

Areas of Agreement / Disagreement

Participants express differing levels of understanding regarding the derivation and implications of the boundary condition, indicating that the discussion remains unresolved with multiple viewpoints presented.

Contextual Notes

Some assumptions about the definitions and context of the equations referenced may be missing, and the discussion does not fully resolve the mathematical steps involved in deriving the boundary condition.

HasuChObe
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One of the boundary conditions for a homogeneous uniform waveguide is [tex]\frac{\partial H_z}{\partial n}=0[/tex]. What does this mean physically?
 
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I tried to put it into words, but the equation is clearer.
d/dn means the derivative in the direction perpendicular to the wall.
 
Hello! I have a question related to this. This boundary condition yield from n.B = 0 , but i don't know how, from considering a cylindrical waveguide. I know that there is an equation (first of 8.24 from Jackson) but i don't realice how to use it. If u know, please let me know. Thankss
 
You must mean Eq. (8.30): [tex]\partial_n(B_z)=0[/tex] at the surface.
It follows from (8.24) by dotting it with n. The two terms on the LHS are zero, giving the BC on B_z. Then, it follows That [tex]H_z(x,y)\sim\cos(m\pi x/A)\cos(n\pi y/B)[/tex]
for an AXB rectangular guide.
 
Last edited:
Thank you so much!
 

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