What does this boundary condition mean?

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The boundary condition \(\frac{\partial H_z}{\partial n}=0\) indicates that the magnetic field component \(H_z\) is constant at the waveguide's boundary, meaning there is no magnetic field leakage. This condition arises from the requirement that the magnetic field normal to the surface must be zero, derived from the equation \(n \cdot B = 0\). The discussion references Jackson's equations, specifically Eq. (8.24) and Eq. (8.30), to clarify the derivation of this boundary condition. The resulting magnetic field distribution in a rectangular waveguide is expressed as \(H_z(x,y) \sim \cos(m\pi x/A)\cos(n\pi y/B)\). Understanding these equations is crucial for analyzing wave propagation in cylindrical and rectangular waveguides.
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One of the boundary conditions for a homogeneous uniform waveguide is \frac{\partial H_z}{\partial n}=0. 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): \partial_n(B_z)=0 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 H_z(x,y)\sim\cos(m\pi x/A)\cos(n\pi y/B)
for an AXB rectangular guide.
 
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Thank you so much!
 
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