What does this boundary condition mean?

HasuChObe

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?

Meir Achuz

I tried to put it into words, but the equation is clearer.
d/dn means the derivative in the direction perpendicular to the wall.

Aguss

Hello!! I have a question related to this. This boundary condition yield from n.B = 0 , but i dont know how, from considering a cylindrical waveguide. I know that there is an equation (first of 8.24 from Jackson) but i dont realice how to use it. If u know, please let me know. Thankss

Meir Achuz

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.

Aguss

Thank you so much!