What does this boundary condition mean?

[HasuChObe]

One of the boundary conditions for a homogeneous uniform waveguide is $$\frac{\partial H_z}{\partial n}=0$$. 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 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

 

[Meir Achuz]

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.

 

[Aguss]

Thank you so much!