What does this boundary condition mean?

In summary, the boundary condition \frac{\partial H_z}{\partial n}=0 for a homogeneous uniform waveguide means that the derivative of the H_z component in the direction perpendicular to the wall is equal to zero. This condition is derived from Eq. (8.30) by dotting it with n and results in the equation H_z(x,y)\sim\cos(m\pi x/A)\cos(n\pi y/B) for an AxB rectangular guide.
  • #1
HasuChObe
31
0
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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  • #2
I tried to put it into words, but the equation is clearer.
d/dn means the derivative in the direction perpendicular to the wall.
 
  • #3
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
 
  • #4
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.
 
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  • #5
Thank you so much!
 

FAQ: What does this boundary condition mean?

What is a boundary condition?

A boundary condition is a set of rules or constraints that are applied to a mathematical, physical, or computational model to define the behavior of the system at the boundaries or edges of the model.

Why are boundary conditions important?

Boundary conditions are important because they allow us to accurately model and predict the behavior of a system. They provide information about how the system behaves at its boundaries, which can significantly affect the overall behavior of the system.

How do boundary conditions affect the accuracy of a model?

Boundary conditions play a critical role in determining the accuracy of a model. If the boundary conditions are incorrect or not well-defined, the model's predictions may be inaccurate. Therefore, it is essential to carefully consider and accurately define the boundary conditions in a model.

What are some common types of boundary conditions?

Some common types of boundary conditions include Dirichlet boundary conditions, which specify the value of a variable at a boundary, and Neumann boundary conditions, which specify the derivative of a variable at a boundary. Other types include periodic, symmetric, and anti-symmetric boundary conditions.

Can boundary conditions change during a simulation?

In most cases, boundary conditions are fixed and do not change during a simulation. However, there are some situations where boundary conditions may be time-dependent, such as in a dynamic system with changing boundaries. In these cases, the boundary conditions would need to be updated accordingly during the simulation.

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