# Electromagnetic boundary conditions for symmetric model

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1. Apr 1, 2015

### Alan Kirp

Since the article does not contain any mathematical formulations, I was wondering how the boundary conditions can be expressed in terms of magnetic vector potential.

From what I have gathered, the Perfect Magnetic Conductor boundary condition corresponds to a Zero Neumann boundary condition, where the normal derivative of the magnetic vector potential is set to zero at the boundary:

$${\mathbf{\hat{n}} } \cdot \dfrac{\partial \mathbf{A}}{\partial \mathbf r} = 0$$

From the above, how can one prove that this forces the magnetic flux density vector to cut the boundary at right angle?

Also, I am having trouble figuring out what the Magnetic Insulation boundary condition corresponds to. Is it a Dirichlet boundary condition?

If yes, is it $${\mathbf{\hat{n}} \cdot {\mathbf A}} = 0$$, or just $${\mathbf A} = 0$$

If it is the former, I can see how the magnetic flux density is zero in the normal direction to the boundary and non-zero in the tangential direction.