Electromagnetic boundary conditions for symmetric model

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The discussion revolves around electromagnetic boundary conditions, particularly in relation to magnetic vector potential. The Perfect Magnetic Conductor boundary condition is identified as a Zero Neumann boundary condition, indicating that the normal derivative of the magnetic vector potential is zero at the boundary. This condition implies that the magnetic flux density vector intersects the boundary at a right angle. The inquiry also seeks clarification on the Magnetic Insulation boundary condition, questioning whether it corresponds to a Dirichlet boundary condition and whether it is defined as the magnetic vector potential being zero or its normal component being zero. The conversation highlights the need for mathematical formulations to better understand these boundary conditions in magnetic field modeling.
Alan Kirp
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I stumbled upon this article: http://www.comsol.com/blogs/exploiting-symmetry-simplify-magnetic-field-modeling/

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.

Thanks in advance for your time.
 
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