- #1
Alan Kirp
- 2
- 0
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.
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.