Magnetostatics - boundary condition

  • Thread starter paweld
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  • #1
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Main Question or Discussion Point

Let's consider two media with magnetic permeability [tex] \mu_1, \mu_2 [/tex].
What's the condition for magnetostatic vector potential [tex]\vec{A} [/tex]
on the boundary. Is it true that its tangent component should be continuous.
Thanks for replay.
 

Answers and Replies

  • #2
marcusl
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The BC across the magnetic interface is

[tex]\vec{A_+} - \vec{A_-}=\mu_0\vec{M}\times\hat{n}[/tex]

so only the normal component of A is continuous. A_tangential is continuous only in the special case when M is normal to the surface.
 
  • #3
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I don't see your point.
The condition on [tex]\vec{B} [/tex] are the following:
[tex]\vec{n}( \vec{B}^+ - \vec{B}^-) = 0[/tex]
and
[tex]\vec{n} \times (\frac{1}{\mu_1}\vec{B}^+ -\frac{1}{\mu_2} \vec{B}^-) = 0[/tex]
Vector potential satisfies the condition [tex] \nabla \times \vec{A} = \vec{B} [/tex].
I'm exacly asking if the above conditions implies that some components of A are continous.
 
  • #4
Meir Achuz
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I don't agree with Marcus. Since curl A is finite, A tangential is continuous.
Since div A is zero, A normal is continuous.
 
  • #5
marcusl
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Clem is right, I am wrong. Please disregard my post above.
 

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