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Magnetostatics - boundary condition

  1. May 5, 2010 #1
    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.
     
  2. jcsd
  3. May 5, 2010 #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.
     
  4. May 5, 2010 #3
    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.
     
  5. May 5, 2010 #4

    clem

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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.
     
  6. Aug 10, 2010 #5

    marcusl

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    Clem is right, I am wrong. Please disregard my post above.
     
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