Magnetostatics - boundary condition

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Discussion Overview

The discussion revolves around the boundary conditions for the magnetostatic vector potential \(\vec{A}\) at the interface between two media with different magnetic permeabilities \(\mu_1\) and \(\mu_2\). Participants explore the continuity conditions for the components of \(\vec{A}\) and the implications of magnetic boundary conditions.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether the tangent component of the magnetostatic vector potential \(\vec{A}\) should be continuous at the boundary between two media.
  • Another participant states that the boundary condition for \(\vec{A}\) involves the normal component being continuous, while the tangential component is only continuous under specific conditions related to the magnetization \(\vec{M}\).
  • A different participant presents conditions on the magnetic field \(\vec{B}\) and inquires if these imply continuity for some components of \(\vec{A}\).
  • One participant disagrees with a previous claim, asserting that the tangential component of \(\vec{A}\) is continuous due to the finite curl of \(\vec{A}\), and that the normal component is continuous because the divergence of \(\vec{A}\) is zero.
  • A later reply acknowledges a mistake and retracts a previous statement, indicating a shift in perspective regarding the continuity of \(\vec{A}\).

Areas of Agreement / Disagreement

Participants express differing views on the continuity of the components of \(\vec{A}\) at the boundary, with no consensus reached on the conditions that govern this continuity.

Contextual Notes

Participants reference specific mathematical conditions and relationships involving the magnetic field and vector potential, but the discussion does not resolve the implications of these conditions on the continuity of \(\vec{A}\).

paweld
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Let's consider two media with magnetic permeability \mu_1, \mu_2.
What's the condition for magnetostatic vector potential \vec{A}
on the boundary. Is it true that its tangent component should be continuous.
Thanks for replay.
 
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The BC across the magnetic interface is

\vec{A_+} - \vec{A_-}=\mu_0\vec{M}\times\hat{n}

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.
 
I don't see your point.
The condition on \vec{B} are the following:
\vec{n}( \vec{B}^+ - \vec{B}^-) = 0
and
\vec{n} \times (\frac{1}{\mu_1}\vec{B}^+ -\frac{1}{\mu_2} \vec{B}^-) = 0
Vector potential satisfies the condition \nabla \times \vec{A} = \vec{B}.
I'm exacly asking if the above conditions implies that some components of A are continous.
 
I don't agree with Marcus. Since curl A is finite, A tangential is continuous.
Since div A is zero, A normal is continuous.
 
Clem is right, I am wrong. Please disregard my post above.
 

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