# Magnetostatics - boundary condition

## Main Question or Discussion Point

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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marcusl
Gold Member
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.

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.

Meir Achuz
Homework Helper
Gold Member
I don't agree with Marcus. Since curl A is finite, A tangential is continuous.
Since div A is zero, A normal is continuous.

marcusl