Boundary conditions on magnetostatic

AI Thread Summary
In magnetostatic problems, the boundary conditions for the magnetic vector potential (A) depend on the specifics of the situation. Above and below a surface current (K), the vector potentials must be equal, but their derivatives exhibit a discontinuity. This discontinuity is expressed as the difference in the normal derivatives of A across the current sheet being equal to negative the product of the permeability of free space (μ₀) and the surface current (K). Understanding these conditions is crucial for accurately solving magnetostatic problems. Additional resources, such as relevant articles, can provide further insights into these boundary conditions.
cubates
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Hi

I'm trying to solve a magnetostatic problem and I'm not sure which boundary conditions must be applied to the magnetic vector potential (A) on magnetostatic problems?

Thanks in advance.
 
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Your boundary conditions will depend on your particular problem. Across a surface current (K) the boundary conditions are that the vector potential (A) above the current sheet is equal to vector potential below sheet. However, the derivative of A has a discontinuity:

\partial A_{above}/ \partial n - \partial A_{below}/\partial n = -\mu_0 K

where n is a direction perpendicular to the plane. This article might prove to be useful to you:
http://www.physics.sfsu.edu/~lea/courses/ugrad/360notes14.PDF"
 
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