1. The problem statement, all variables and given/known data In Griffiths, the following boundary condition is given without proof: ∂Aabove/∂n-∂Abelow/∂n=-μ0K for the change in the magnetic vector potential A across a surface with surface current density K, where n is the normal direction to the surface. A later problem asks for a proof of this, by using cartesian coordinates at the surface, with z perpendicular to the surface and x parallel to the current, and using the first three equations below. 2. Relevant equations ∇.A=0 Aabove=Abelow Babove-Bbelow=μ0(Kxn) where n is a unit normal (I'm dropping all of the hats on my unit vectors). The above information tell us K=Kx n=z 3. The attempt at a solution First of all I have probably a really silly question because I know it's blatantly wrong, but why isn't this the case Babove-Bbelow=μ0(Kxz) (∇xAabove)-(∇xAbelow)=μ0(Kxz) ∇x(Aabove-Abelow)=μ0(Kxz) 0=μ0(Kxz) because Aabove=Abelow Aside from that, the solution states that because Aabove=Abelow all over the surface, ∂A/∂x and ∂A/∂y are also the same above and below the surface. Where does this come from, and why not ∂A/∂z? I can't get any further than this at present. Thanks for any help.