Solving a Magnetic Problem with Maxwell Equation

[we are the robots]

Hi, I'm very lost in this problem, anyone can help me?
The problem is this:

In steady state the magnetic field H satisifes the Maxwell equation delxH=J , where J is the current density (per square meter). At the boundary between two media there is a surface current density K (perimeter). Show that a boundary contidion on H is
nx(H2-H1)=K.
n is a unit vector normal to the surface and out of medium 1.
Hint: consider a narrow loop perpendicular to the interface as shown in the figure. (The figure is attached).

Note: del x H is the curl of H.
Any ideas?
Thank you.

 

[Bonfield]

The hint is a good one.

First integrate and then apply Stokes theorem to your curl H = J equation to get the equivalent integral form. You will have a line integral of H around a closed curve, which you should make your rectangular loop. The other side of the equation will have the total current flowing through the loop, which is related to K. Set this up carefully, and you will have the result you want.