The magnetic field in a medium with one horizontal interface

The Magnetic Field in a Medium with One Horizontal Interface 

Let us place the dipole at the origin of coordinates and direct the dipole moment along the x-axis  

As is well known, the field equations have the form  

Letting u = — div A we will obtain equation for the potential VU + k A = 0 where k = iafiu. 

We will look for a solution, assuming that component Ey = 0. 

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