# Applying method of images to magnetic dipoles

I want to apply the method of images to quasi-stationary calculate the 2D magnetic field distribution of a magnetic dipole and a half space with certain electrical properties (permeability, conductivity). The setup is illustrated in the sketch below: The two conductors L1 and L2 are carrying a sinusoidal AC current in opposite directions. This represents an approximation of a magnetic dipole, thereafter referred to as the magnetic dipole. The conductors are surrounded by air. However, there is also a half space (yellow colored) with different permeability ($$\mu_h$$) and conductivity ($$\kappa_h$$) values.

For the case $$\kappa_h = 0 S/m$$ method of images provides an analytical solution for the calculation of magnetic field distribution in the upper half space:

$$\textbf{H} = \textbf{H}_D(0,h) - \eta \cdot \textbf{H}_D(0,-h)$$

where $$\textbf{H}_D(x_0,y_0)$$ is the magnetic field distribution of a magnetic dipole at position $$(x_0,y_0)$$ in air and $$\eta = \frac{\mu_h - \mu_0}{\mu_h + \mu_0}$$

Now I am wondering if the method of images can be applied to the case of a conductive half space ($$\mu_h = \mu_0$$ and $$\kappa_h > 0 S/m$$) as well. In this case occurring eddy currents will affect the field distribution in the upper half space. Does anybody know how to consider these? Can the method of images be applied? Does anybody know specific literature which covers this topic? Any comments will be greatly appreciated!  