of Eqs. (\[Ampere-BC\]) are well defined and they represent self-induced surface charge and current densities, respectively. An immediate consequence of the boundary conditions (\[Ampere-BC\]-\[Faraday-BC\]) is that the presence of a magnetic field crossing the surface $\Sigma $ is sufficient to generate an electric field, even in the absence of free electric charges. Many interesting magnetoelectric effects due to a $\theta$-boundary have been highlighted using different approaches. For example, electric charges close to the interface $\Sigma$ induce magnetic mirror monopoles (and vice versa) [@science; @Kim1; @Kim2]. Also, the propagation of electromagnetic waves across a $\theta$-boundary have been studied finding that a non trivial Faraday rotation of the polarizations appears [@ZH; @Kim1; @Kim2; @Hehl]. It is worth mentioning that with the modified boundary conditions, several properties of conductors still hold for static fields as far as the conductor does not lie in the $\Sigma $-boundary, in particular, conductors are equipotential surfaces and the electric field just outside the conductor is normal to its surface.

The Green’s function method {#Green}
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In this section we use the GF method to solve static boundary-value problems in $\theta $-ED in terms of the electromagnetic potential $A^{\mu}$. Certainly one could solve for the electric and magnetic 