The electromagnetic field response, caused by an inhomogeneity in a homogeneous isotropic full space, is modelled and discussed. Maxwell's equations are solved by using Green's method which leads to a singular inhomogeneous Fredholm integral equation of the second kind. This equation contains some serious difficulties related to the evaluation of singular integrals when doing standard point collocation discretization. We state and prove a result, which avoids these diffi-culties. We also discuss some other attempts to avoid these difficulties in the literature.