Problem formulations arising from modeling quasi-stationary electromagnetic processes in the lower atmosphere are investigated. These processes are described using the system of Maxwell’s equations in the quasi-stationary electrical approximation. Mathematical formulations of direct problems of determining electric and magnetic fields at given sources and results on the unique solvability of these problems in the corresponding functional spaces are discussed. The issue of the possibility of obtaining information about electromagnetic fields and their sources is studied, depending on the given, natural from a physical point of view, boundary conditions. A functional space is determined, the projection of the source onto which is unambiguously reconstructed from boundary observations of tangential components of electromagnetic fields. The problem of simultaneous determination of the source from the certainty class and the corresponding fields based on the results of boundary observations is obtained. The existence and uniqueness of the solution of the problem is proved, and the application of the Galerkin method to solve it is justified. An alternative optimization formulation of the problem under consideration is presented and the feasibility of using an iterative dual algorithm for an approximate solution of the problem is substantiated, estimates of the convergence of the algorithm are obtained. The results of the work can be used in the study of quasi-stationary electromagnetic processes in weakly conductive media.