The paper presents formulations of optimal control problems for various quasi-stationary approximations for the system of Maxwell equations in inhomogeneous media. The problems under consideration relate to non-classical evolutionary problems of mathematical physics (the time derivative is under the action of the projection operator onto the space of potential vector fields). The current density of sources is used as control for the considered systems of differential equations, the objective functionals include the deviation of the electric and magnetic fields from the fields of a given configuration over a finite time interval and takes into account Joule losses. The studied optimal control problems are treated as convex optimization problems in Hilbert spaces. The main result of the work is the necessary first-order optimality conditions for the problems under consideration, formulated in terms of solutions of the corresponding adjoint problems.