Solutions of the electromagnetic field by means of potentials under the Lorentz condition are described in this paper. The solution represented by the superposition of TM and TE modes is well known. It is explained why this solution has been exclusively accepted. The possibility of applying the Coulomb gauge is discussed. Due to the noncovariant field requirement, application of the Coulomb condition is unavoidable in quantum theory. In both cases, the longitudinal modes with their possible applications are described.