Wave equations are derived for the scalar and vector potentials of guided electromagnetic waves propagating in a laterally bounded magnetized plasma along the axis of the static magnetic field. Solutions are given in the Coulomb and the Lorentz gauge. These solutions are used in a critical examination of the conceptual basis of the quasistatic theory because they allow convenient partitioning of the high‐frequency electric field into a lamellar and a rotational part. In the quasistatic approximation the electric field is considered to be entirely lamellar, i.e., the gradient of a scalar potential that is not consistent with Maxwell's equations. To avoid inconsistencies the problem is formulated so that the dynamic scalar potential replaces the quasistatic potential. The rotational part of the electric field is readily obtained as the time derivative of the vector potential. Exact quantitative comparison of two parts of the electric field is made possible in this way and the relative importance of each part is evaluated for a few typical cases of interest. There exist some waves with dispersion characteristics that can not be obtained with the quasistatic formula although the condition that the phase velocity be smaller than the velocity of light presumed to be necessary for the applicability of the quasistatic approximation is satisfied. In these waves the rotational part of the electric field is comparable or greater than the lamellar part. Conversely, in modes with dispersion characteristics that can be well approximated with the quasistatic formula even when the phase velocity exceeds the velocity of light the lamellar part of the electric field is much larger than the rotational part. It can be inferred that the essential element of the quasistatic theory is the assumption that the high‐frequency electric field is predominantly lamellar rather than the condition that the phase velocity be smaller than the velocity of light and related criteria.