Stochastic wave equations are derived to describe electromagnetic wave propagation in an isotropic medium in which the electric permittivity and the magnetic permeability are weakly-random functions of time. Approximate analytical solutions are obtained using separation of variables and the WKB method for some configurations that can be used to model the electromagnetic field in the ionosphere. The form of the initial and boundary conditions determines whether the solution takes a form representing a direct current electric field or continuous pulsation electromagnetic waves. The temporal variation of the calculated induced electromotive force (EMF) is in agreement with observations.
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