The transformation of a plane harmonic wave caused by a time jump of the permittivity inside a dielectric sphere is investigated. The exact expressions for the transformed field are obtained as a solution of an initial and boundary value electromagnetic problem for the Maxwell's equations based on the longitudinal and the transverse spherical vector functions.

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Electromagnetic transients due to presence of boundaries of time-varying medium are investigated. A half-restricted plasma with a plane boundary and a completely restricted plasma in a cylinder and in a sphere are considered. It is shown that interaction of an electromagnetic wave with the time varying plasma changes drastically in the presence of the boundaries compared to the unbounded time varying plasma.

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