The unsteady axisymmetric problem being considered is related to the identification of the components of electromagnetic field in moving space with spherical enclosure filled with homogeneous isotropic conductor. The model used includes Maxwell's equations and generalized Ohm's law. In order to find a solution, a series expansion in Legendre polynomials and Laplace time transform are applied. Integral representations of the components of the electromagnetic field with Green's function kernels have been generated.