  In the present work, we execute the Lie symmetry analysis on the
Einstein-Maxwell field equations in the plane symmetric spacetime. Under the
background of the plane symmetric space-time we compute the Lie point
symmetries, perform the similarity reductions and obtain exact solutions in
connection to the evolutionary scenario of the universe. The special feature of
the study is that it deals with the electromagnetic energy of the inhomogeneous
universe through the non-vanishing component of electromagnetic field tensor
$F_{12}$ and assumes that the free gravitational field is of Petrov type-II
non-degenerate. We have found that the electromagnetic field tensor is positive
and increasing function of time. To validate the solution set, we examine with
detailed discussions several physical as well as geometrical features of a
specific sub-case of the model.
