Electromagnetic source equivalence is considered for the case of an isotropic nonhomogeneous medium. Equivalent transformations of the transversally oriented (with respect to a chosen axis) current sources into longitudinally oriented sources are derived. They allow the reduction of any given distribution of arbitrarily oriented sources to an equivalent distribution of single-component parallel electric and magnetic sources. The technique is referred to as source scalarization; and, together with a recently developed vector potential field representation in an isotropic, nonhomogeneous, lossy medium, which may contain sources of arbitrary orientation, it is applied to produce a complete description of the field in terms of two scalar wave potentials. The proposed source scalarization technique is illustrated by a simple numerical example: the radiation of an electromagnetic pulse by an asymmetrical loop of magnetic currents.