A system of partial differential equations governing unsteady multidimensional electro-magneto-hydrodynamic flows has been rewritten in its fully conservative ( divergence-free) form. Linear polarization and magnetization effects were allowed while assuming an incompressible fluid and a single type of electrically charged particles in the flow. Both vector operator formulation and a scalar Cartesian coordinate system formulation have been derived in detail. The resulting My conservative forms are suitable for further transformations to other coordinate systems or for direct discretization leading to their numerical integration.
