The force density and the kinetic energy-momentum tensor of electromagnetic fields in matter

We determine the invariant expression of the force density that the electromagnetic field exerts on dipolar matter and construct the non-symmetric energy-momentum tensor of the electromagnetic field in matter which is consistent with that force and with Maxwell equations. We recover Minkowski's expression for the momentum density. We use our results to discuss momentum exchange of an electromagnetic wave-packet which falls into a dielectric block. In particular we show that the wave-packet pulls the block when it enters and drags it when it leaves. The usual form of the center of mass motion theorem does not hold for this system but a modified version of the theorem which includes a spin contribution is shown to be satisfied.