Eshelby's energy-momentum tensor useful for studying material forces acting on various kinds of inhomogeneities is constructed in the exact nonlinear theory of deformable dielectrics. This is achieved by examining the possible changes of reference configurations relative to fixed, locally defined, `reference crystals'. The electroelastic energy-momentum tensor thus obtained does not involve the Maxwell stress of free electric fields. Electric effects manifest themselves through the ultimate decomposition of the Cauchy stress in a symmetric `elastic' part and an interaction part involving electric polarization. When the electroelastic body is made of the same material at all points, the electroelastic energy-momentum is shown to satisfy a remarkable differential identity involving the torsion of the material connection. In the quasi-linear approximation, the material force thus defined leads to the notion of path-independent integral which should be useful in studying cracks in electrodeformable ceramics. Various extensions and generalizations are briefly discussed, and the Peach-Koehler force acting on a dislocation element is found by an independent method in an appendix.