In an attempt to give a solution to a controversy existing in the literature for the generalization of the Rice \(J\)-integrals to electroelasticity, the authors reconsider the problem in a more general context. Two formulations of the theory of electroelasticity are proposed, giving rise to two distinct energy release rates, and therefore two distinct \(J\)-integrals. This duality pertains to a general feature of continuum mechanics of electromagnetic media, according to which certain quantities may be regarded as volume source densities or transformed into surface contributions in view of Maxwell's equations. In order to favorize one of the two formulations, the authors investigate a particular fracture problem for which one of the two formulations becomes inadequate. This is the case of electrically conducting cracks propagating through a linear anisotropic dielectric, for which the asymptotic solution for the electric field near the crack-tip was obtained and used to show that the energy balance in one of the two formulations contains a diverging integral. The authors conclude that for this type of fracture problems, only the representation of the (free) electric field action as a surface force can be adopted.