An alternative derivation of the electric force density for elastic solids from a Maxwell balance equation

The forces that arise in the interaction of electrostatic fields and elastic solids have been addressed by several authors using the method of virtual work, considering the free energy. In the present work, we obtain the same results using an electrostatic momentum balance equation equivalent to the macroscopic Maxwell equations and the usual assumptions about the permittivity. We offer a new method that gives better understanding of the electromagnetic balance equations. This method is based on the idea that the macroscopic Maxwell equations, from which the balance equation is deduced, and the constitutive relations are sufficient for the derivation of the force density. (author)