Equality of the Kelvin and Korteweg–Helmholtz Force Densities Inside Dielectric Materials

The net force is enough to predict the motion of an object, but to predict its deformation, the distribution of the force inside the object should be known. In the continuum electromechanics, various expressions are used to calculate the electric forces acting on a dielectric object. The Kelvin and the Korteweg–Helmholtz forces are the most common electric body forces. The net force resulting from both of these “forces” is equal, but the distribution of these two forces inside a dielectric material is different because the expressions of both these forces lose their physical manifestation in the derivation process. This article is primarily aimed at revealing the common mistakes that are made when deriving volumetric force density. Then, the concept of an infinitesimal particle and external electric field is introduced. By using this concept, the electric force density inside a dielectric material is uniquely determined irrespective of the force expression, which is shown analytically and numerically.