We address the problem of the force exerted on a dielectric slab partially introduced into a charged parallel plate capacitor. This elementary problem is usually solved calculating this force as the gradient of an energy and attributing its origin to the action of the fringing field outside the capacitor on the dipoles of the dielectric slab. By applying Maxwell's theory of electromagnetic stresses, we show that this force acts at the interface dielectric-vacuum and originates from the action of these stresses. This approach permits to obtain the force as a volume integration of a force density, or as a surface integral of a stress tensor. This force density and the stress tensor are part of a momentum balance equation derived from Maxwell's equations.

We give theoretical foundation to torque densities proposed in the past, like the one used by Beth to study experimentally the action of circularly polarized radiation on a birefringent material, or that proposed by Mansuripur to resolve a seeming paradox concerning the Lorentz force law and relativity. Our results provide new insights into electromagnetic theory, since they provide a unified and general treatment of the balance of lineal and angular momentum that permits a better assessment of some torques. Thus in this work we extend the derivations we have made of balance equations for electromagnetic linear momentum to balance equations for electromagnetic angular momentum. These balance equations are derived from the macroscopic Maxwell equations by means of vector and tensor identities and from the different ways in which these equations are written in terms of fields E, D, B, and H, as well as polarizations P, and M. Therefore these balance equations are as sound as the macroscopic Maxwell equations, with the limitations of the constitutive relations.

We analyze the familiar effect of the pulling of a magnetizable rod by a magnetic field inside a solenoid. We find that the analogy with the pulling of a dielectric slab by a charged capacitor is not as direct as usually thought. Indeed, there are two possibilities to pursue the analogy, according to the correspondence used, either → E B and → D H , or → E H and → D B. One of these results in an incorrect sign in the force, while the other gives the correct result. We avoid this ambiguity in the usual energy method applying a momentum balance equation derived from Maxwell's equations. This method permits the calculation of the force with a volume integration of a force density, or with a surface integration of a stress tensor. An interpretation of our results establishes that the force acts at the interface and has its origin in Maxwell´s magnetic stresses at the medium-vacuum interface. This approach provides new insights and a new perspective of the origin of this force.

We present a non-relativistic approach to the equivalent polarization () 2 1 eq eq c = × P v M , that appears in a magnetized medium in motion. We apply an analogous method to that used by Panofsky and Phillips to calculate the symmetric effect, the equivalent magnetization that appears in a polarized dielectric in motion, eq = × M P v , This method is based on a particular expression of Maxwell's equations and the application of the convective derivative. These authors argue, however, that the equivalent polarization can be obtained only with a relativistic approach. We show that with the same method, but with a different and equivalent expression of Maxwell's equations, this effect can also be calculated. In this way both effects can be considered relativistic effects to first order in v/c.

With the insight provided by a balance equation of electromagnetic momentum, we compare the force on a dielectric slab inside a capacitor with the force on a magnetizable rod inside a solenoid. We conclude that these forces are not exactly analogous, as usually thought. We present a device that is a proper analogy of the case of a dielectric slab inside a capacitor. Our analysis shows the significance of the electrostatic and magnetostatic pressures to the understanding of these effects and shows the conceptual differences between both cases.