We present a momentum balance equation derived directly from Maxwell's equations. This equation contains a force density, which we call Maxwell's force density, which generalizes the Lorentz force density, now including total fields rather than only external fields, and arbitrary charge and current distributions. As a test for this balance equation we derive for gases the electrostatic and magnetostatic Helmholtz force densities. This deduction will be useful for advanced undergraduates and graduate students, as well as for specialists interested in the conceptual aspects of electromagnetism.

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In this work, we modeled and simulated the electric potential generated by point charges in the region of grounded conductor planes for Yukawa poten- with different values of µ . We observe that the electric potential decreases as the value of µ increases and that does not allow all the charge to be distributed on the surface of the conductor.

We explore the consequences of a force density, , studied by some authors, for the device designed by Lai (1980 Am. J. Phys. 48 658) to analyse which definition of electromagnetic momentum density, either Minkowski's or Abraham's, is consistent with mechanical torques that arise from the change in time of a magnetic field, which produces an induced electric field that acts on free and polarization charges. It is found that Minkowski's definition is consistent with the mechanical torques associated with free charges, while Abraham's is consistent with mechanical torques associated with both free and polarization charges. We show that with this new force density Lai's work (1980 Am. J. Phys. 48 658) can be extended to include magnetic media. The results are consistent with Abraham's definition of electromagnetic momentum density, extending in this way its usefulness to magnetic media.