Origin of the Laplace Force Applied to a Current-Carrying Wire Immersed in a Magnetic Field

The macroscopic force (called the Laplace force) acting on a wire carrying an electric current placed in a magnetic field is a consequence of the Lorentz force acting on each charge inside the wire. Typically, the Laplace force is explained as a magnetic force resulting from the interaction of the moving charges with the external magnetic field. Such an interpretation, however, is too simplistic and does not take into account all the interactions between the various charge populations inside the wire. This leads to a series of paradoxes that might hinder the understanding of this subject. For instance, a magnetic force cannot do any work, while a current-carrying wire in a magnetic field represents the paradigm to understand the working principle of an electric motor. Here, we will solve this and other inconsistencies by showing, with simple arguments comprehensible to undergraduate students, that the Laplace force is instead an electrostatic force