The classic problem of determining the force on a current-carrying wire in a magnetic field is critically analysed. A common explanation found in many introductory textbooks is to represent the force on the wire as the sum of the forces on charge carriers. In this approach neither the nature of the forces involved nor their application points are fully discussed. In this paper we provide an alternative microscopic explanation that is suitable for introductory electromagnetism courses at university level. By considering the wire as a superposition of a positive and a negative cylindrical charge distributions, we show that the electrons are subject to both magnetic and electric forces, whereas the ionic lattice of the metal is dragged by an electric force. Furthermore, an analysis of the orders of magnitude involved in the problem gives counterintuitive results with valuable educational potential. We argue that this approach allows one to discuss different aspects of the physical knowledge, which are relevant in physics education.