For the force on a current-carrying wire placed in a uniform magnetic field, the author developed an approach based on two thought experiments to obtain the linear dependence of the magnetic force on both the current and wire length. This thought-experiment approach relies mainly on building a conceptual argument without relying on advanced math. The analysis of the physics at a microscopic level is consistent with the proposed thought-experiment reasoning as well.
A current-carrying wire placed in a magnetic field experiences a force F whose magnitude is directly proportional to the current I and the length of the wire l inside the magnetic field. This dependence is introduced to introductory physics students in two standard ways. One method obtains the dependence through a direct quantitative experiment.1,2 Many ways to experimentally demonstrate the force–current–length relationships can be found in the literature.3–7 The other common method is to theoretically derive...