A New Perspective of the Force on a Magnetizable Rod inside a Solenoid

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.