Maxwell Stress and Force on Current-Carrying Conductor

Abstract

This article contains a new derivation of the formula, BLi, for a force on a current-carrying conductor placed in a magnetic field. This derivation uses the concept of Maxwell stress. The conductor is assumed to be a rectangular bar with negligible width, but with finite height and finite length. The bar is placed in a magnetic field that is parallel to its height and perpendicular to its length. The force on the conductor is determined by finding compressive stresses on the two surfaces parallel to the field. This is accomplished by recognizing that flux density at the two surfaces is modified by the current in the bar.