Comparison of the Ampère and Biot-Savart magnetostatic force laws in their line-current-element forms
The force laws of Ampère and Biot-Savart in magnetostatics are compared using the geometrical model of a closed curve to represent a current loop. The two laws give identical results when forces between separate current loops are considered and also for the force exerted by a current loop on a rectilinear part of itself. According to both laws, these self-forces diverge wherever the curvature of the curve representing the current loop is not equal to zero. Differences in the predictions of the two laws are shown to appear only as differences in diverging forces when evaluating forces of a current loop on a part of itself and to be entirely due to the oversimplified and unrealistic geometrical model used for the current loop.