Equivalence of the Lorentz and Ampere force laws in magnetostatics

Abstract

The Lorentz and Ampere laws are shown to be equivalent in magnetostatics. Both predict equal and opposite forces on complementary parts of a current distribution, and only a normal force on a current element. There is no force along the element. The illusory differences between the two are attributed to the incorrect integration of the differential forms of the laws, and to the inappropriate use of line current elements as sources, instead of surface or volume elements.