Conservation of linear and angular momentum and the interaction of a moving charge with a magnetic dipole

Abstract

The operation of the laws of momentum and angular momentum conservation in the interactions between current-carrying bodies and charged particles is analyzed using the correct expression for the force on a magnetic dipole, which takes into account the possible presence of hidden momentum in a current-carrying body. At nonrelativistic velocities, Newton’s third law holds for the interactions, and thus the mechanical momentum associated with the motion of current-carrying bodies and charged particles in a closed system is conserved itself in the nonrelativistic limit. There is no conflict with overall linear momentum conservation because the electromagnetic field momentum is equal and opposite to the hidden momentum of the current-carrying bodies. However, the field angular momentum in a system is not compensated by hidden angular momentum, and thus only the sum of mechanical angular momentum, which must include any hidden angular momentum, and field angular momentum is conserved.