MAGNETIC INTERACTIONS BETWEEN CHARGED PARTICLES

The Lorentz forces exerted by freely moving charges upon one another are not equal and opposite. Conservation of canonical momentum requires, however, that the generalized forces (with components dL/dxj) be equal and opposite. Elementary arguments show that the magnetic interaction terms in the Lagrangian are identical with Darwin's even in the absence of retardation; they arise from relative motion and can therefore not be peremptorily excluded from every nonrelativistic problem involving charged particles, for instance in plasma physics. The formulation of, and separation of variables in, two-body problems with noncentral forces calls for some care because of the wobble motion of the center of mass. In hydrogenic atoms the effects of the magnetic interaction are extremely small; they are contained in the known relativistic correction to the reduced mass correction to the fine structure. © 1968, American Association of Physics Teachers. All rights reserved.