Recently, Mansuripur has called into question the validity of the Lorentz force in connection with relativistic electromagnetic theory. Here, we present some very simple point-charge systems treated through order in order to clarify some aspects of relativistic controversies both old and new. In connection with the examples, we confirm the validity of the relativistic conservation laws. The relativistic examples make clear that external forces may produce a vanishing torque in one inertial frame and yet produce a non-zero torque in another inertial frame, and that the conservation of angular momentum will hold in both frames. We also discuss a relativistic point-charge model for a magnetic moment and comment on the interaction of a point charge and a magnetic moment. Mansuripur's claims of incompatibiltiy between the Lorentz force and relativity are seen to be invalid.
REFERENCES
See the list of references in Griffiths' resource letter (Ref. 10) under the heading “D. Momentum and Mass.”
See Ref. 2, pp. 596–598. C. G. Darwin was the grandson of the famous Darwin of evolution.
See the list of references in Griffiths' resource letter (Ref. 10) under the heading “C. Hidden Momentum.”
Indeed, some authors seem to feel that simply making reference to “hidden momentum” excuses them from properly accounting for the flow of energy and momentum in an electromagnetic system.
