  The interaction of a point charge and a magnetic moment (and by extension a
point charge and a solenoid) is explored within well-defined point-charge
magnetic-moment models where full calculations are possible. It is shown
explicitly how the "hidden mechanical momentum" is introduced by the "hidden"
external forces of constraint, requiring a prescribed response (through order
1/c^2) of the system to electromagnetic forces. These external forces often go
unmentioned in the textbook and research literature. The dependence of "hidden
mechanical momentum" upon detailed external (nonelectromagnetic) forces may
undermine the idea's usefulness in describing nature. Some statements of
dubious validity in the textbook literature are noted.
