Larmor theorem ($\mathbf{\omega }=-e\mathbf{B}/(2m)$)

For particles with the same charge-to-mass ratio, rotationally invariant mutual central forces, and a weak uniform magnetic field, a frame with the displayed angular velocity cancels the velocity-dependent magnetic Lorentz force against the Coriolis force. The remaining rotational and magnetic terms are quadratic in $\mathbf{B}$. Thus, to first order in the field, the rotating-frame equations coincide with the zero-field equations. This is the classical dynamical basis of Larmor precession; equality is an approximation rather than an exact removal of the magnetic field.