Relativistic cyclotron orbit
= Relativistic cyclotron orbit
{title2=$\omega_\tau=qB/m$}
In a constant <magnetic field> $B\widehat z$ with no <electric field>, a charged relativistic particle moves in a circle in the perpendicular plane. Its angular frequency with respect to <proper time> is
$$
\omega_\tau=\frac{qB}{m},
$$
whereas its angular frequency in an inertial coordinate time is $\omega_t=qB/(\gamma m)$. The orbit radius at speed $v$ is
$$
R=\frac{\gamma mv}{|q|B}.
$$