 Solution

Take the initial velocity perpendicular to a uniform magnetic field. The magnetic Lorentz force is perpendicular to the motion, has constant magnitude $|q|vB$, and supplies the centripetal force:The rotation sense is fixed by $q\mathbf{v}\times \mathbf{B}$. A component of velocity parallel to the field remains constant and produces a helical motion in a uniform magnetic field; a circle requires that component to vanish. The speed-independent cyclotron frequency here assumes nonrelativistic motion.