Suppose a particle of mass m and charge q enters a region of uniform magnetic field of induction \(\vec B\). In below figure \(\vec B\) points into the page. The magnetic force \(\vec F_m\) on the particle is always perpendicular to the velocity of the particle, \(\vec v\). Assuming the charged particle started moving in a plane perpendicular to \(\vec B\), its motion in the magnetic field is a uniform circular motion, with the magnetic force providing the centripetal acceleration.
Charge q moving anticlockwise in a plane perpendicular to \(\vec B\) into the page
If the charge moves in a circle of radius R,
where p = mv is the linear momentum of the particle. Equation (1) is known as the cyclotron formula because it describes the motion of a particle in a cyclotron-the first of the modern particle accelerators.
