Motion of charged particles
The simplest magnetic field B is a constant one– straight parallel field lines and constant field intensity. In such a field, if an ion or electron enters perpendicular to the field lines, it can be shown to move in a circle (the field only needs to be constant in the region covering the circle).
If q is the charge of the particle, m its mass, v its velocity and Rg the radius of the circle all one needs do is notice that the centripetal force mv2/Rg must equal the magnetic force qvB. One gets.
Rg = mv/(qB)