In a magnetic field, a moving charged particle experiences a force, F that is given by the Lorentz force law:

F = q(v x B)                    .........................................................................................(11.4)

where, v is the velocity of the moving charged particle and B is the magnetic field strength.

The direction of the force can be determined using the right hand rule; If the fingers represent the magnetic field (B) and the thumb represents the velocity (v), then the direction of the force is given by the direction of the palm (Figure 11.2A). As the force is always perpendicular to the velocity, the deflected particle moves in a circular path (Figure 11.2B) .

Figure 11.2 The right hand rule showing the direction of the Lorentz force in a magnetic field (A) and the circular path taken by the particle (B).

The Lorentz force therefore provides the particle a centripetal force. Therefore, equation 11.4 can be written as

        ...............................................................................................(11.5)

where, r is the radius of the circular path

Rearranging in terms of r:

             ..................................................................................................(11.6)
               ...................................................................................................(11.7)