both v and B and acts like a centripetal force. It has a magnitude q v B . Equating the two expressions for centripetal force, m v / r = q v B , which gives r = m v / qB ( . ) for the radius of the circle described by the charged particle.
The larger the momentum, the larger is the radius and bigger the circle described. If ω is the angular frequency, then v = ω r . So, ω = π ν = q B / m [ . (a)] which is independent of the velocity or energy .
Here ν is the frequency of rotation. The independence of ν from energy has important application in the design of a cyclotron (see Section . . ).
The time taken for one revolution is T = π / ω ≡ / ν . If there is a component of the velocity parallel to the magnetic field (denoted by v || ), it will make the particle move along the field and the path of the particle would be a helical one (Fig. . ).
The distance moved along the magnetic field in one rotation is called pitch p . Using Eq. [ . (a)], we have p = v || T = π m v || / q B [ .
(b)] The radius of the circular component of motion is called the radius of the helix . FIGURE . Circular motion FIGURE . Helical motion