# Straight line

If the direction of is parallel or antiparallel to ,

*Î¸*= 0 or 180^{o}and therefore*F*= 0. Hence, the trajectory of the particle is a straight line (Fig. 3).**Fig. 3**

# Circular path

If is perpendicular to , i.e.,

*Î¸*= 90^{o}. Hence, particle will experience a maximum magnetic force*F*_{max}*=*which acts in a direction perpendicular to the motion of charged particle. Therefore the trajectory of the particle is a circle (Fig. 4).**qvB****Fig. 4**

- In this case, path of charged particle is circular and magnetic force provides the necessary centripetal force, i.e., â‡’ radius of path
*p*= momentum of charged particle and*K*= kinetic energy of the charged particle (gained by the charged particle after accelerating through potential difference*V*). Then - If
*T*is the time period of the particle then*T*= 2*Ï€**m*/*qB*(i.e., time period (or frequency) is independent of the speed of particle).

# Helical path

When a charged particle is moving at an angle to the field (other than 0

^{o}, 90^{o}, or 180^{o}), it describes a path called helix.- The radius of this helical path is
- Time period and frequency do not depend on velocity and so they are given by
*T*= 2*Ï€**m*/*qB*and*v*=*qB*/2*Ï€**m*.

**Fig. 5**

- The
*pitch*of the*helix*, (i.e., linear distance travelled in one rotation) will be given by - If the pitch value is
*p*, then number of pitches obtained in length*l*given as