# Straight line

If the direction of is parallel or antiparallel to , Î¸ = 0 or 180o 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¸ = 90o. Hence, particle will experience a maximum magnetic force Fmax = qvB which acts in a direction perpendicular to the motion of charged particle. Therefore the trajectory of the particle is a circle (Fig. 4).

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

where 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 = 2Ï€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 0o, 90o, or 180o), 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 = 2Ï€m/qB and v = qB/2Ï€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

Number of pitches and time required