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Straight line

If the direction of 81580.png is parallel or antiparallel to 81586.png, θ = 0 or 180o and therefore F = 0. Hence, the trajectory of the particle is a straight line (Fig. 3).
Fig. 3

Circular path

If 81599.png is perpendicular to 81605.png, i.e., θ = 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., 81612.png 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 81644.png
  • If T is the time period of the particle then T = 2πm/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 81656.png
  • Time period and frequency do not depend on velocity and so they are given by T = 2πm/qB and v = qB/2πm.
Fig. 5
  • The pitch of the helix, (i.e., linear distance travelled in one rotation) will be given by 81667.png
  • If the pitch value is p, then number of pitches obtained in length l given as
    Number of pitches81676.png and time required 81682.png

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