Question

If a velocity has both perpendicular and parallel components when moving through a magnetic field, the path followed by a charged particle is:
(A) Circular
(B) Elliptical
(C) Linear
(D) Helical

Answer 1

Hint A particle moving in a magnetic field will experience force only if the magnetic field is perpendicular to it. This is because the force on a particle in a magnetic field is the cross product of velocity and direction of the magnetic field.

Complete step by step solution
When a particle is moving in a magnetic field, it experiences force according to the given formula
 \[F\, = \,q(v\, \times B)\]
 \[F\, = \,qvB\sin \theta \]
Where \[\theta \] is the angle between the velocity and the magnetic field.
This force will act perpendicular to the direction of motion of the particle. This centripetal force will be equal to
 \[
  \dfrac{{m{v^2}}}{r}\, = \,qvB \\
  v\, = \,\dfrac{{qrB}}{m} \\
 \]
Thus this force will make the particle move in a circular path. Whereas there will be no external force acting on the particle in the direction of the magnetic field. The resultant of these 2 forces will make the particle move in a helical path.

Therefore the correct answer is option D.

Note This concept is used in a particle accelerator, where the magnetic field rotates the particle in a circular motion and the electric field speeds up the particle.