question_answer

Directions : (11-15)

Helical Motion

The path of a charged particle in magnetic field depends upon angle between velocity and magnetic field.

If velocity \[\overrightarrow{v}\] is at angle \[\theta \] to \[\overrightarrow{B}\] component of velocity parallel to magnetic field \[\left( v\,\sin \theta  \right)\]reamains constant and component of velocity perpendicular to magnetic field (v sin\[\theta \]) is responsible for circular motion, thus the charge particle moves in a helical path.

The plane of the circle is perpendicular to the magnetic field and the axis of the helix is parallel to the magnetic field.

The charged particle moves along helical path touching the line parallel to the magnetic field passing through the starting point after each rotation.

Radius of circular path is \[r=\frac{mv\,\sin \theta }{qB}\]

Hence the resultant path of the charged particle will be a helix, with its axis along the direction of \[\overrightarrow{B}\] as shown in figure.

When a positively charged particle enters into a uniform magnetic field with uniform velocity, its trajectory can be (i) a straight line (ii) a circle (iii) a helix.

A) (i) only

B) (i) or (ii)

C) (i) or (iii)

D) any one of (i), (ii) and (iii).