question_answer

A charged particle of mass m and charge q travels on a circular path of radius r that is perpendicular to a magnetic field B. The time taken by the particle to complete one revolution is                [AIEEE 2005]

A) \[\frac{2\pi mq}{B}\]

B) \[\frac{2\pi {{q}^{2}}B}{m}\]

C) \[\frac{2\pi qB}{m}\]

D) \[\frac{2\pi m}{qB}\]

Correct Answer: D

Solution :

[d] When a charge is projected in a magnetic field it follows the circular path. Clearly, there will be a centripetal force which is responsible to move the charge on the circular path.

Magnetic force,

...(i)

Centripetal force,

From Eqs. (i) and (ii), we get,

The time taken by the particle to complete one revolution,

\[T=\frac{2\pi r}{v}=\frac{2\,\pi \,mv}{vqB}\,=\frac{2\,\pi m}{qB}\]