question_answer

An \[\alpha \] particle is moving along a circle of radius R with a constant angular velocity \[\omega .\] Point A lies in the same plane at a distance 2R from the centre. Point A records magnetic field produced by \[\alpha \] particle. If the minimum time interval between two successive times at which A records zero magnetic field is 't', the angular speed \[\omega ,\] in terms of t is:

A) \[\frac{2\pi }{t}\]

B) \[\frac{2\pi }{3t}\]

C) \[\frac{\pi }{3t}\]           

D) \[\frac{\pi }{t}\]

Correct Answer: B

Solution :

Point A shall record zero magnetic field (due to a-particle) when the a-particle is at position P and Q as shown in figure. The time taken by a-particle to go from P to Q is

\[t=\frac{1}{3}\,\,\frac{2\pi }{\omega }\] or         \[\omega =\frac{2\pi }{3t}\]