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 shell record zero magnetic field (due to \[\alpha -\] particle) when the \[\alpha -\] particle is at position P and Q as shown in figure. The time taken by \[\alpha -\] particle to go from P to Q is

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