question_answer

A uniform magnetic field of magnitude IT exists in       region y>0 is along k direction as shown. A particle of charge 1 C is projected from point \[(-\sqrt{3},-1)\]  towards origin with speed 1 m/sec. If mass of particle is 1 kg, then co-ordinates of centre of circle in which particle moves are-                

A) \[(1,\,\sqrt{3})\]

B) \[(1,\,-\sqrt{3})\]

C) \[\left( \frac{1}{2},-\frac{\sqrt{3}}{2} \right)\]

D) \[\left( \frac{\sqrt{3}}{2},-\frac{1}{2} \right)\]

Correct Answer: C

Solution :

[c] The centre will be at C as shown : Coordinates of the centre are    \[(r\,\cos \,{{60}^{o}},-r\,\sin \,{{60}^{o}})\] where r = radius of circle      \[=\frac{mv}{Bq}=\frac{1\times 1}{1\times 1}=1\] i.e., \[\left( \frac{1}{2},-\frac{\sqrt{3}}{2} \right)\]