question_answer

A particle of mass m and having a positive charge q is projected from origin with a speed \[{{v}_{0}}\]along the positive \[x-\]axis in a magnetic field \[\vec{B}=-{{B}_{0}}\hat{k}\]where B is a positive constant. If the particle passes through  (0, y, 0), then y is equal to:

A) \[\frac{2m{{v}_{0}}}{q{{B}_{0}}}\]                    

B) \[\frac{m{{v}_{0}}}{qB}\]

C) \[\frac{m{{v}_{0}}}{qB}\]                          

D) \[\frac{2m{{v}_{0}}}{q{{B}_{0}}}\]   

Correct Answer: D

Solution :

Path of the particle is a circle. y = 2 (radius of circle) or diameter \[=\frac{2m{{v}_{0}}}{q{{B}_{0}}}\] Hence, the correction option is [d].