question_answer

A particle of mass m and charge q moves with a constant velocity v along the positive x direction. It enters a region containing a uniform magnetic field B directed along the negative z direction, extending from  x = a to x = b. The minimum value of v required so that the particle can just enter the region \[x>b\] is                       [IIT-JEE (Screening) 2002]

A)            \[qb\,B/m\]                         

B)            \[q(b-a)B/m\]

C)            \[qa\,B/m\]                          

D)            \[q(b+a)B/2m\]

Correct Answer: B

Solution :

                   In the figure, the z-axis points out of the paper, and the magnetic field is directed into the paper, existing in the region between PQ and RS. The particle moves in a circular path of radius r in the magnetic field. It can just enter the region x > b for \[r\ge (b-a)\] Now, \[r=\frac{mv}{qB}\ge (b-a)\] or \[v\ge \frac{q(b-a)B}{m}\] Þ \[{{\nu }_{\min }}=\frac{q(b-a)B}{m}\]