Magnetic Effects Of Current Question 145
Question: 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]
Options:
A) $ qb,B/m $
B) $ q(b-a)B/m $
C) $ qa,B/m $
D) $ q(b+a)B/2m $
Show Answer
Answer:
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} $
BETA
