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 required so that the particle can just enter the region x > b is 

(a) [(qbB)/m] 

(b) q(b – a)(B/m) 

(c) [(qaB)/m] 

(d) q(b + a)(B/2m)

Answer 1

The correct option (b) q(b – a)(B/m)

Explanation:

If the radius of circular path of a particle of mass m and charge q moving with velocity Ʋ perpendicular to magnetic field B is r then

 (mV²/r) = qVB

∴   V = [(qBr)/m]

∴   V_min = (qB/m)r_min

and  r_minimum= b – a

Hence

V_min = (qB/m)(b – a)