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 $\overrightarrow{B}$ 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

Given data

Charge =q

Velocity =v Having Positive x direction

Magnetic field B having negative z direction

X=a to x= b

Concepts used moving charges and magnetism

Explanation

In the figure, the z-axis points to the outside of the plate, and the magnetic field points to the plate in the PQ and RS field. Particles follow a circular path of radius r in a magnetic field. can enter the field 

$r=\frac{mv}{qB}\ge (b-a)$

$v\ge \frac{q(b-a)B}{m}$

$x>b$ and $r>(b-a)$

$v_{\text{min}}\ge \frac{q(b-a)B}{m}$