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 gt b is

Options

A. The direction of the magnetic field is `-z`-direction.
B. The direction of the magnetic field is `+z`-direction.
C. The magnitude of the magnetic field `(50piM)/(3Q)` units.
D. The magnitude of the magnetic field `(100piM)/(3Q)` units.

Answer

A,C

Explanation

Component of final velocity of particle is in positive `y` direction.
Centre of circle is present on positive `y` axis.so magnetic field is present in negative `z`-direction Angle of deviation is `30^(@)` because
`tan theta=v_(y)/v_(x)=1/sqrt3`
`theta=pi/6`
`omegat=theta`
`theta=(QB)/Mt`
`B=(Mtheta)/(Qt)`
`B=((500Mpi)/(3Q))`