A particle of mass`M` and positive charge `Q`, moving with a constant velocity ` vec(u_(1)) = 4 hat(i) ms^(-1)`, enters a region of uniform static magnetic field , normal to the ` x-y ` plane. The region of the magnetic field extends from ` x= 0` to ` x = L` for all values of `y`. After passing through this region, the particle emerges on the other side after `10 milliseconds` with a velocity `vec(u_(2)) = 2 (sqrt(3 hat(i) + hat(j))) ms^(-1)` . The correct statement(s) is (are)

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))`