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 is `(50 pi M)/(3Q)` units
D. The magnitude of the magnetic field is `(100piM )/(3Q)` units

Answer

A, C

Explanation

`u=4hati,v=2(sqrt(3)hati+hatj)`
According to the figure, magnetic field should be in `ox` direction, or along
-z directio. Further `tan theta=(v_(y))/(v_(x))=2/(2sqrt(3))=1/(sqrt(3)):. theta =30^(@)` or `(pi)/6=` angle of v with x-axis = angle rotated by the particle
`-Wt=((BQ)/m)t :. B=(piM)/(6Qt)=(50piM)/(6 Qt)=(50piM)/(3Q)` units (As `t=10^(-3)s)`