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 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)`