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 (sqrt3 hat(i) + hat(j))) ms^(-1)` . The correct statement(s) is (are)

Options

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

Answer

A, C

Explanation

The magnetic field should be in the ` - Z` direction ( Fleming's left hand rule)
` tan theta = ( v_(y))/(v_(x)) = (2)/(2sqrt(3))`
:. `theta = (pi)/(6)`
` Angle = ( arc)/(radius) = ( speed xx time)/( radius) `
:. (pi)/(6) = ( 4xx 10xx10^(-3))/(Mxx4//QB)` [ :. radius ` = ( Mv)/(QB)`]
:. ` B = ( 50 pi M)/( 3Q)`
`(a) and (c)` are the correct options.