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

Answer

a, c

Explanation

According to YA given velocity particle should move in the first quadrant. So magnetic field is along negative, direction. Hence option (a) is correct.

Angle rotated inside magnetic field can be written as follows:
` tan theta = v_(y)/v_(x) = - 1/sqrt3 rArr theta = pi/6`
Time taken to cross the magnetic field can be written as follows:
` t = theta/(2pi) (2 pi M)/(QB) = (pi M)/(6 Q B)`
Time taken in the magnetic field ` = 10 xx 10^(-3) = (pi M)/(6 QB) `
` B = (pi M)/(60 xx 10^(-3) Q) = (1000 pi M)/(60 Q) = (50 pi M)/(3Q)`
We can see that option (c) is also correct.