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Question:

A particle of mass M and positive charge Q, moving with a constant velocity u1=4î m/s, 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 u2=2(√3î+ĵ)m/s. The correct statement(s) is (are).

The direction of the magnetic field is +z direction.

The magnitude of the magnetic field is 100πM/3Q units.

The direction of the magnetic field is -z direction.

The magnitude of the magnetic field is 50πM/3Q units.

Solution:

The correct options are
A. The direction of the magnetic field is -z direction.
C. The magnitude of the magnetic field is 50πM/3Q units.
Sol. (A, C)
So magnetic field is along -ve, z-direction.
Time taken in the magnetic field = 10 × 10⁻³ = 10⁻² s
B = πM/6Q
B = πM/(60 × 10⁻³Q) = 1000πM/60Q = 50πM/3Q