A particle of mass M and positive charge Q, moving with a constant velocity \left(\overset{\rightarrow}{u}\right)_{1} = 4 \hat{i} \textrm{ }\textrm{ } \left(ms\right)^{- 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 value of y. After passing through this region, the particle emerges on the other side after 10 milliseconds with velocity \left(\overset{\rightarrow}{u}\right)_{2} = 2 \left(\right. \sqrt{3} \textrm{ } \hat{i} + \hat{j} \left.\right) \textrm{ }\textrm{ } \left(ms\right)^{- 1} . The correct statement(s) is (are)

Engineering

Physics

Magnetic Field

Motion of Charged Particle in Uniform Magnetic Field

Lorentz Force

Question

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 value of y. After passing through this region, the particle emerges on the other side after 10 milliseconds with velocity ${\vec{u}}_{2} = 2 (\sqrt{3} \hat{i} + \hat{j}) {ms}^{- 1}$ . The correct statement(s) is (are)

The direction of the magnetic field is –z direction

The direction of the magnetic field is +z direction

The magnitude of the magnetic field $\frac{50 πM}{3 Q}$ units.

The magnitude of the magnetic field is $\frac{100 πM}{3 Q}$ units.

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30º $\to$ 10 ms

360º $\to$ 120 ms

$120 \times 1 0^{- 3} = \frac{2 πM}{QB}$

$B = \frac{πM}{QB} \times \frac{10^{3}}{60}$