A particle of mass M and positive charge Q, moving with a constant velocity enters a region of uniform static magnetic field, normal to the plane. The region of the magnetic field extends from to for all values of . After passing through this region,

Question

A particle of mass M and positive charge Q, moving with a constant velocity ${\vec{u}}_{1} = 4 \hat{i} {m s}^{- 1},$ 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) [2013]

Smart Achievers · Accepted Answer

(1, 3)

According to Fleming's left-hand rule, magnetic field should be in the $- z$ direction.

From figure, $\tan θ = \frac{v_{y}}{v_{x}} = \frac{2}{2 \sqrt{3}}$

$∴$ $θ = \frac{π}{6}$

Angle rotated by the particle $= \frac{arc}{radius} = \frac{speed \times time}{radius}$

$\frac{π}{6} = \frac{4 \times 10 \times 10^{- 3}}{M \times v / Q B}$ $[∵ radius = \frac{M v}{Q B}]$

$∴$ $B = \frac{50 π M}{3 Q}$

Solution

1 The direction of the magnetic field is $- z$ direction.

2 The direction of the magnetic field is $+ z$ direction.

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

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

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Solution

1 The direction of the magnetic field is -z direction.

2 The direction of the magnetic field is +z direction.

3 The magnitude of the magnetic field is 50πM3Q units.

4 The magnitude of the magnetic field is 100πM3Q units.

Ans. (1, 3) According to Fleming's left-hand rule, magnetic field should be in the -z direction. From figure, tanθ=vyvx=223 ∴ θ=π6 Angle rotated by the particle =arcradius=speed×timeradius π6=4×10×10-3M×v/QB [∵ radius=MvQB] ∴ B=50πM3Q

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1 The direction of the magnetic field is $- z$ direction.

2 The direction of the magnetic field is $+ z$ direction.

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

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