Question

A particle of mass M and positive charge Q, moving with a constant velocity $u_1=4\hat{i}m{s}^{-1}$
, 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 $y.A$fter passing through this region, the particle emerges on the other side after 10 milliseconds with a velocity ${\overrightarrow{u}}_2=2(\sqrt{3}\hat{i}+\hat{j})m/s^{-1}$.The correct statement(s) is (are).

• A. The direction of the magnetic field is-z direction.
• B. The direction ofthe magnetic field $is+z$direction.
• C. The magnitude ofthe magnetic field $\frac{50\pi M}{3Q}$ units.
• D. The magnitude ofthe magnetic field is $\frac{100\pi M}{3Q}$units.

Answer 1

Answer: (A), (C)

The correct options are
A The direction of the magnetic field is-z direction.
C The magnitude ofthe magnetic field $\frac{50\pi M}{3Q}$ units.

$Sol.(A,C)$
So magnetic field is along-ve, z-direction.
Time taken in the magnetic field $=10\times {10}^{-3}=\frac{\pi M}{6QB}$
$B=\frac{\pi M}{60\times {10}^{-3}Q}=\frac{1000\pi M}{60Q}$

$=\frac{50\pi M}{3Q}$