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 $y$. After passing through this region, the particle emerges on the other side after 10 milliseconds with a velocity ${\vec{u}}_2=2(\sqrt{3}i+\hat{j})m/s^{-1}$. The correct statement(s) is (are)

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

Answer 1

Answer: (A), (C)

So magnetic field is along $-ve,z$-direction.
Time taken in the magnetic field $=10\times 10^{-3}=\frac{\pi M}{6QB}$
$B=\frac{\pi M}{60\times 10^{-3}Q}=\frac{1000\pi M}{60Q}$
$=\frac{50\pi M}{3Q}$