Question

A particle of mass $M$ and positive charge $Q$, moving with a constant velocity $u _{1}=4 \hat{i}ms ^{-1}$, 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 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: (C)

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

Answer 2

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