Question

A particle of specific charge $q / m=\pi C\, kg ^{-1}$ is projected from the origin toward positive $x$-axis with a velocity of $10 \,m s ^{-1}$ in a uniform magnetic field $\vec{B}=-2 \hat{k} T$. The velocity $\vec{v}$ of particle after time $t=1 / 12 s$ will be $\left(\right.$ in $\left.m s ^{-1}\right)$

• A. $5[\hat{i}+\sqrt{3} \hat{j}]$
• B. $5[\sqrt{3} \hat{i}+\hat{j}]$
• C. $5[\sqrt{3} \hat{i}-\hat{j}]$
• D. $5[\hat{i}+\hat{j}]$

Answer 1

Answer: (B)

Time period, $T=\frac{2 \pi m}{q B}=\frac{2 \pi}{\pi \times 2}=1 \,s$

Thus, particle will be at point $P$ after $t=\frac{1}{12} s$
$\vec{v}=10[\cos 30 \hat{i}+\sin 30 \hat{j}]$
$\vec{v}=10\left[\frac{\sqrt{3}}{2} \hat{i}+\frac{1}{2} \hat{j}\right]=5[\sqrt{3} \hat{i}+\hat{j}] ms ^{-1}$