Question

A particle of specific charge $\frac{\text{q}}{\text{m}}=\pi Ck{g}^{-1}$ is projected from the origin towards positive x-axis with a velocity of $10m{s}^{-1}$ in a uniform magnetic field $\overrightarrow{B}=-2\hat{\text{k}}T$ . The velocity $\overrightarrow{v}$ of the particle after time $t=\frac{1}{12}s$ will be (in $m{s}^{-1}$ )

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

Answer 1

Answer: (B)

Time period, $\text{T}=\frac{2\pi \text{m}}{\text{qB}}=\frac{2\pi }{\pi \times 2}=1s$
Thus, the particle will be at point P after $\text{t}=\frac{1}{12}\text{s}$

$\overrightarrow{v}=10\left[cos30\hat{\text{i}}+\text{sin }30\hat{\text{j}}\right]$
$\overrightarrow{v}=10\left[\frac{\sqrt{3}}{2}\hat{\text{i}}+\frac{1}{2}\hat{\text{j}}\right]=5\left[\sqrt{3}\hat{\text{i}}+\hat{\text{j}}\right]{\text{m s}}^{-1}$