Question

A particle of specific charge $\frac{\textit{q}}{\textit{m}}=\pi \, C \, kg^{- 1}$ is projected from the origin towards positive x-axis with a velocity of $10 \, m \, s^{- 1}$ in a uniform magnetic field $\overset{ \rightarrow }{B}=-2 \, \hat{\text{k}} \, T$ . The velocity $\overset{ \rightarrow }{v}$ 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, $\text{T} = \frac{2 \pi \text{m}}{\text{qB}} = \frac{2 \pi }{\pi \times 2} = 1 s$
Thus, the particle will be at point P after $\text{t}=\frac{1}{1 2} \, \text{s}$

$\overset{ \rightarrow }{\text{v}} = 1 0 \left[cos 3 0 \hat{\text{i}} + \text{sin } 3 0 \hat{\text{j}}\right]$
$\overset{ \rightarrow }{\text{v}} = 1 0 \left[\frac{\sqrt{3}}{2} \hat{\text{i}} + \frac{1}{2} \hat{\text{j}}\right] = 5 \left[\sqrt{3} \hat{\text{i}} + \hat{\text{j}}\right] \text{m s}^{- 1}$