Question

A charged particle carrying charge $1\mu \text{C}$ is moving with velocity $(2\hat{i}+3\hat{j}+4\hat{k}){\text{ms}}^{-1}.$ If an external magnetic field of $(5\hat{i}+3\hat{j}-6\hat{k})\times {10}^{-3}\text{T}$ exists in the region where the particle is moving then the force on the particle $\overrightarrow{F}\times {10}^{-9}\text{N}.$ The vector $\overrightarrow{F}$ is-

• A. $-0.30\hat{i}+0.32\hat{j}-0.09\hat{k}$
• B. $-30\hat{i}+32\hat{j}-9\hat{k}$
• C. $-300\hat{i}+320\hat{j}-90\hat{k}$
• D. $-3.0\hat{i}+3.2\hat{j}-0.9\hat{k}$

Answer 1

The correct option is B $-30\hat{i}+32\hat{j}-9\hat{k}$

$\text{Given},q=1\mu \text{C}=1\times {10}^{-6}\text{C}$

$\overrightarrow{V}=(2\hat{i}+3\hat{j}+4\hat{k}){\text{ms}}^{-1}\text{and}$

$\overrightarrow{B}=(5\hat{i}+3\hat{j}-6\hat{k})\times {10}^{-3}\text{T}$

$\overrightarrow{F}=q(\overrightarrow{V}\times \overrightarrow{B})={10}^{-6}\times {10}^{-3}\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& 3& 4\\ 5& 3& -6\end{array}\right|$

$=(-30\hat{i}+32\hat{j}-9\hat{k})\times {10}^{-9}\text{N}$

$\therefore \overrightarrow{F}=(-30\hat{i}+32\hat{j}-9\hat{k})$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.