Question

An electric charge $+q$ moves with velocity $10\hat{i}\text{m/s}$ in an electromagnetic field given by $\overrightarrow{E}=3\hat{i}+\hat{j}+2\hat{k}$ and $\overrightarrow{B}=\hat{i}+\hat{j}-3\hat{k}$. The $y$-component of the force experienced by $+q$ is equal to $xq$. Find the value of $x$. (All quantities are in SI units)

• A. 31
• B. 31.0
• C. 31.00

Answer 1

Answer: (A), (B), (C)

$\overrightarrow{F}=q\overrightarrow{E}+q\overrightarrow{v}\times \overrightarrow{B}$
$\Rightarrow F=q(3\hat{i}+\hat{j}+2\hat{k})+q\left(10\hat{i}\right)\times (\hat{i}+\hat{j}-3\hat{k})$
$\Rightarrow F=q(3\hat{i}+\hat{j}+2\hat{k}+10\hat{k}+30\hat{j})$
$\Rightarrow F=q(3\hat{i}+31\hat{j}+12\hat{k})$
$\therefore F_{\left(j\right)}=31q$