Question

An electric charge $+q$ moves with velocity $\vec{v}=3\hat{i}+\hat{k},$ in an electromagnetic field given by : $\vec{E}=3\hat{i}+\hat{j}+2\hat{k}$ and $\vec{B}=\hat{i}+\hat{j}+3\hat{k}.$ The $y$ - component of the force experienced by $+q$ is :

• A. 11 q
• B. 5 q
• C. 3 q
• D. 2 q

Answer 1

Answer: (A)

$\vec{F}=q\left[\vec{E}+\vec{v}\times \vec{B}\right]$
$=q\left[\begin{array}{c}3\hat{i}+\hat{j}+\hat{k}+\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& 4& 1\\ 1& 1& -3\end{array}\right|\end{array}\right]$
$=q\left[3\hat{i}+\hat{j}+2\hat{k}+\hat{i})-12-1)-\hat{j}\left(-9-1\right)+\hat{k}\left(3-4\right)\right]$
$=q\left[3\hat{i}+\hat{j}+2\hat{k}-13\hat{i}+10\hat{j}-\hat{k}\right]$
$=q\left[-10\hat{i}+11\hat{j}+\hat{k}\right]$
$=F_y=11q\hat{j}.$