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)

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