Question

An electric charge $+q$ moves the velocity $\overrightarrow{V}=3\hat{i}+4\hat{j}+\hat{k}$ , in an electromagnetic field given by:
$\overrightarrow{E}=3\hat{i}+\hat{j}+2\hat{k}$ and $\overrightarrow{B}=\hat{i}+\hat{j}-\widehat{3k}$. The $y-$component of the force experienced by $q$ is :

• A. $3q$
• B. $2q$
• C. $11q$
• D. $5q$

Answer 1

The correct option is C $11q$

The charge Experiences both Electric magnetic Force, $(\overrightarrow{Fe},\overrightarrow{Fm})$

Given by :

$\overrightarrow{Fe}=q\overrightarrow{E}=q(3\hat{i}+\hat{j}+2\hat{k})$

and, $\overrightarrow{Fm}=q(\overrightarrow{V}\times \overrightarrow{B})$

$q=\left[\right(3\hat{i}+4\hat{j}+\hat{k})\times (\hat{i}+\hat{j}-3\hat{k}\left)\right]$

$q=(-13\hat{i}+10\hat{j}-\hat{k})$

Thus,

Net force on charge :

$\overrightarrow{F}=\overrightarrow{Fe}+\overrightarrow{Fm}$

$\overrightarrow{F}=q(-10\hat{i}+11\hat{j}+\hat{k})N$

$\therefore$ y-component of $\overrightarrow{F}=11q$