Question

An electric charge $+q$ moves with velocity $\overrightarrow{v}=3\hat{i}+4\hat{j}+\hat{k}$ in the presence of electric and magnetic fields 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 ?

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

Answer 1

The correct option is B $11q$

Using Lorentz's force equation,

$\overrightarrow{F}=q(\overrightarrow{E}+(\overrightarrow{v}\times \overrightarrow{B}\left)\right)$

Given,

$\overrightarrow{E}=3\hat{i}+\hat{j}+2\hat{k}\overrightarrow{V}=3\hat{i}+4\hat{j}+\hat{k}\overrightarrow{B}=\hat{i}+\hat{j}-3\hat{k}$

Putting values in $\overrightarrow{F}$ we get,


$\overrightarrow{F}=q[3\hat{i}+\hat{j}+2\hat{k}+(3\hat{i}+4\hat{j}+\hat{k})\times (\hat{i}+\hat{j}-3\hat{k}\left)\right]$

$=q[3\hat{i}+\hat{j}+2\hat{k}+3\hat{k}+9\hat{j}-4\hat{k}-12\hat{i}+\hat{j}-\hat{i}]$

$\overrightarrow{F}=q[-10\hat{i}+11\hat{j}+\hat{k}]$

$|{\overrightarrow{F}}_y|=11q$

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

Why this question ? To familiarize oneself how to use Lorentz force equation in different scenarios and to make vector calcualtion familiar.