Question

A particle of mass $m$ and charge $q$ is in electric and magnetic field given by,
$\overrightarrow{E}=2\hat{i}+3\hat{j},\overrightarrow{B}=4\hat{j}+6\hat{k}.$
The charged particle is shifted from the origin to the point $P(x=1,y=1)$ along a straight path. The magnitude of the total work done is :

• A. $5q$
• B. $0.15)q$
• C. $\left(0.35\right)q$
• D. $\left(2.5\right)q$

Answer 1

The correct option is A $5q$

Resultant force on the charged particle is,

${\overrightarrow{F}}_{\text{net}}=q\overrightarrow{E}+q(\overrightarrow{v}\times \overrightarrow{B})$

$=(2q\hat{i}+3q\hat{j})+q(\overrightarrow{v}\times \overrightarrow{B})$

The particle is moving in $x-y$ plane while the magnetic field is in $y-z$ plane, so that, the work done by magnetic field will be equal to zero.
So, the required work done is given by,
$W={\overrightarrow{F}}_{\text{net}}.\overrightarrow{S}=(2q\hat{i}+3q\hat{j}).(\hat{i}+\hat{j})$
$=2q+3q=5q$

Hence, $\left(B\right)$ is the correct answer.