Question

There is an electric field $E$ in the $\text{x-}$direction. If the work done by electric field in moving a charge of $0.2\text{C}$ through a distance of $2\text{m}$ along a line making an angle ${60}^{\circ }$ with the $\text{x-}$axis is $4\text{J}$, then what is the value of $E$ ?

• A. $\sqrt{3}{\text{NC}}^{-1}$
• B. $4{\text{NC}}^{-1}$
• C. $5{\text{NC}}^{-1}$
• D. $20{\text{NC}}^{-1}$

Answer 1

The correct option is D $20{\text{NC}}^{-1}$

Work done $W$, by electric field $E$, in moving charge through distance $d$ is given by,
$W=\overrightarrow{F}\cdot \overrightarrow{d}=Fd\cos \theta =qEd\cos \theta$

Given,

$W=4\text{J}$, $d=2\text{m}$, $\theta ={60}^{\circ }$, $q=0.2\text{C}$,

Substituting the values in the above equation, we get
$4=0.2\times E\times 2\times \cos {60}^{\circ }$

$\therefore E=20{\text{NC}}^{-1}$

Hence, option (d) is the correct answer.