Question

The electric filed intensity at all point in space is given by $\overrightarrow{E}=(\sqrt{3}\hat{i}-\hat{j})\text{V/m}$. The equipotential lines in $xy$ plane will be represented by :

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

The electric field is given by
$\overrightarrow{E}=(\sqrt{3}\hat{i}-\hat{j})$

Thus, $\overrightarrow{E}$ is uniform, hence equipotential field will be perpendicular to $\overrightarrow{E}$ and equally spaced.

$\tan \theta =\left|\begin{array}{c}\frac{Ey}{Ex}\end{array}\right|=\left|\begin{array}{c}\frac{1}{\sqrt{3}}\end{array}\right|$

$\therefore \theta ={30}^{\circ }$

Thus, $\overrightarrow{E}$ makes an angle $\theta ={30}^{\circ }$ from $x-$axis in clockwise direction.


Since, equipotential line will be perpendicular to $\overrightarrow{E}$, thus it makes ${60}^{\circ }$ angle with $+vex-$axis in anticlockwise direction.

Also, the direction of electric field is towards the low potential region.

$\therefore \left(c\right)$ is correct representation.