Question

A uniform electric field exists in space. No work is required to be done to move a charge on the line $y=x$. Which of the following may represent the direction of electric field?

• A. $\hat{i}+\hat{j}$
• B. $\hat{i}-\hat{j}$
• C. $-\hat{i}-\hat{j}$
• D. $-\hat{i}+\hat{j}$

Answer 1

Answer: (B), (D)

$-\hat{i}+\hat{j}$

Given, line $y=x$

We know that, work done, $w=q\Delta V$

As there is no work done along the line $y=xi.e.$ the line represent equipotential line.

And as we know that, equipotential surface is always perpendicular to electric field.

Hence, the possible direction of electric field is $\hat{i}-\hat{j}$ or $-\hat{i}+\hat{j}$.

Therefore, options $\left(B\right)$ and $\left(D\right)$ are correct.