A point charge q moves from point P to S along the path PQRS in a uniform electric field $\vec{E}$ pointing parallel to the positive direction of the x-axis. The coordinate of the point P, Q, R and S are (a, b, 0), (2a, 0, 0), (a, −b, 0) and (0, 0, 0) respectively. The work done by the field in the above process is given by the expression
Answer & explanation
Correct answer: option 2
The work done is independent of the path followed and is equal to $(q \vec{E}) . \vec{r}$
where $\vec{r}=$ displacement from P to S
Here, $\vec{r}=a \hat{i}-b \hat{j}$, while $\vec{E}=E \hat{i}$
∴ work = $-(q E \hat{i}) . (a \hat{i}+b \hat{j})=-q a E$
Hence, B is correct choice.