A point charge q moves from point P to point S along the path PQRS in a uniform electric field E pointing parallel to the positive direction of the x-axis. The coordinate of the points 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 |
qaE -qaE q$(\sqrt{a^2+b^2})E$ $3qE\sqrt{a^2+b^2}$ |
-qaE |
The work done is independent of the path followed and is equal to $(q \vec{E}) . \vec{r}$, where $\vec{r}$ = displacement vector $\overline{PS}=-a \hat{i}-b \hat{j}$, while $\overline{E}=E \hat{i}$ ∴ Work = $q \overline{E} . \overline{r}=-qaE$ ∴ (B) |