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Question: A point charge q moves from point P to point S along the path PQRS in a uniform electric field \(\ov...

A point charge q moves from point P to point S along the path PQRS in a uniform electric field E→\overrightarrow{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

A

qaE

B

–qaE

C

q(a2+b2)E(\sqrt{a^{2} + b^{2})E}

D

3qEa2+b2\sqrt{a^{2} + b^{2}}

Answer

–qaE

Explanation

Solution

The work done is independent of the path followed and is

equal to (qE→) 6mu.r→\overrightarrow{E})\mspace{6mu}.\overrightarrow{r}, where r→\overrightarrow{r}=displacement vector

PSˉ=−ai^−bj^P\bar{S} = - a\widehat{i} - b\widehat{j}, while Eˉ=Ei^\bar{E} = E\widehat{i}

∴ work = qEˉ⋅rˉ=−qaE\bar{E} \cdot \bar{r} = - qaE