Q. The displacement of a charge $Q$ in the electric field $\overrightarrow{E} = e_{1}\widehat{i} + e_{2}\widehat{j} + e_{3}\widehat{k}$ is $\overrightarrow{r} = a\widehat{i} + b\widehat{j}$. The work done is
A) $Q(ae_{1} + be_{2})$
B) $Q\sqrt{\left( ae_{1} \right)^{2} + \left( be_{2} \right)^{2}}$
C) $Q(e_{1} + e_{2})\sqrt{a^{2} + b^{2}}$
D) $Q\left( \sqrt{e_{1}^{2} + e_{2}^{2}} \right)(a + b)$
Explanation
(a) By using $W = Q(\overrightarrow{E}.\mathrm{\Delta}\overrightarrow{r})$
$\Rightarrow W = Q\left\lbrack \left( e_{1}\widehat{i} + e_{2}\widehat{j} + e_{3}\widehat{k} \right).\left( a\widehat{i} + b\widehat{j} \right) \right\rbrack = Q(e_{1}a + e_{2}b)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.