Question

The displacement of a charge Q in the electric field $E = e_{1}\widehat{i} + e_{2}\widehat{j} + e_{3}\widehat{k}$ is $\widehat{r} = a\widehat{i} + b\widehat{j}$. The work done is

• A. $Q(ae_{1} + be_{2})$
• B. $Q\sqrt{(ae_{1})^{2} + (be_{2})^{2}}$
• C. $Q(e_{1} + e_{2})\sqrt{a^{2} + b^{2}}$
• D. $Q(\sqrt{e_{1}^{2} + e_{2}^{2})}\mspace{6mu}(a + b)$

Answer 1

Answer: (A)

$Q(ae_{1} + be_{2})$

Answer 2

By using $W = Q(\overset{\rightarrow}{E}.\Delta\overset{\rightarrow}{r})$

⇒$W = Q\lbrack(e_{1}\widehat{i} + e_{2}\widehat{j} + e_{3}\widehat{k}).(a\widehat{i} + b\widehat{j})\rbrack = Q(e_{1}a + e_{2}b)$