Question

The displacement of a charge Q in the electric field $E=e_1\hat{i}+e_2\hat{j}+e_3\hat{k}$ is $\hat{r}=a\hat{i}+b\hat{j}$. The work done is

• A. $Q(a{e}_1+b{e}_2)$
• B. $Q\sqrt{(a{e}_1{)}^2+(b{e}_2{)}^2}$
• C. $Q(e_1+e_2)\sqrt{a^2+b^2}$
• D. $Q\left(\sqrt{e_1^2+e_2^2}\right)(a+b)$

Answer 1

The correct option is A $Q(a{e}_1+b{e}_2)$

By using $W=Q(\stackrel{\rightharpoonup }{E}.\Delta \stackrel{\rightharpoonup }{r})$
$\Rightarrow W=Q\left[\right(e_1\hat{i}+e_2\hat{j}+e_3\hat{k}).(a\hat{i}+b\hat{j}\left)\right]=Q(e_{1}a+e_{2}b)$