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 $\hat{r}=a\hat{1}+b\hat{j}$. The work done is-

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

Answer 1

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

The work done,$W=\overrightarrow{F}.\hat{r}=Q\overrightarrow{E}.\hat{r}$
$W=Q(e_1\hat{i}+e_2\hat{j}+e_3\hat{k}).(a\hat{i}+b\hat{j})$
$W=Q(a{e}_1+b{e}_2)$