Question

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

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

Answer 1

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

$\overrightarrow{F}=Q\overrightarrow{E}$

$W=\overrightarrow{r}.\overrightarrow{F}$

$⟹W=Q\overrightarrow{r}.\overrightarrow{E}$

$⟹W=Q(e_1\hat{i}+e_2\hat{j}+e_3\hat{k}).(a\hat{i}+b\hat{j})$

$⟹W=Q(a{e}_1+b{e}_2)$

Answer-(C)