Question

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

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

Answer 1

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

$\overrightarrow{F_Q}=Q\overrightarrow{E}W=\overrightarrow{F_Q}\cdot \overrightarrow{r}$

$=Q(e_1\hat{i}+e_2\hat{j}+e_3\hat{k})\cdot (a\hat{i}+b\hat{j})=Q(e_{1}a+e_{2}b)=Q(a{e}_1+b{e}_2)$