Question

Charge $Q$ is given a displacement $\overrightarrow{r}=a\hat{i}+b\hat{j}$ in an electric field $\overrightarrow{E}=E_1\hat{i}+E_2\hat{j}$. The work done is :

• A. $Q(E_{1}a+E_{2}b)$
• B. $Q\sqrt{(E_{1}a{)}^2+(E_{2}b{)}^2}$
• C. $Q(E_1+E_2)\sqrt{a^2+b^2}$
• D. $Q\sqrt{(E_1^2+E_2^2{)}^2}\sqrt{a^2+b^2}$

Answer 1

The correct option is A $Q(E_{1}a+E_{2}b)$

Work done in the presence of electric field E is $W=\overrightarrow{F}.\overrightarrow{r}=q\overrightarrow{E}.\overrightarrow{r}$
$W=Q\left[\right(E_1\hat{i}+E_2\hat{j}).(a\hat{i}+b\hat{j}\left)\right]$
$W=Q(E_{1}a+E_{2}b)$