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. $Q\sqrt{(E_1^2+E_2^2)}\sqrt{a^2+b^2}$

Answer 1

Answer: (A)

$Q(E_{1}a+E_{2}b)$

The force on the charge Q is $\overrightarrow{F}=Q\overrightarrow{E}$
The work done , $W=\overrightarrow{F}.\overrightarrow{r}=Q\overrightarrow{E}.\overrightarrow{r}=Q(E_1\hat{i}+E_2\hat{j}).(a\hat{i}+b\hat{j})=Q(E_{1}a+E_{2}b)$