Question

Charge $Q$ is given a displacement $\vec{r}=a \hat{i}+b \hat{j}$ in an electric field $\vec{E}=E_{1} \hat{i}+E_{2} \hat{j} .$ The work done is

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

Answer 1

Answer: (A)

$ W=\vec{F} \cdot \vec{r}=(Q \vec{E}) \cdot(\vec{r})=Q\left(E_{1} \hat{i}+E_{2} \hat{j}\right) \cdot(a \hat{i}+b \hat{j})$
$=Q E_{1} a+Q E_{2} b$