Question

Two charges $q_1$ and $q_2$ are placed $30cm$ apart, as shown in the figure. A third charge $q_3$ is moved along the arc of a circle of radius $40cm$ from $C$ to $D$ . The change in the potential energy of the system is $\frac{q_3}{4\pi {\in }_o}k$ where $k$ is -

• A. $8q_1$
• B. $6q_1$
• C. $8q_2$
• D. $6q_2$

Answer 1

Answer: (C)

$U_{\text{1}}\text{ =}\frac{{\text{kq}}_{\text{1}}{\text{q}}_{\text{3}}}{4\pi {ϵ}_0\times \text{0.4}}\text{+}\frac{{\text{kq}}_{\text{1}}{\text{q}}_{\text{2}}}{4\pi {ϵ}_0\times \text{0.3}}\text{+}\frac{{\text{kq}}_{\text{2}}{\text{q}}_{\text{3}}}{4\pi {ϵ}_0\times \text{0.5}}$
$U_{\text{2}}\text{=}\frac{{\text{kq}}_{\text{1}}{\text{q}}_{\text{2}}}{4\pi {ϵ}_0\times \text{0.3}}\text{+}\frac{{\text{kq}}_{\text{2}}{\text{q}}_{\text{3}}}{4\pi {ϵ}_0\times \text{0.1}}\text{+}\frac{{\text{kq}}_{\text{1}}{\text{q}}_{\text{3}}}{4\pi {ϵ}_0\times \text{0.4}}$
$\therefore \Delta U=\frac{8k{q}_2{q}_3}{4\pi {\left(ϵ\right)}_0}=8q_2\left(\frac{q_3}{4\pi {\left(ϵ\right)}_0}\right)\Rightarrow k=8q_2$