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 $\frac{q_3}{4\pi {\epsilon }_o}k$, where $k$ is

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

Answer 1

Answer: (C)

The potential energy when $q_3$ is at point $C$
$U_1=\frac{1}{4\pi {\epsilon }_0}\left[\frac{q_1{q}_3}{0.40}+\frac{q_2{q}_3}{\sqrt{(0.40{)}^2+(0.30{)}^2}}\right]$
The potential energy when $q_3$ is at point D
$U_2=\frac{1}{4\pi {\epsilon }_0}\left[\frac{q_1{q}_3}{0.40}+\frac{q_2{q}_3}{0.10}\right]$
Thus charge in potential energy is $\Delta U=U_2-U_1$
$\Rightarrow \frac{q_3}{4\pi {\epsilon }_0}k=\frac{1}{4\pi {\epsilon }_0}\left[\frac{q_1{q}_3}{0.40}+\frac{q_2{q}_3}{0.10}-\frac{q_1{q}_3}{0.40}-\frac{q_2{q}_3}{0.50}\right]$
$\Rightarrow k=\frac{5q_2-q_2}{0.50}=\frac{4q_2}{0.50}=8q_2$