Question

Two charges $q_1$ and $q_2$ are placed 30 cm apart, as shown in the figure.

A third charge $q_3$ is moved along the are of a circle of radius 40cm from C to D. The change in the potential energy of the system is $\frac{q_3}{4\pi {\epsilon }_0}$ k. where k is

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

Answer 1

Answer: (C)

The potential energy when $q_3$ is at point C
$U_1=\frac{1}{4\pi {\epsilon }_0}[\frac{q_1{q}_3}{0.40}+\frac{q_2{q}_3}{\sqrt{(0.40{)}^2+(0.30{)}^2}}]$
The potential energy when $q_3$ is at point D
$U_2=\frac{1}{4\pi {\epsilon }_0}[\frac{q_1{q}_3}{0.40}+\frac{q_2{q}_3}{0.10}]$
Thus change in potential energy is

$△U=U_2-U_1$
$\Rightarrow \frac{q_3}{4\pi {\epsilon }_0}=k$
= $\frac{1}{4\pi {\epsilon }_0}[\frac{q_1{q}_3}{0.40}+\frac{q_2{q}_3}{0.10}-\frac{q_1{q}_3}{0.40}-\frac{q_2{q}_3}{0.50}]$
$\Rightarrow k=\frac{5q_2-q_2}{0.50}=\frac{4q_2}{0.50}=8q_2$.