Question

Two charges $q$${}_1$ and $q$${}_2$ are placed $30cm$ apart as shown in figure. A third charge $q$${}_3$ is moved along the arc of a circle of radius $40cm$ from C to D. The change in potential energy of the system is $\frac{q_{3}k}{4\pi {\epsilon }_0}$ where k is :

• A. 8q${}_1$
• B. 6q${}_1$
• C. 8q${}_2$
• D. 6q${}_2$

Answer 1

Answer: (C)

8q${}_2$

The potential energy of the system of three point charges is given by-

$$U=\frac{1}{4\pi {ϵ}_o}(\frac{q_1{q}_2}{r_{12}}+\frac{q_2{q}_3}{r_{23}}+\frac{q_3{q}_1}{r_{31}})$$

In the above energy equation only one term will change in displacing charge $q_3$ from C to D, other two terms will be unchanged. Because the distance between $q_1$ and $q_3$ will remain unchanged in moving the charge $q_3$ from C to D.

Thus the change in potential energy of the system is the change in the second term only, or,

$$\Delta U=\frac{q_2{q}_3}{4\pi {ϵ}_o}(\frac{1}{0.1}-\frac{1}{0.5})=\frac{8q_2{q}_3}{4\pi {ϵ}_o}$$