Question

Three point charges $q,\,-2q$ and $-2q$ are placed at the vertices of an equilateral triangle of side $a$ . The work done by some external force to increase their separation to $2a$ will be

• A. negative
• B. $\frac{1}{4\pi\varepsilon_{0}} \frac{2q^{2}}{a}$
• C. $\frac{1}{4\pi\varepsilon_{0}} \frac{3q^{2}}{a}$
• D. zero

Answer 1

Answer: (D)

zero

Answer 2

According to the question work done in increasing the separation from $a$ to $2a$ is $W=U_{f} - U_{i}$ Here, $U_{i} =\frac{1}{4\pi\varepsilon_{0}} \left[\frac{q\left(-2q\right)}{a} + \frac{q\left(-2q\right)}{a} + \frac{\left(-2q\right) \left(-2q\right)}{a}\right]$ $= \frac{1}{4\pi\varepsilon_{0}a}\left[-2q^{2} - 2q^{2} +4q^{2}\right]=0$ Similarly, $U_{f}$ is also zero. Hence, $W=0$