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)

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 $