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. $\frac{1}{4\pi {\epsilon }_0}\frac{2q^2}{a}$
• C. $\frac{1}{4\pi {\epsilon }_0}\frac{3q^2}{a}$
• 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, $U_i=\frac{1}{4\pi {\epsilon }_0}\left[\frac{q\left(-2q\right)}{a}+\frac{q\left(-2q\right)}{a}+\frac{\left(-2q\right)\left(-2q\right)}{a}\right]$
$=\frac{1}{4\pi {\epsilon }_{0}a}\left[-2q^2-2q^2+4q^2\right]=0$
Similarly, $U_f$ is also zero.
Hence, $W=0$