question_answer

Three point charges q, - 2 q and -2 q 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)  \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{2{{q}^{2}}}{a}\]

C)  \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{3{{q}^{2}}}{a}\]                             

D)  zero

Correct Answer: D

Solution :

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