question_answer

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

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 \[2a\] is                                 \[W={{U}_{f}}-{{U}_{i}}\] Here, \[{{U}_{i}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\left[ \frac{q(-2q)}{a}+\frac{q(-2q)}{a}+\frac{(-2q)(-2q)}{a} \right]\]      \[=\frac{1}{4\pi {{\varepsilon }_{0}}a}[-2{{q}^{2}}-2{{q}^{2}}+4{{q}^{2}}]=0\] Similarly,\[{{U}_{f}}\]is also zero. Hence,  \[W=0\]