Question

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

Answer 1

Answer: (D)

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