Electrostatics Question 376

Question: Two equal charges $ q $ are placed at a distance of $ 2a $ and a third charge $ -2q $ is placed at the midpoint. The potential energy of the system is [MP PMT 1997]

Options:

A) $ \frac{q^{2}}{8\pi {\varepsilon _{0}}a} $

B) $ \frac{6q^{2}}{8\pi {\varepsilon _{0}}a} $

C) $ -\frac{7q^{2}}{8\pi {\varepsilon _{0}}a} $

D) $ \frac{9q^{2}}{8\pi {\varepsilon _{0}}a} $

Show Answer

Answer:

Correct Answer: C

Solution:

$ U _{system}=\frac{1}{4\pi {\varepsilon _{0}}}\frac{(q)(-2q)}{a}+\frac{1}{4\pi {\varepsilon _{0}}}\frac{(-2q)(q)}{a}+\frac{1}{4\pi {\varepsilon _{0}}}\frac{(q)(q)}{2a} $

$ U _{system}=-\frac{7q^{2}}{8\pi {\varepsilon _{0}}a} $



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