Three point charges +Q+2 Q and q are placed at the vertices of an equilateral triangle. The value of charge q in terms of Q , so that electrical potential energy of the system is zero, is given by

Step-by-step solution

For the system's electrical potential energy to be zero, the total potential energy must satisfy U_ total = 0 . The potential energy between two charges q₁ and q₂ separated by distance a is k q₁ q₂ a , where k = 1 4 ₀ . The three pairs contribute: U₁₂ = k(Q)(2Q) a = 2kQ^2 a U₁₃ = kQq a U₂₃ = k(2Q)q a = 2kQq a Summing these gives U_ total = k a (2Q^2 + 3Qq) . Setting this equal to zero and solving yields 2Q^2 + 3Qq = 0 , so q = - 2 3 Q . Final answer: C