Three point charges +q, +2q and +Q are placed at the vertices of an equilateral triangle. If the potential energy of the system of three charges is zero, the value of Q in terms of q is

Step-by-step solution

Let the side length of the equilateral triangle be a . The total potential energy of the system of three charges is the sum of the potential energies of all pairs of charges: U = 1 4 ₀ ( q 2q a + 2q Q a + Q q a ) Given that the potential energy of the system is zero, U = 0 . 1 4 ₀ a (2q^2 + 2qQ + qQ) = 0 2q^2 + 3qQ = 0 q(2q + 3Q) = 0 Since q 0 , we have: 2q + 3Q = 0 Q = - 2q 3 Answer: -2q 3