Three point charges Q, +2q and +q are placed at the vertices of a right-angled isosceles triangle of length 2 a as shown in figure. The net electrostatic potential energy of the configuration is zero, if Q is equal to

Step-by-step solution

The net electrostatic potential energy of a system of three charges is given by the sum of the potential energies of all pairs of charges. Let the charges be q₁ = Q , q₂ = 2q , and q₃ = q . From the given right-angled isosceles triangle, the distances between the charges are: Distance between Q and 2q , r₁₂ = 2 a Distance between Q and q , r₁₃ = 2 a Distance between 2q and q (hypotenuse), r₂₃ = ( 2 a)^2 + ( 2 a)^2 = 2a^2 + 2a^2 = 4a^2 = 2a The net potential energy U is: U = 1 4 ₀ ( q₁ q₂ r₁₂ + q₁ q₃ r₁₃ + q₂ q₃ r₂₃