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

Step-by-step solution

The electrostatic potential energy of the system is the sum of pairwise interactions between the three charges. Let Q₁ = Q , Q₂ = -2q , and Q₃ = -2q be placed at the vertices of an isosceles right triangle with legs of length l . For charges separated by distance r , the potential energy is U = k q_a q_b r , where k = 1 4 ₀ . The pairwise distances are: r₁₂ = l , r₁₃ = l , and r₂₃ = l 2 . The total potential energy is: U_ total = k ( Q(-2q) l + Q(-2q) l + (-2q)(-2q) l 2 ) Simplifying: U_ total = k (- 4Qq l + 4q^2 l