Two charges of equal magnitude ' q ' are placed in air at a distance ' 2 r ' apart and third charge ' -2 q ' is placed at mid point. The potential energy of the system is ( ₀= . permittivity of free space)

Step-by-step solution

Potential energy of ' n ' point charges, U = 1 4 ₀ _ all pairs q _ j q _ k r _ jk For 3 point charges, aligned & U=- q(2 q) 4 ₀ r - q(2 q) 4 ₀ r + q(q) 4 ₀(2 r) & U=- 2 q^2 4 ₀ r - 2 q^2 4 ₀ r + q^2 4 ₀(2 r) & U=- 4 q^2 8 ₀ r - 4 q^2 8 ₀ r + q^2 8 ₀ r & U=- 7 q^2 8 ₀ r aligned