Question

Charges Q1, Q2, and Q3 are at (-d,0), (0,0), and (d,0). Q1=Q3, Q2>0. Find the nature and value of Q1 for zero potential energy.

Hint:

Potential energy of a system of charges.

Answer 1

U = (1/4πε₀)[(Q₁Q₂/r₁₂) + (Q₂Q₃/r₂₃) + (Q₁Q₃/r₁₃)]. r₁₂ = d, r₂₃ = d, r₁₃ = 2d. For U=0: Q₁Q₂ + Q₂Q₃ + Q₁Q₃/2 = 0. Since Q₁ = Q₃: 2Q₁Q₂ + Q₁²/2 = 0. Solving gives Q₁ = -4Q₂.