Three charges +2q, +3q and -4q are situated at (0, -3a), (2a, 0) and (-2a, 0) respectively in the xy plane. The resultant dipole moment about origin i $s___$
Options

Question

Three charges +2q, +3q and -4q are situated at (0, -3a), (2a, 0) and (-2a, 0) respectively in the xy plane. The resultant dipole moment about origin i s___

G1 Physics · Accepted Answer

The electric dipole moment of a collection of point charges about the chosen origin is p⃗ = Σqᵢr⃗ᵢ. For the charge +2q at (0, -3a), p⃗₁ = 2q(-3aĵ) = -6qaĵ. For the charge +3q at (2a, 0), p⃗₂ = 3q(2aî) = 6qaî. For the charge -4q at (-2a, 0), p⃗₃ = (-4q)(-2aî) = 8qaî. Therefore, p⃗ = p⃗₁+p⃗₂+p⃗₃ = 14qaî-6qaĵ = 2qa(7î-3ĵ). Correct option: C.