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 is ____ .

Solution

Physics sir · 3 steps

Multiply each charge by its own position vector, add them up, and multiply out every sign.

1. Use the definition. For a set of point charges, the dipole moment about the origin is the sum of each charge times its position vector. The net charge here is +q, not zero, so the answer depends on the origin. That is why the question fixes it.

   p⃗ = Σᵢ qᵢ r⃗ᵢ

   Charge	Position r⃗	q r⃗
   +2q	-3a ĵ	-6qa ĵ
   +3q	2a î	+6qa î
   -4q	-2a î	(-4q)(-2a) î = +8qa î

2. Add the terms. The î terms give 6qa + 8qa = 14qa. The only ĵ term is -6qa. So p⃗ = 14qa î - 6qa ĵ.
3. So. Taking 2qa out gives p⃗ = 2qa(7î - 3ĵ), which is option (a).

The idea to keep. Dipole moment of many charges is Σ qᵢr⃗ᵢ. A negative charge on the negative axis gives a positive term, so always multiply the signs out.

Answer from the NTA final answer key. Solution by PrepWiser.