The electric field due to a short electric dipole at a large distance (r) from center of dipole on the equatorial plane varies with distance as :

Solution

Physics sir · 3 steps

Two opposite charges almost cancel far away, so a dipole's field falls one power faster than 1/r².

1. Set up. Take charges +q and -q a distance 2a apart, with dipole moment p = q × 2a. A point on the equatorial plane at distance r is √(r² + a²) from each charge.
2. Add the components. Both charges give fields of equal size kq/(r² + a²). Their components along the perpendicular bisector cancel. The components parallel to the dipole axis add, each carrying a factor a/√(r² + a²).

   E = (k (2qa))/(r² + a²)^(3/2) ≈ kp/r³ (r ≫ a)

3. So. For a short dipole at a large distance, E ∝ 1/r³, which is option (d).

The idea to keep. Point charge: 1/r². Dipole, on the axis or the equator: 1/r³. The axial field 2kp/r³ is just twice the equatorial field kp/r³.

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