The electrostatic potential due to an electric dipole at a distance 'r' varies as :

Solution

Physics sir · 3 steps

Two opposite charges almost cancel each other's potential, so one extra power of r appears: 1/r².

1. Start from two charges. A dipole is +q and -q separated by 2a, with dipole moment p = q × 2a. The potential at a point is the sum of kq/r₁ and -kq/r₂.
2. Nearly cancelling terms. Far from the dipole, r₁ and r₂ differ only by about 2a cos θ. The two 1/r terms almost cancel, and what is left carries an extra factor of (2a cos θ)/r.

   V = 1/4πε₀ (p cos θ)/r²

3. So. For a fixed direction θ, the dipole potential falls off as 1/r², which is option (c).

The idea to keep. Each step up from a single charge to a dipole adds one power of r. A point charge gives V ∝ 1/r and E ∝ 1/r². A dipole gives V ∝ 1/r² and E ∝ 1/r³.

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