The electric potential due to an electric dipole depends on

The correct answer is Option (4) → dipole moment, distance from the dipole and the angle between the position vector and the dipole moment vector

For a dipole of moment \( p \), the potential at a point at distance \( r \) from its centre, with the position vector making an angle \( \theta \) with the dipole moment, is (for \( r \) much larger than the dipole length)

    \( \displaystyle V = \frac{1}{4\pi\varepsilon_0}\,\frac{p\cos\theta}{r^{2}} \)

So the potential depends on all three: the dipole moment \( p \), the distance \( r \), and the angle \( \theta \). It is zero on the equatorial line (\( \theta = 90^\circ \)) at every distance, which shows that the distance alone cannot decide the potential.

NCERT (2026-27):
Potential Due to an Electric Dipole – “… The electric potential of a dipole is then given by

    \( \displaystyle V = \frac{1}{4\pi\varepsilon_0}\,\frac{\mathbf{p}\cdot\hat{\mathbf{r}}}{r^2}; \quad (r \gg a) \qquad (2.15) \)”

Potential Due to an Electric Dipole – “… (i) The potential due to a dipole depends not just on r but also on the angle between the position vector r and the dipole moment vector p.”