Choose the correct statement regarding dependence of electric potential at a point due to an electric dipole:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → inversely proportional to the square of the distance from the center of dipole and depends on the angle between the position vector \( \vec{r} \) and dipole moment vector \( \vec{p} \)
The potential of a dipole at a point at distance r from its centre, for \( r \gg a \), is
\( \displaystyle V = \frac{1}{4\pi\varepsilon_0}\,\frac{p\cos\theta}{r^{2}} \)
where \( \theta \) is the angle between \( \vec{r} \) and the dipole moment \( \vec{p} \). It depends on the distance r (as \( 1/r^{2} \)), on the dipole moment p and on the angle \( \theta \).
Why the other options are incorrect
Option (1) depends on the position vector \( \vec{r} \) from the center of the dipole only — Incorrect. The potential also depends on the dipole moment p (it is proportional to it).
Option (2) depends on the dipole moment vector \( \vec{p} \) only — Incorrect. It also depends on the distance r and on the angle \( \theta \).
Option (3) inversely proportional to the distance from the center of the dipole — Incorrect. The \( 1/r \) fall-off is that of a single point charge; for a dipole it is \( 1/r^{2} \).
NCERT (2026-27):
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. … (ii) The electric dipole potential falls off, at large distance, as 1/r2, not as 1/r, characteristic of the potential due to a single charge.”