The electric potential due to an electric dipole
(A) depends on \( r \), where \( r \) is the magnitude of position vector \( \vec{r} \)
(B) depends on the angle between the position vector \( \vec{r} \) and the dipole moment vector \( \vec{p} \)
(C) falls off at long distances, as \( 1/r^{2} \)
(D) does not depend upon the distance separating the charges
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (B) and (C) only
At a point far from a dipole, the potential is given by the dipole potential formula, where \( \theta \) is the angle between \( \vec{r} \) and \( \vec{p} \).
\( \displaystyle V = \frac{p\cos\theta}{4\pi\varepsilon_0\,r^{2}} \)
(A) depends on \( r \), where \( r \) is the magnitude of position vector \( \vec{r} \) — Correct. \( V \) changes with the distance \( r \) from the dipole.
(B) depends on the angle between the position vector \( \vec{r} \) and the dipole moment vector \( \vec{p} \) — Correct. The factor \( \cos\theta \) gives this dependence.
(C) falls off at long distances, as \( 1/r^{2} \) — Correct. For a single charge \( V \propto 1/r \); the two opposite charges partly cancel, so the dipole potential falls one power faster.
(D) does not depend upon the distance separating the charges — Incorrect. The dipole moment \( p = q\,(2a) \) contains the separation \( 2a \) of the charges, so \( V \) depends on it.
NCERT (2026-27):
Potential Due to an Electric Dipole – “… The important contrasting features of electric potential of a dipole from that due to a single charge are clear from Eqs. (2.8) and (2.15): (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.”