Electric field intensity at a point varies as \( \displaystyle\frac{1}{r^{3}} \) due to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → a short electric dipole
The field of a short electric dipole of moment p, at a distance r much larger than its length, is
\( \displaystyle E_{\text{axis}} = \frac{1}{4\pi\varepsilon_0}\,\frac{2p}{r^{3}},\qquad E_{\text{equator}} = \frac{1}{4\pi\varepsilon_0}\,\frac{p}{r^{3}} \)
so \( E\propto1/r^{3} \). The fields of the two equal and opposite charges nearly cancel, which is why it falls faster than the field of a single charge.
Why the other options are incorrect
Option (1) a point charge — Incorrect. By Coulomb's law \( E\propto1/r^{2} \).
Option (3) a line charge of infinite length — Incorrect. \( E = \lambda/2\pi\varepsilon_0r \), so \( E\propto1/r \).
Option (4) a plane infinite sheet of charge — Incorrect. \( E = \sigma/2\varepsilon_0 \), which does not depend on the distance.
NCERT (2026-27):
The Field of an Electric Dipole – “… Notice the important point that the dipole field at large distances falls off not as 1/r2 but as 1/r3.”