Match List I with List IIList IList II(Quantity)(Variation with dista…

The correct answer is Option (4) → A-IV, B-III, C-I, D-II

List II uses the symbol \( \alpha \) for "proportional to" (\( \propto \)). For far points (\( r \) much greater than the size of the charge system), each higher multipole falls off one power of \( r \) faster than the one before it. The potential of each falls one power slower than its field.

(A) Electric field intensity (E) due to a single charge — this matches (IV) \( \alpha\displaystyle\frac{1}{r^{2}} \). By Coulomb's law the field of a point charge falls as the inverse square of the distance.

    \( \displaystyle E = \frac{1}{4\pi\varepsilon_0}\,\frac{q}{r^{2}} \)

(B) Electric field intensity due to electric dipole — this matches (III) \( \alpha\displaystyle\frac{1}{r^{3}} \). The fields of the two opposite charges nearly cancel at large distance, leaving a field that falls as the inverse cube.

    \( \displaystyle E_{\mathrm{axis}} = \frac{1}{4\pi\varepsilon_0}\,\frac{2p}{r^{3}} \)

(C) Electric potential (V) due to a single charge — this matches (I) \( \alpha\displaystyle\frac{1}{r} \). The potential of a point charge falls as the first power of the distance.

    \( \displaystyle V = \frac{1}{4\pi\varepsilon_0}\,\frac{q}{r} \)

(D) Electric field intensity due to a quadrupole — this matches (II) \( \alpha\displaystyle\frac{1}{r^{4}} \). A quadrupole is two equal and opposite dipoles side by side; their fields nearly cancel, so the field falls one power faster than a dipole field.

NCERT (2026-27):
Potential Due to an Electric Dipole – “… Further, the field falls off, at large distance, not as 1/r² (typical of field due to a single charge) but as 1/r³.”

Potential Due to an Electric Dipole – “… (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.”