Match List-I with List-IIList-IList-IIQuantityVariation with distance…

The correct answer is Option (3) → (A) - (II), (B) - (III), (C) - (IV), (D) - (I)

How a field or potential falls with distance \( r \) depends on the shape of the charge distribution.

(A) Electric field due to a point charge — this matches (II) Inversely proportional to the square of the distance. The field lines spread over a sphere of area \( 4\pi r^{2} \).

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

(B) Electric potential due to a point charge — this matches (III) Inversely proportional to the distance. The potential is the work per unit charge in bringing a test charge from infinity.

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

(C) Electric field due to uniformly charged infinite plane sheet — this matches (IV) Independent of the distance. The field lines stay parallel, so the field is the same at every distance.

    \( \displaystyle E = \frac{\sigma}{2\varepsilon_0} \)

(D) Electric field due to an electric dipole — this matches (I) Inversely proportional to the cube of the distance. The two opposite charges partly cancel, so at large distance the field falls one power faster than for a point charge.

    \( \displaystyle E \propto \frac{p}{4\pi\varepsilon_0\,r^{3}} \)

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.”

Field Due to a Uniformly Charged Infinite Plane Sheet – “… Note that the above application of the Gauss’ law has brought out an additional fact: E is independent of x also.”