Match List - I with List - II.
| List – I | List – II | ||
|---|---|---|---|
| (A) | Electric potential (V) due to a single charge | (I) | \( \propto r^{0} \) |
| (B) | Electric flux due to a positive point charge through sphere of radius r | (II) | \( \propto\displaystyle\frac{1}{r^{2}} \) |
| (C) | Electric intensity (E) due to a point charge | (III) | \( \propto\displaystyle\frac{1}{r} \) |
| (D) | Electric intensity (E) due to dipole | (IV) | \( \propto\displaystyle\frac{1}{r^{3}} \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(III), (B)-(I), (C)-(II), (D)-(IV)
The question asks how each quantity depends on the distance r from a point charge q (or, for the dipole, from its centre).
(A) Electric potential (V) due to a single charge — this matches (III) \( \propto 1/r \). The potential of a point charge is \( V = \frac{q}{4\pi\varepsilon_0 r} \).
(B) Electric flux due to a positive point charge through sphere of radius r — this matches (I) \( \propto r^{0} \). By Gauss’s law the flux is \( q/\varepsilon_0 \) whatever the radius, because the same field lines cross every sphere around the charge.
(C) Electric intensity (E) due to a point charge — this matches (II) \( \propto 1/r^{2} \). By Coulomb’s law \( E = \frac{q}{4\pi\varepsilon_0 r^{2}} \).
(D) Electric intensity (E) due to dipole — this matches (IV) \( \propto 1/r^{3} \). At distances much larger than the size of the dipole its field falls as \( E\propto p/r^{3} \).
NCERT (2026-27):
Summary – “… If potential at infinity is chosen to be zero; potential at a point with position vector r due to a point charge Q placed at the origin is given is given by
\( \displaystyle V(\mathbf{r}) = \frac{1}{4\pi\varepsilon_0}\frac{Q}{r} \)”
Gauss’s Law – “… (i) Gauss’s law is true for any closed surface, no matter what its shape or size.”
Summary – “… Electric field due to a point charge q has a magnitude \( |q|/4\pi\varepsilon_0 r^2 \); it is radially outwards from q, if q is positive, and radially inwards if q is negative.”
The Field of an Electric Dipole – “… Notice the important point that the dipole field at large distances falls off not as \( 1/r^2 \) but as \( 1/r^3 \).”