Match List-I with List-II
| List-I | List-II |
| (A) \( E \) is independent of \( r \) | (I) For a point charge |
| (B) \( E \propto \frac{1}{r} \) | (II) For a short dipole |
| (C) \( E \propto \frac{1}{r^{2}} \) | (III) For a linear charge distribution |
| (D) \( E \propto \frac{1}{r^{3}} \) | (IV) For a surface charge distribution on an infinite plane sheet |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) - (IV), (B) - (III), (C) - (I), (D) - (II)
How the electric field falls with distance \( r \) depends on the shape of the charge distribution.
(A) \( E \) is independent of \( r \) — this matches (IV) For a surface charge distribution on an infinite plane sheet. The field of an infinite plane sheet is the same at every distance, because the lines stay parallel.
\( \displaystyle E = \frac{\sigma}{2\varepsilon_0} \)
(B) \( E \propto 1/r \) — this matches (III) For a linear charge distribution. For a long line charge the lines spread out in a circle around the line.
\( \displaystyle E = \frac{\lambda}{2\pi\varepsilon_0\,r} \)
(C) \( E \propto 1/r^{2} \) — this matches (I) For a point charge. The lines spread over a sphere of area \( 4\pi r^{2} \).
\( \displaystyle E = \frac{q}{4\pi\varepsilon_0\,r^{2}} \)
(D) \( E \propto 1/r^{3} \) — this matches (II) For a short dipole. The two opposite charges of a dipole partly cancel, so the field falls one power faster than for a point charge.
\( \displaystyle E = \frac{p}{4\pi\varepsilon_0\,r^{3}}\ \text{(on the axis, at } r \gg a\text{)} \)
NCERT (2026-27):
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.”
Summary – “… (i) Thin infinitely long straight wire of uniform linear charge density λ
\( \displaystyle \mathbf{E} = \frac{\lambda}{2\pi\varepsilon_0 r}\,\hat{\mathbf{n}} \)”
Summary – “… The 1/r3 dependence of dipole electric fields should be noted in contrast to the 1/r2 dependence of electric field due to a point charge.”