Match List I with List - II.
| List – I | List – II | ||
|---|---|---|---|
| (A) | Electric potential due to a point charge | (I) | \( \propto \displaystyle\frac{1}{r^{2}} \) |
| (B) | Electric potential due to a dipole on axial line | (II) | \( \propto \displaystyle\frac{1}{r^{3}} \) |
| (C) | Electric field Intensity due to a dipole on axial line | (III) | \( \propto \displaystyle\frac{1}{r} \) |
| (D) | Electric field Intensity due to a quadrupole | (IV) | \( \propto \displaystyle\frac{1}{r^{4}} \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(III), (B)-(I), (C)-(II), (D)-(IV)
Each time the charge distribution goes one step higher (point charge, dipole, quadrupole), the far-field falls off by one more power of r.
(A) Electric potential due to a point charge — this matches (III) \( \propto 1/r \). \( V = \frac{q}{4\pi\varepsilon_0 r} \).
(B) Electric potential due to a dipole on axial line — this matches (I) \( \propto 1/r^{2} \). \( V = \frac{p}{4\pi\varepsilon_0 r^{2}} \) on the axis (for \( r \gg a \)), one power of r lower than a single charge.
(C) Electric field Intensity due to a dipole on axial line — this matches (II) \( \propto 1/r^{3} \). \( E = \frac{2p}{4\pi\varepsilon_0 r^{3}} \) on the axis.
(D) Electric field Intensity due to a quadrupole — this matches (IV) \( \propto 1/r^{4} \). A quadrupole is two opposite dipoles side by side, so its potential falls as \( 1/r^{3} \) and its field, one power faster, as \( 1/r^{4} \).
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.”
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.”