Match List I with List II
| LIST I Quantity | LIST II Variation with distance r | ||
|---|---|---|---|
| A. | Electric potential (V) due to a single charge | I. | \( \propto \displaystyle\frac{1}{r} \) |
| B. | Capacitance of an isolated sphere of radius (r) | II. | \( \propto \displaystyle\frac{1}{r^{3}} \) |
| C. | Electric field intensity (E) due to a short electric dipole | III. | \( \propto \displaystyle\frac{1}{r^{2}} \) |
| D. | Electric field intensity (E) due to a single charge | IV. | \( \propto r \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A-I, B-IV, C-II, D-III
(A) Electric potential (V) due to a single charge — this matches (I) \( \propto 1/r \). The potential of a point charge is \( V = \frac{q}{4\pi\varepsilon_0 r} \).
(B) Capacitance of an isolated sphere of radius (r) — this matches (IV) \( \propto r \). The capacitance of an isolated sphere is \( C = 4\pi\varepsilon_0 r \), so it grows in direct proportion to the radius.
(C) Electric field intensity (E) due to a short electric dipole — this matches (II) \( \propto 1/r^{3} \). At a distance r much larger than the dipole length, the field of a dipole of moment p falls as \( E\propto p/r^{3} \) (on the axis \( E = \frac{2p}{4\pi\varepsilon_0 r^{3}} \)).
(D) Electric field intensity (E) due to a single charge — this matches (III) \( \propto 1/r^{2} \). By Coulomb's law the field of a point charge is \( E = \frac{q}{4\pi\varepsilon_0 r^{2}} \).