Match List – I with List – II.
| LIST I | LIST II | ||
|---|---|---|---|
| A. | Electrical permittivity | I. | \( \mathrm{N\,m^{2}\,C^{-1}} \) |
| B. | Electric flux | II. | \( \mathrm{N^{-1}\,m^{-2}\,C^{2}} \) |
| C. | Electric field | III. | \( \mathrm{C\,m^{-2}} \) |
| D. | Surface charge density | IV. | \( \mathrm{N\,C^{-1}} \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A-II, B-I, C-IV, D-III
Each unit follows from the defining equation of the quantity.
(A) Electrical permittivity — this matches (II) \( \mathrm{N^{-1}\,m^{-2}\,C^{2}} \). From Coulomb's law \( F = \frac{q_1q_2}{4\pi\varepsilon_0 r^{2}} \), \( \varepsilon_0 = \frac{q_1q_2}{4\pi F r^{2}} \), whose unit is \( \frac{\mathrm{C^{2}}}{\mathrm{N\,m^{2}}} \).
(B) Electric flux — this matches (I) \( \mathrm{N\,m^{2}\,C^{-1}} \). The flux is \( \Phi = EA \), so its unit is \( \mathrm{N\,C^{-1}}\times\mathrm{m^{2}} \).
(C) Electric field — this matches (IV) \( \mathrm{N\,C^{-1}} \). The field is force per unit charge, \( E = F/q \).
(D) Surface charge density — this matches (III) \( \mathrm{C\,m^{-2}} \). It is charge per unit area, \( \sigma = q/A \).