Match List I with List II
| LIST I | LIST II |
| A. Charge on an electron | I. 1 |
| B. Electric permittivity of free space | II. \( 1.6\times10^{-19}\,\mathrm{C} \) |
| C. Number of lines of force from 1 C of charge in free space | III. \( 8.85\times10^{-12}\,\mathrm{C^2\,N^{-1}\,m^{-2}} \) |
| D. Dielectric constant of vacuum | IV. \( 1.13\times10^{11} \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A-II, B-III, C-IV, D-I
The items are standard constants of electrostatics; the unit attached to each value in List II helps to place it.
(A) Charge on an electron — this matches (II) \( 1.6\times10^{-19}\,\mathrm{C} \). This is the elementary charge \( e \) (the electron carries \( -e \)).
(B) Electric permittivity of free space — this matches (III) \( 8.85\times10^{-12}\,\mathrm{C^2\,N^{-1}\,m^{-2}} \). Its unit follows from Coulomb's law, \( \varepsilon_0 = q_1 q_2/(4\pi F r^{2}) \).
(C) Number of lines of force from 1 C of charge in free space — this matches (IV) \( 1.13\times10^{11} \). By Gauss's law the flux leaving a charge \( q \) is \( q/\varepsilon_0 \), and the number of lines is taken equal to the flux.
\( \displaystyle \frac{q}{\varepsilon_0} = \frac{1}{8.85\times10^{-12}} \approx 1.13\times10^{11} \)
(D) Dielectric constant of vacuum — this matches (I) 1. The dielectric constant is \( K = \varepsilon/\varepsilon_0 \), and for vacuum \( \varepsilon = \varepsilon_0 \).