Match List-I with List-II
| List-I (Physical quantity) | List-II (Dimensions) | ||
|---|---|---|---|
| (A) | Linear charge density | (I) | [ML3T-3A-1] |
| (B) | Electric flux | (II) | [L-1TA] |
| (C) | Dipole moment | (III) | [M-1L-3T4A2] |
| (D) | Dielectric permittivity | (IV) | [LTA] |
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)
Write each quantity from its defining formula, with charge \( [Q] = [\mathrm{AT}] \) and force \( [F] = [\mathrm{MLT^{-2}}] \).
(A) Linear charge density — this matches (II) [L-1TA]. It is charge per unit length.
\( \displaystyle [\lambda] = \frac{[Q]}{[L]} = [\mathrm{L^{-1}TA}] \)
(B) Electric flux — this matches (I) [ML3T-3A-1]. Flux is field times area, and the field is force per unit charge.
\( \displaystyle [\phi] = \frac{[F]}{[Q]}[L^{2}] = \frac{[\mathrm{MLT^{-2}}]}{[\mathrm{AT}]}[\mathrm{L^{2}}] = [\mathrm{ML^{3}T^{-3}A^{-1}}] \)
(C) Dipole moment — this matches (IV) [LTA]. It is charge times separation, \( p = q \times 2a \).
(D) Dielectric permittivity — this matches (III) [M-1L-3T4A2]. From Coulomb’s law, \( \varepsilon = q_1 q_2/(4\pi F r^{2}) \).
\( \displaystyle [\varepsilon] = \frac{[\mathrm{AT}]^{2}}{[\mathrm{MLT^{-2}}][\mathrm{L^{2}}]} = [\mathrm{M^{-1}L^{-3}T^{4}A^{2}}] \)
NCERT (2026-27):
Summary – …
