Match the LIST-I with LIST-II
| LIST-I (Physical Quantity) | LIST-II (Unit) | ||
|---|---|---|---|
| A. | Magnetisation | I. | \( T\,\mathrm{m^{-1}\,A} \) |
| B. | Magnetic energy density | II. | \( \mathrm{N\,m\,rad^{-1}} \) |
| C. | Torsion constant | III. | \( \mathrm{A\,m^{-1}} \) |
| D. | Magnetic moment | IV. | \( \mathrm{J\,T^{-1}} \) |
[Here symbols have their usual meaning]
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A-III, B-I, C-II, D-IV
Each unit follows from the defining relation of the quantity.
(A) Magnetisation — this matches (III) \( \mathrm{A\,m^{-1}} \). Magnetisation is the magnetic moment per unit volume: \( \mathrm{A\,m^{2}}/\mathrm{m^{3}} = \mathrm{A\,m^{-1}} \).
(B) Magnetic energy density — this matches (I) \( T\,\mathrm{m^{-1}\,A} \). Energy density is \( B^{2}/2\mu_0 \), measured in \( \mathrm{J\,m^{-3}} \), and with \( \mathrm{T} = \mathrm{N\,A^{-1}\,m^{-1}} \):
\( \mathrm{T\,m^{-1}\,A} = (\mathrm{N\,A^{-1}\,m^{-1}})(\mathrm{A\,m^{-1}}) = \mathrm{N\,m^{-2}} = \mathrm{J\,m^{-3}} \)
(C) Torsion constant — this matches (II) \( \mathrm{N\,m\,rad^{-1}} \). It is the restoring torque per unit angle of twist, \( \tau = k\theta \).
(D) Magnetic moment — this matches (IV) \( \mathrm{J\,T^{-1}} \). From \( U = -\vec{m}\cdot\vec{B} \), magnetic moment is energy per unit field.
NCERT (2026-27):
Magnetisation and Magnetic Intensity – “… We define magnetisation M of a sample to be equal to its net magnetic moment per unit volume:
\( \displaystyle \mathbf{M} = \frac{\mathbf{m}_{\text{net}}}{V} \qquad (5.7) \)
M is a vector with dimensions L–1 A and is measured in a units of A m–1.”
The Moving Coil Galvanometer – “… In equilibrium \( k\phi = NIAB \) where k is the torsional constant of the spring; i.e. the restoring torque per unit twist.”