Which of the following correctly describes the magnetisation \( \vec{M} \) of a sample?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( M=m_{\mathrm{net}}/V \)
Option (1) It is a scalar quantity. — Incorrect. The magnetic moments of the atoms add up vectorially, and magnetic moment is a vector. So magnetisation is a vector with a direction.
Option (2) It has dimensions \( [\mathrm{L^{-1}}] \). — Incorrect. Magnetic moment has dimensions \( [\mathrm{L^{2}A}] \) and volume \( [\mathrm{L^{3}}] \), so magnetisation has dimensions \( [\mathrm{L^{-1}A}] \). The current dimension A cannot be left out.
Option (3) Its SI unit is \( \mathrm{A\,m^{2}} \). — Incorrect. \( \mathrm{A\,m^{2}} \) is the unit of magnetic moment. Dividing it by a volume in \( \mathrm{m^{3}} \) gives \( \mathrm{A\,m^{-1}} \), the unit of magnetisation.
Option (4) \( M=m_{\mathrm{net}}/V \) — Correct. The magnetisation of a sample is defined as its net magnetic moment per unit volume.
NCERT (2026-27):
Magnetisation and Magnetic Intensity – “We have seen that a circulating electron in an atom has a magnetic moment. In a bulk material, these moments add up vectorially and they can give a net magnetic moment which is non-zero. We define magnetisation M of a sample to be equal to its net magnetic moment per unit volume:
\( \displaystyle \mathbf{M}=\frac{\mathbf{m}_{\mathrm{net}}}{V} \qquad (5.7) \)
M is a vector with dimensions L–1 A and is measured in a units of A m–1.”