Case: Read the passage and answer the question.
The magnetic susceptibility of a substance is a measure of how readily it responds to an external magnetic field. It gives a measure of the ability of a substance to acquire magnetism. It has no units. Mathematically, it is defined as the ratio of the magnetisation to the magnetic intensity. The susceptibility of a certain substance is \( 2.3\times10^{-5} \).
Match List-I with List-II.
| List-I | List-II |
|---|---|
| (A) Magnetisation \(M\) | (I) Has the same unit as \(\mu_0\) |
| (B) Magnetic intensity \(H\) | (II) Net magnetic moment per unit volume |
| (C) Relative magnetic permeability \(\mu_r\) | (III) Dimensionless analogue of the dielectric constant |
| (D) Magnetic permeability \(\mu\) | (IV) Contribution to the field due to external factors such as the current in a solenoid |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(II), (B)-(IV), (C)-(III), (D)-(I)
(A) Magnetisation \(M\) — This matches (II) Net magnetic moment per unit volume. The atomic moments of a sample add up, and \( M \) is this sum divided by the volume.
(B) Magnetic intensity \(H\) — This matches (IV). \( H \) is the part set by external causes, such as the current in the windings. \( M \) is the part due to the material itself.
(C) Relative magnetic permeability \(\mu_r\) — This matches (III). It is a pure number, \( \mu_r=1+\chi \), and plays the role of the dielectric constant.
(D) Magnetic permeability \(\mu\) — This matches (I). Since \( \mu=\mu_0\mu_r \) and \( \mu_r \) has no unit, \( \mu \) is measured in the same unit as \( \mu_0 \).
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:”
\( \mathbf{M}=\frac{\mathbf{m}_{net}}{V} \qquad (5.7) \)
Magnetisation and Magnetic Intensity – “… We have partitioned the contribution to the total magnetic field inside the sample into two parts: one, due to external factors such as the current in the solenoid. This is represented by H. …”
Magnetisation and Magnetic Intensity – “… we obtain,”
\( B=\mu_0(1+\chi)H \qquad (5.14) \)
\( \;\;=\mu_0\mu_r H=\mu H \qquad (5.15) \)
“where μr= 1 + χ, is a dimensionless quantity called the relative magnetic permeability of the substance. It is the analog of the dielectric constant in electrostatics. …”
Magnetisation and Magnetic Intensity – “… The magnetic permeability of the substance is μ and it has the same dimensions and units as μ0; μ = μ0μr = μ0 (1+χ).”