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 \( 2.3\times10^{-5} \).
What is the magnetic permeability of the substance?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 1.26\times10^{-6}\,\mathrm{T\,m\,A^{-1}} \)
The relative permeability is \( \mu_r=1+\chi \), and the magnetic permeability of the substance is \( \mu=\mu_0\mu_r \), with \( \mu_0=4\pi\times10^{-7}\,\mathrm{T\,m\,A^{-1}} \).
\( \begin{aligned} \mu_r &= 1+\chi \\ &= 1+2.7\times10^{-5} \\ &= 1.000027 \end{aligned} \)
\( \begin{aligned} \mu &= \mu_0\mu_r \\ &= 4\pi\times10^{-7}\,\mathrm{T\,m\,A^{-1}}\times1.000027 \\ &\approx 1.26\times10^{-6}\,\mathrm{T\,m\,A^{-1}} \end{aligned} \)
Therefore, the susceptibility is so small that \( \mu \) is almost equal to \( \mu_0 \).
NCERT (2026-27):
Magnetisation and Magnetic Intensity – “… 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. The magnetic permeability of the substance is μ and it has the same dimensions and units as μ0; μ = μ0μr = μ0 (1+χ).”