A superconducting sample is placed in a uniform external magnetic field \(B_0 = 4\pi\times10^{-3}\ \mathrm{T}\). The magnetisation of the sample is (take \(\mu_0 = 4\pi\times10^{-7}\ \mathrm{T\,m\,A^{-1}}\))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(-1.0\times10^{4}\ \mathrm{A\,m^{-1}}\)
A superconductor is a perfect diamagnet. It pushes the field lines out completely, and its magnetic susceptibility is \( \chi=-1 \). The magnetic intensity \( H \) comes from the external field. Outside the sample there is no magnetisation, so \( H=B_0/\mu_0 \).
\( B_0=4\pi\times10^{-3}\ \mathrm{T} \)
\( \mu_0=4\pi\times10^{-7}\ \mathrm{T\,m\,A^{-1}} \)
\( \chi=-1 \)
\( \begin{aligned} H &= \frac{B_0}{\mu_0} \\ &= \frac{4\pi\times10^{-3}}{4\pi\times10^{-7}} \\ &= 1.0\times10^{4}\ \mathrm{A\,m^{-1}} \end{aligned} \)
\( \begin{aligned} M &= \chi H \\ &= (-1)\times1.0\times10^{4} \\ &= -1.0\times10^{4}\ \mathrm{A\,m^{-1}} \end{aligned} \)
The minus sign shows that the magnetisation points opposite to \( H \).
NCERT (2026-27):
Magnetisation and Magnetic Intensity – “It is convenient to introduce another vector field H, called the magnetic intensity, which is defined by \( \mathbf{H}=\mathbf{B}/\mu_0-\mathbf{M} \) …”
Magnetisation and Magnetic Intensity – “… This influence is mathematically expressed as M = χH”
Diamagnetism – “The most exotic diamagnetic materials are superconductors. … Here the field lines are completely expelled! χ= –1 and μr = 0. …”