A cylindrical paramagnetic sample has radius $2.0,\text{cm}$ and length $5.0,\text{cm}$. It is placed in a uniform magnetic field of $B=0.75,\text{T}$. The measured magnetization of the sample is $M=5.4\times 10^{-2},{\text{A,m}}^{-1}$. (a) Calculate the magnetic susceptibility $\chi$ of the material. (b) State whether the material is paramagnetic or diamagnetic. (c) Find the total magnetic moment $\mu$ of the sample.

Step-by-step solution

1. Compute the volume: $V=\pi r^{2}l=\pi (0.02,\text{m}{)}^2\times 0.05,\text{m}=6.28\times 10^{-5},{\text{m}}^3$.
2. Calculate the magnetic field strength $H$ using $B={\mu }_0(H+M)$: $H=\frac{B}{{\mu }_0}-M=\frac{0.75}{4\pi \times 10^{-7}}-0.054\approx 5.96\times 10^5,{\text{A,m}}^{-1}$.
3. Determine the susceptibility: $\chi =\frac{M}{H}=5.4\times 10^{-2},/,5.96\times 10^5\approx 9.1\times 10^{-8}$.
4. Since $chi>0$, the material is paramagnetic.
5. Compute the magnetic moment: $\mu =M,V=5.4\times 10^{-2}\times 6.28\times 10^{-5}\approx 3.4\times 10^{-6},{\text{A,m}}^2$.

Concept tested: Magnetic susceptibility

Published 19 September 2026 · How this solution was prepared and checked