Question #43291

A paramagnetic solid with a Curie temperature $T_c$ is placed in a uniform external magnetic field $B_0$. The magnetic dipole moment of its individual atoms is independent of the macroscopic volume. At an initial temperature $T_0$ ($T_0 > T_c$), the volume magnetic susceptibility of the material is $\chi_0$ (where $\chi_0 \ll 1$). The solid is then heated to a temperature $T$. The coefficient of volume thermal expansion of the solid is $\gamma$. The interaction magnetic potential energy density is defined as $u = -\vec{M} \cdot \vec{B}_0$, where $\vec{M}$ is the magnetization vector. Which of the following expressions gives the magnitude of the magnetic potential energy density of the solid at temperature $T$? (Assume $\mu_0$ is the vacuum permeability and $\gamma(T - T_0) \ll 1$).