For which of the following substances, the magnetic susceptibility is independent of temperature? (A) diamagnetics only (B) paramagnetics only (A) ferromagnetism only (D) diamagnetism and paramagnetism both

Magnetic Susceptibility and Temperature Dependence:
The magnetic susceptibility of a material describes how much the material becomes magnetized when exposed to an external magnetic field. The temperature dependence of the magnetic susceptibility varies for different types of materials. Let's examine each of the given options.
1. Diamagnetism:
• Diamagnetic materials are materials that do not have any intrinsic magnetic dipole moment and are only weakly repelled by a magnetic field. When placed in a magnetic field, they develop a small induced magnetic moment in the opposite direction to the applied field.
• The magnetic susceptibility of diamagnetic materials is generally negative and very small.
• Temperature dependence: The magnetic susceptibility of diamagnetic materials is independent of temperature. It does not change with temperature because the effect is caused by the motion of electrons and the induced dipoles, which is not significantly affected by temperature.
2. Paramagnetism:
• Paramagnetic materials have unpaired electrons and exhibit a weak attraction to magnetic fields. The magnetic susceptibility of paramagnetic materials is positive but typically small.
• Temperature dependence: The magnetic susceptibility of paramagnetic materials decreases with increasing temperature. This is due to the increased thermal motion of the particles, which tends to randomize the alignment of the magnetic moments, reducing the material's overall magnetization. The susceptibility χ\chi for paramagnetic materials is inversely proportional to temperature, described by the Curie Law:
χ=CT\chi = \frac{C}{T}
where CC is the Curie constant, and TT is the absolute temperature.
3. Ferromagnetism:
• Ferromagnetic materials have a spontaneous magnetization even in the absence of an external magnetic field, due to the alignment of magnetic domains within the material.
• Temperature dependence: The magnetic susceptibility of ferromagnetic materials is strongly temperature-dependent. As the temperature increases, thermal agitation disrupts the alignment of the magnetic domains, and above a certain temperature known as the Curie temperature (Tc), the material loses its ferromagnetic properties and becomes paramagnetic. Below the Curie temperature, the susceptibility is high, but it decreases as the temperature approaches TcT_c.
Conclusion:
• Diamagnetic materials have magnetic susceptibility that is independent of temperature.
• Paramagnetic and ferromagnetic materials both show a temperature-dependent susceptibility.
Answer:
The correct answer is (A) Diamagnetics only.