Answer the following questions:
$(a)$ Why does a paramagnetic sample display greater magnetisation (for the same magnetising field) when cooled?
$(b)$ Why is diamagnetism, in contrast, almost independent of temperature?
$(c)$ If a toroid uses bismuth for its core, will the field in the core be (slightly) greater or (slightly) less than when the core is empty?
$(d)$ Is the permeability of a ferromagnetic material independent of the magnetic field? If not, is it more for lower or higher fields?
$(e)$ Magnetic field lines are always nearly normal to the surface of a ferromagnet at every point. (This fact is analogous to the static electric field lines being normal to the surface of a conductor at every point.) Why?
$(f)$ Would the maximum possible magnetisation of a paramagnetic sample be of the same order of magnitude as the magnetisation of a ferromagnet?

$(a)$ Due to random thermal motion, the alignment of atomic dipoles is disrupted at higher temperatures. Cooling reduces this thermal agitation, allowing more dipoles to align with the external field, resulting in greater magnetization.
$(b)$ Diamagnetism arises from the orbital motion of electrons, which is an inherent property of the atoms. Since this motion is not significantly affected by thermal agitation, diamagnetism is almost independent of temperature.
$(c)$ Bismuth is a diamagnetic substance. Since diamagnetic materials expel magnetic field lines, the magnetic field in the core will be slightly less than when the core is empty.
$(d)$ No, the permeability of a ferromagnetic material is not independent of the magnetic field. It is higher for lower magnetic fields and decreases as the field increases due to the saturation effect.
$(e)$ Ferromagnetic materials have a very high relative permeability $(\mu_r \gg 1)$. Because the material is highly permeable, the magnetic field lines tend to concentrate inside it, making them nearly normal to the surface, similar to how electric field lines behave at the surface of a conductor.
$(f)$ Yes, the maximum possible magnetization of a paramagnetic sample can be of the same order of magnitude as that of a ferromagnet, provided that the sample is subjected to very high magnetizing fields at very low temperatures to achieve saturation.