5.16 Answer the following questions:

(a) Why does a paramagnetic sample display greater magnetization (for the same magnetizing 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 magnetization of a paramagnetic sample be of the same order of magnitude as the magnetization of a ferromagnet?

<p><strong>5.16 (a)&nbsp;</strong>Due to random thermal motion of molecules, the alignment of dipoles gets disrupted at high temperatures. On cooling, this disruption is reduced. Hence, a paramagnetic sample displays greater magnetisation when cooled.</p><p><strong> (b)</strong> The induced dipole moment in a diamagnetic substance is always opposite to the magnetising field. Hence, the internal motion of atoms (which is related to the temperature) does not affect the diamagnetism of a material.</p><p><strong> (c)</strong> Bismuth is a diamagnetic substance. Hence, a toroid with a bismuth core has a magnetic field slightly greater than toroid whose core is empty.</p><p><strong> (d)</strong> The permeability of ferromagnetic materials is not independent of the applied magnetic field. It is greater for a lower field and vice versa.</p><p><strong> (e)</strong> The permeability of a ferromagnetic material is not less than one. It is always greater than one. Hence, magnetic field lines are always nearly normal to the surface of such materials at every point.</p><p><strong> (f)</strong> The maximum possible magnetisation of a paramagnetic sample can be of the same order of magnitude as the magnetisation of a ferromagnet. This requires high magnetising fields for saturation.</p>

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