A sample of the paramagnetic salt to which the magnetization...

A sample of the paramagnetic salt to which the magnetization curve of Fig. $32-14$ applies is held at room temperature $(300 \mathrm{~K})$. At what applied magnetic field will the degree of magnetic saturation of the sample be (a) $50 \%$ and (b) $90 \% ?$ (c) Are these fields attainable in the laboratory?

A sample of the paramagnetic salt to which the magnetization curve of Fig. $32-14$ applies is held at room temperature $(300 \mathrm{~K})$. At what applied magnetic field will the degree of magnetic saturation of the sample be (a) $50 \%$ and
(b) $90 \% ?$
(c) Are these fields attainable in the laboratory?

Key Concepts

Langevin Function

The Langevin function mathematically describes the magnetization of a paramagnetic material as a function of the applied magnetic field and temperature. It is derived from statistical mechanics by considering the thermal agitation of magnetic moments, and it relates the ratio of the observed magnetization to the saturation magnetization via the dimensionless parameter, which is proportional to the product of the magnetic field and the magnetic moment divided by the thermal energy.

Magnetization Curve

A magnetization curve plots the magnetization of a material as a function of the applied magnetic field. It is used to understand how the magnetic moments in a material respond to different field strengths. For paramagnets, the curve typically shows a gradual increase in magnetization with increasing field strength, approaching an asymptotic maximum value.

Magnetic Saturation

Magnetic saturation refers to the state in which the magnetization of a material reaches a maximum value despite further increases in the applied magnetic field. In paramagnetic systems, complete saturation is rarely achieved because thermal agitation prevents all magnetic moments from aligning perfectly; instead, the degree of magnetic saturation expresses what fraction of the theoretical saturation moment has been reached.

Paramagnetism

Paramagnetism is the property of certain materials to become magnetized in the presence of an external magnetic field, due to the alignment of magnetic moments of atoms or ions. In paramagnetic materials, the magnetic moments are randomly oriented at zero field but tend to align partially with the field when it is applied, leading to a net magnetization proportional to the applied field at low field strengths.

Please give Ace some feedback