Question

A sample of the paramagnetic salt to which the magnetization curve of Fig 32-14 applies is to be tested to see whether it obeys Curie’s law. The sample is placed in a uniform 0.50T magnetic field that remains constant throughout the experiment. The magnetization M is then measured at temperatures ranging from 10 to 300K. Will it be found that Curie’s law is valid under these conditions?

Short answer

Yes, the magnetization obeys Curie’s law under the given conditions.

Step-by-step solution

Identification of the given data

The magnitude of the external magnetic field is $B_{ext}=0.50T$

The range of temperature range for the measurement of magnetization is, 10K to 300K

Expression for Curie’s law

The expression for Curie’s law is as follows,

$\mathrm{M}=\mathrm{C}\frac{{\mathrm{B}}_{ext}}{\mathrm{T}}$

Here, C is the Curie’s constant,${\mathrm{B}}_{ext}$is theexternal magnetic field, and Tis the temperature.

Verification of the curie’s law according to the given conditions

Determine the ratio of the magnetic field to the temperature for 10K.

$\begin{array}{c}\frac{B_{ext}}{T}=\frac{0.50T}{10K}\\ =0.050T/K\end{array}$

Similarly, determine the ratio of the magnetic field to the temperature for 300K.

$\begin{array}{c}\frac{B_{ext}}{T}=\frac{0.50T}{300K}\\ =0.0016\\ =16.0\times {10}^{-4}T/K\end{array}$

From the above calculation, it can be observed that both points fall in the region where the magnetization is the linear function of ratio $\left(\frac{B_{ext}}{T}\right)$. From the graph, it can be said that both the points are quite close to the origin.

Thus, it can be concluded that the magnetization obeys Curie’s law.