39P - Fundamentals Of Physics

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?

Step-by-Step Solution

Answer

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

Step 1: Identification of the given data

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

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

Step 2: 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 the external magnetic field, and T is the temperature.

Step 3: Verification of the curie’s law according to the given conditions

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

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

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

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

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.