Chapter 32: Q64P (page 971)

A sample of the paramagnetic salt to which the magnetization curve of Fig. 32-14 applies is immersed in a uniform magnetic field of $2.0 T$ . At what temperature will the degree of magnetic saturation of the sample be (a) $50 %$ and (b) $90 %$
?

Short Answer

Expert verified

(a) The temperature at which the degree of magnetic saturation of the sample is $50 %$ is $4K$ .

(b) The temperature at which the degree of magnetic saturation of the sample is $90 %$ is localid="1664195147119" $2K$ .

Step by step solution

Listing the given quantities:

Magnetic field, $B = 2.0 T$

Understanding the concepts of Curie Law:

To determine the temperature at which the sample is $50 %$ magnetically saturated, use the Curie law formula. You must use the value from the graph for the $90 %$ .

Formula:

$\frac{M}{M_{max}} = \frac{B}{T}$

Here, $\frac{M}{M_{max}}$ is the magnetic saturation, $B$ is the magnetic field, $T$ and is the temperature.

(a) Calculations of the temperature at which the degree of magnetic saturation of the sample is 50%:

For the Curie law,

$\frac{M}{M_{max}} = \frac{B}{T} T = \frac{B}{\frac{M}{M_{max}}}$

Substitute $50 % (= 0.50)$ for $\frac{M}{M_{m a x}}$ and the given data in the above equation.

$\begin{array}{rcl} T & = & \frac{2.0 T}{0.50} \\ = & 4 K \end{array}$

Hence, the temperature at which the degree of magnetic saturation of the sample at $50 %$ is $4 K$ .

(b) Calculations of the temperature at which the degree of magnetic saturation of the sample is 90%:

For the Curie law,

$\frac{M}{M_{max}} = \frac{B}{T} T = \frac{B}{\frac{M}{M_{max}}}$

Substitute $90 % (= 0.90)$ for $\frac{M}{M_{max}}$ and the given data in the above equation.

$\begin{array}{rcl} T & = & \frac{2.0T}{0.90} \\ = & 2K \end{array}$

Hence, the temperature at which the degree of magnetic saturation of the sample at $90 %$ is $2K$ .

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A sample of the paramagnetic salt to which the magnetization curve of Fig. 32-14 applies is immersed in a uniform magnetic field of $2.0 T$ . At what temperature will the degree of magnetic saturation of the sample be (a) $50 %$ and (b) $90 %$
?

Short Answer

Step by step solution

Listing the given quantities:

Understanding the concepts of Curie Law:

(a) Calculations of the temperature at which the degree of magnetic saturation of the sample is 50%:

(b) Calculations of the temperature at which the degree of magnetic saturation of the sample is 90%:

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A sample of the paramagnetic salt to which the magnetization curve of Fig. 32-14 applies is immersed in a uniform magnetic field of 2.0T. At what temperature will the degree of magnetic saturation of the sample be (a)50%and (b)90%?

Short Answer

Step by step solution

Listing the given quantities:

Understanding the concepts of Curie Law:

(a) Calculations of the temperature at which the degree of magnetic saturation of the sample is 50%:

(b) Calculations of the temperature at which the degree of magnetic saturation of the sample is 90%:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fluids

Dynamics

Famous Physicists

Oscillations

Atoms and Radioactivity

Fields in Physics

Study anywhere. Anytime. Across all devices.

A sample of the paramagnetic salt to which the magnetization curve of Fig. 32-14 applies is immersed in a uniform magnetic field of $2.0 T$ . At what temperature will the degree of magnetic saturation of the sample be (a) $50 %$ and (b) $90 %$
?