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Chapter 20: Problem 10

There is associated with each atom in paramagnetic and ferromagnetic materials a net magnetic moment. Explain why ferromagnetic materials can be permanently magnetized whereas paramagnetic ones cannot.

Short Answer

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Answer: Ferromagnetic materials can be permanently magnetized due to the aligned magnetic moments within magnetic domains and their ability to lock in place under a strong external magnetic field. In contrast, paramagnetic materials cannot be permanently magnetized because their magnetic moments become randomly oriented once the external magnetic field is removed, due to thermal energy.

Step by step solution

01

Understanding ferromagnetic and paramagnetic materials

Ferromagnetic materials, like iron, cobalt, and nickel, are strongly attracted to magnetic fields due to the presence of unpaired electrons. In these materials, the electron spins align parallel to each other, creating a strong magnetic field. In contrast, paramagnetic materials, such as aluminum and copper, are weakly attracted to magnetic fields. These materials also have unpaired electrons, but their spins align randomly, resulting in a weaker magnetic field.
02

Magnetic domains in ferromagnetic materials

Ferromagnetic materials consist of magnetic domains, which are regions where the magnetic moments of atoms are aligned parallel to each other. In the absence of an external magnetic field, these domains are randomly oriented, and the net magnetization is zero. However, when a ferromagnetic material is placed in an external magnetic field, these domains align with the external field, and the material becomes magnetized.
03

Behavior of paramagnetic materials under a magnetic field

When a paramagnetic material is placed in an external magnetic field, its magnetic moments temporarily align along the direction of the field, similar to what happens in ferromagnetic materials. However, once the external field is removed, thermal energy causes the magnetic moments to become randomly oriented again, resulting in the loss of the induced magnetization. Hence, paramagnetic materials cannot retain magnetization in the absence of a magnetic field.
04

Permanent magnetization of ferromagnetic materials

In ferromagnetic materials, if the external magnetic field is strong enough, the magnetic domains become reoriented and locked in place, even after the external field is removed. This process leads to a permanent magnetization of the material, as the new alignment of magnetic domains persists. In summary, ferromagnetic materials can be permanently magnetized due to the aligned magnetic moments within magnetic domains and their ability to lock in place under a strong external magnetic field. On the other hand, paramagnetic materials cannot be permanently magnetized because their magnetic moments become randomly oriented once the external magnetic field is removed, due to thermal energy.

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Most popular questions from this chapter

Estimate saturation values of \(H\) for singlecrystal iron in [100], [110], and [111] directions.

It is possible to express the magnetic susceptibility \(\chi_{m}\) in several different units. For the discussion of this chapter, \(\chi_{m}\) was used to designate the volume susceptibility in SI units, that is, the quantity that gives the magnetization per unit volume \(\left(\mathrm{m}^{3}\right)\) of material when multiplied by \(H\). The mass susceptibility \(\chi_{m}(\mathrm{~kg})\) yields the magnetic moment (or magnetization) per kilogram of material when multiplied by \(H ;\) similarly, the atomic susceptibility \(\chi_{m}\) (a) gives the magnetization per kilogram-mole. The latter two quantities are related to \(\chi_{m}\) through the relationships $$ \begin{aligned} &\chi_{m}=\chi_{m}(\mathrm{~kg}) \times \text { mass density (in } \mathrm{kg} / \mathrm{m}^{3} \text { ) } \\ &\left.\chi_{m}(\mathrm{a})=\chi_{m}(\mathrm{~kg}) \times \text { atomic weight (in } \mathrm{kg}\right) \end{aligned} $$ When using the cgs-emu system, comparable parameters exist, which may be designated by \(\chi_{m}^{\prime}, \chi_{m}^{\prime}(\mathrm{g})\), and \(\chi_{m}^{\prime}(\mathrm{a})\); the \(\chi_{m}\) and \(\chi_{m}^{\prime}\) are related in accordance with Table 20.1. From Table \(20.2, \chi_{m}\) for silver is \(-2.38 \times 10^{-5}\); convert this value into the other five susceptibilities

The following data are for a transformer steel: \begin{tabular}{cccc} \hline \multicolumn{3}{c}{\(\boldsymbol{B}\)} \\ \(\boldsymbol{H}(\mathrm{A} / \mathrm{m})\) & \((\) teslas \()\) & \(\boldsymbol{H}(\mathbf{A} / \mathrm{m})\) & \(\boldsymbol{B}\) (teslas) \\ \hline 0 & 0 & 200 & \(1.04\) \\ 10 & \(0.03\) & 400 & \(1.28\) \\ 20 & \(0.07\) & 600 & \(1.36\) \\ 50 & \(0.23\) & 800 & \(1.39\) \\ 100 & \(0.70\) & 1000 & \(1.41\) \\ 150 & \(0.92\) & & \\ \hline \end{tabular} (a) Construct a graph of \(B\) versus \(H\). (b) What are the values of the initial permeability and initial relative permeability? (c) What is the value of the maximum permeability? (d) At about what \(H\) field does this maximum permeability occur? (e) To what magnetic susceptibility does this maximum permeability correspond?

Briefly describe the phenomenon of magnetic hysteresis, and why it occurs for ferromagnetic and ferrimagnetic materials.

Assume there exists some hypothetical metal that exhibits ferromagnetic behavior and that has (1) a simple cubic crystal structure (Figure \(3.24\) ), (2) an atomic radius of \(0.153 \mathrm{~nm}\), and (3) a saturation flux density of \(0.76\) tesla. Determine the number of Bohr magnetons per atom for this material.
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