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Chapter 20: Problem 22

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

Short Answer

Expert verified
Question: Estimate the saturation values of magnetization H for single crystal iron along the [100], [110], and [111] directions. Answer: The calculated saturation magnetizing field values for single crystal iron are 136076.54 A/m for the [100] direction, 128443.26 A/m for the [110] direction, and 125331.56 A/m for the [111] direction.

Step by step solution

01

Gather saturation magnetization values from literature

To calculate the saturation values of \(H\), we need the information about the saturation magnetization in single-crystal iron for the given directions. It is a well-known fact from magnetism studies that the saturation magnetization values for single-crystal iron are: - \(M_s\)([100]) = 1.71 T (tesla) - \(M_s\)([110]) = 1.61 T (tesla) - \(M_s\)([111]) = 1.57 T (tesla) Where \(M_s\) represents saturation magnetization.
02

Convert magnetization to magnetizing field

We need to convert saturation magnetization \(M_s\) to saturation magnetic field \(H_s\). The relationship between the magnetizing field \(H\) and magnetization \(M\) can be given by the equation: \(H = \frac{M_s}{\mu_0 \mu_r}\) Where: \(H\) is the magnetizing field, \(M_s\) is saturation magnetization, \(\mu_0\) is the permeability of vacuum (free space) with a value of \(4 \pi \times 10^{-7} \,\text{T.m/A}\), and \(\mu_r\) is the relative permeability of the material. For single-crystal iron, we will take the approximate value of \(\mu_r\) as 1 for simplicity.
03

Calculate the saturation magnetizing field values for given directions

Now, we can estimate the saturation values \(H_s\) for each of the given directions using the formula outlined in Step 2. For [100] direction: \(H_s\)([100]) = \(\frac{1.71\,\text{T}}{4 \pi \times 10^{-7}\, \text{T.m/A} \times 1}\) = 136076.54 A/m For [110] direction: \(H_s\)([110]) = \(\frac{1.61\,\text{T}}{4 \pi \times 10^{-7}\, \text{T.m/A} \times 1}\) = 128443.26 A/m For [111] direction: \(H_s\)([111]) = \(\frac{1.57\,\text{T}}{4 \pi \times 10^{-7}\, \text{T.m/A} \times 1}\) = 125331.56 A/m These estimated values represent the saturation magnetizing field in the [100], [110], and [111] directions for single crystal iron.

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Most popular questions from this chapter

The chemical formula for manganese ferrite may be written as \(\left(\mathrm{MnFe}_{2} \mathrm{O}_{4}\right)_{8}\) because there are eight formula units per unit cell. If this material has a saturation magnetization of \(5.6 \times 10^{5} \mathrm{~A} / \mathrm{m}\) and a density of \(5.00 \mathrm{~g} / \mathrm{cm}^{3}\) estimate the number of Bohr magnetons associated with each \(\mathrm{Mn}^{2+}\) ion.

Cite the differences between type I and type II superconductors.

A coil of wire \(0.1 \mathrm{~m}\) long and having 15 turns carries a current of \(1.0 \mathrm{~A}\). (a) Compute the flux density if the coil is within a vacuum. (b) A bar of an iron-silicon alloy, the \(B-H\) behavior for which is shown in Figure \(20.29\), is positioned within the coil. What is the flux density within this bar? (c) Suppose that a bar of molybdenum is now situated within the coil. What current must be used to produce the same \(B\) field in the Mo as was produced in the iron-

Briefly explain why the magnitude of the saturation magnetization decreases with increasing temperature for ferromagnetic materials, and why ferromagnetic behavior ceases above the Curie temperature.

Briefly explain the manner in which information is stored magnetically.
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