Chapter 20: Problem 24
Cite the differences between hard and soft magnetic materials in terms of both hysteresis behavior and typical applications.
Chapter 20: Problem 24
Cite the differences between hard and soft magnetic materials in terms of both hysteresis behavior and typical applications.
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Get started for freeA coil of wire \(0.5 \mathrm{~m}\) long and having 20 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-silicon alloy (part b) using \(1.0 \mathrm{~A}\) ?
The formula for samarium iron garnet \(\left(\mathrm{Sm}_{3} \mathrm{Fe}_{5} \mathrm{O}_{12}\right)\) may be written in the form \(\mathrm{Sm}_{3}^{c} \mathrm{Fe}_{2}^{a} \mathrm{Fe}_{3}^{d} \mathrm{O}_{12}\), where the superscripts \(a, c\), and \(d\) represent different sites on which the \(\mathrm{Sm}^{3+}\) and \(\mathrm{Fe}^{3+}\) ions are located. The spin magnetic moments for the \(\mathrm{Sm}^{3+}\) and \(\mathrm{Fe}^{3+}\) ions positioned in the \(a\) and \(c\) sites are oriented parallel to one another and antiparallel to the \(\mathrm{Fe}^{3+}\) ions in \(d\) sites. Compute the number of Bohr magnetons associated with each \(\mathrm{Sm}^{3+}\) ion, given the following information: (1) each unit cell consists of eight formula \(\left(\mathrm{Sm}_{3} \mathrm{Fe}_{5} \mathrm{O}_{12}\right)\) units; (2) the unit cell is cubic with an edge length of \(1.2529 \mathrm{~nm} ;\) (3) the saturation magnetization for this material is \(1.35 \times 10^{5} \mathrm{~A} / \mathrm{m} ;\) and (4) there are 5 Bohr magnetons associated with each \(\mathrm{Fe}^{3+}\) ion.
The magnetization within a bar of some metal alloy is \(1.2 \times 10^{6} \mathrm{~A} / \mathrm{m}\) at an \(H\) field of \(200 \mathrm{~A} / \mathrm{m}\). Compute the following: (a) the magnetic susceptibility, (b) the permeability, and (c) the magnetic flux density within this material. (d) What type(s) of magnetism would you suggest is (are) being displayed by this material? Why?
A ferromagnetic material has a remanence of \(1.0\) tesla and a coercivity of \(15,000 \mathrm{~A} / \mathrm{m}\). Saturation is achieved at a magnetic field strength of \(25,000 \mathrm{~A} / \mathrm{m}\), at which the flux density is \(1.25\) teslas. Using these data, sketch the entire hysteresis curve in the range \(H=-25,000\) to \(+25,000 \mathrm{~A} / \mathrm{m}\). Be sure to scale and label both coordinate axes.
It is possible to express the magnetic susceptibility \(\chi_{m}\) in several different units. For the discussion in this chapter, \(\chi_{m}\) is 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 last two quantities are related to \(\chi_{m}\) through the following relationships: $$ \begin{aligned} &\chi_{m}=\chi_{m}(\mathrm{~kg}) \times \text { mass density }\left(\text { in } \mathrm{kg} / \mathrm{m}^{3}\right) \\ &\chi_{m}(a)=\chi_{m}(\mathrm{~kg}) \times \text { atomic weight }(\text { in } \mathrm{kg}) \end{aligned} $$ When using the cgs-emu system, comparable parameters exist that may be designated by \(\chi_{m}^{\prime}\), \(\chi_{m}^{\prime}(\mathrm{g})\), and \(\chi_{m}^{\prime}(a) ;\) the \(\chi_{m}\) and \(\chi_{m}^{\prime}\) are related in accordance with Table 20.1. From Table 20.2, \(\chi_{m}\) for copper is \(-0.96 \times 10^{-5}\); convert this value into the other five susceptibilities.
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