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Chapter 32: 39P (page 969)

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?

Short Answer

Expert verified

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

Step by step solution

01

Identification of the given data

The magnitude of the external magnetic field is Bext=0.50T

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

02

Expression for Curie’s law

The expression for Curie’s law is as follows,

M=CBextT

Here, C is the Curie’s constant,Bextis theexternal magnetic field, and Tis the temperature.

03

Verification of the curie’s law according to the given conditions

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

BextT=0.50T10K=0.050T/K

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

BextT=0.50T300K=0.0016=16.0×10−4T/K

From the above calculation, it can be observed that both points fall in the region where the magnetization is the linear function of ratio BextT. 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.

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Most popular questions from this chapter

Figure 32-25 represents three rectangular samples of a ferromagnetic material in which the magnetic dipoles of the domains have been directed out of the page (encircled dot) by a very strong applied field B0 . In each sample, an island domain still has its magnetic field directed into the page (encircled X ). Sample 1 is one (pure) crystal. The other samples contain impurities collected along lines; domains cannot easily spread across such lines.

The applied field is now to be reversed and its magnitude kept moderate. The change causes the island domain to grow. (a) Rank the three samples according to the success of that growth, greatest growth first. Ferromagnetic materials in which the magnetic dipoles are easily changed are said to be magnetically soft; when the changes are difficult, requiring strong applied fields, the materials are said to be magnetically hard. (b) Of the three samples, which is the most magnetically hard?

Consider a solid containing Natoms per unit volume, each atom having a magnetic dipole moment μ→. Suppose the direction ofμ→can be only parallel or anti-parallel to an externally applied magnetic field (this will be the case if is due to the spin of a single electron). According to statistical mechanics, the probability of an atom being in a state with energy Uis proportional toe-UKT, where Tis the temperature and kis Boltzmann’s constant. Thus, because energy Uis, the fraction of atoms whose dipole moment is parallel to is proportional toeμBKTand the fraction of atoms whose dipole moment is anti-parallel to is proportional toe-μBKT. (a) Show that the magnitude of the magnetization of this solid isM=μNtanh(μBkT). Here tanh is the hyperbolic tangent function:tanh(x)=(ex-e-x)/(ex+e-x)(b) Show that the result given in (a) reduces toM=Nμ2B/kTforμB≪kT(c) Show that the result of (a) reduces torole="math" localid="1662964931865" M=Nμforrole="math" localid="1662964946451" μB≫kT.(d) Show that both (b) and (c) agree qualitatively with Figure.

Question: Figure 32-35a shows the current i that is produced in a wire of resistivity1.62×10-8Ωm . The magnitude of the current versus time is = 10.0A is shown in Figure b. The vertical axis scale is set by ts= 50.0ms and the horizontal axis scale is set by . Point P is at radial distance 9.00 mm from the wire’s centre. (a) Determine the magnitude of the magnetic field B→iat point P due to the actual current i in the wire at t= 20 ms, (b) At t = 40 ms, and (c) t = 60 ms . Next, assume that the electric field driving the current is confined to the wire. Then Determine the magnitude of the magnetic field at point P due to the displacement current id in the wire at (d) t = 20 ms , (e) At t = 40 ms , and (f) At t= 60 ms . At point P at 20 s, what is the direction (into or out of the page)of (g) B→iand (h) B→id?

: Assume the average value of the vertical component of Earth’s magnetic field is43μT (downward) for all of Arizona, which has an area of 2.95×105km2. (a)What is the magnitude and (b) What is the direction (inward or outward) of the net magnetic flux through the rest of Earth’s surface (the entire surface excluding Arizona)?

An electron is placed in a magnetic field B→ that is directed along azaxis. The energy difference between parallel and antiparallel alignments of the zcomponent of the electron’s spin magnetic moment withB→is6.00×10-25J. What is the magnitude ofB→?
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