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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鈥檚 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鈥檚 law is valid under these conditions?

Short Answer

Expert verified

Yes, the magnetization obeys Curie鈥檚 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鈥檚 law is as follows,

M=CBextT

Here, C is the Curie鈥檚 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脳10鈭�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鈥檚 law.

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Most popular questions from this chapter

Two wires, parallel to a z-axis and a distance 4rapart, carry equal currents i in opposite directions, as shown in Figure. A circular cylinder of radius r and length L has its axis on the z-axis, midway between the wires. Use Gauss鈥� law for magnetism to derive an expression for the net outward magnetic flux through the half of the cylindrical surface above the xaxis. (Hint: Find the flux through the portion of the xzplane that lies within the cylinder.)

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If an electron in an atom has orbital angular momentum with values limited by 3, how many values of (a)Lorb,zand (b)渭orb,zcan the electron have? In terms of h, m, and e, what is the greatest allowed magnitude for (c)Lorb,zand (d)渭orb,z? (e) What is the greatest allowed magnitude for the z component of the electron鈥檚 net angular momentum (orbital plus spin)? (f) How many values (signs included) are allowed for the z component of its net angular momentum?

If an electron in an atom has an orbital angular momentum withm=0, what are the components (a) Lorb,zand (b)渭orb,z? If the atom is in an external magnetic fieldB鈫�that has magnitude35mTand is directed along the z axis, what are (c) the energyUorbassociated with渭orb鈫�and(d) the energyUspinassociated with渭s鈫�? (e) If, instead, the electron hasm=-3, what are (e)Lorb,z? (f) 渭orb,z(g) Uorband (h)Uspin?

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