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Chapter 6: Q6P (page 274)

Question: Of the following materials, which would you expect to be paramagnetic and which diamagnetic: aluminum, copper, copper chloride (Cucl2), carbon, lead, nitrogen (N2), salt (Nacl ), sodium, sulfur, water? (Actually, copper is slightly diamagnetic; otherwise, they're all what you'd expect.)

Short Answer

Expert verified

Carbon, lead nitrogen, sodium chloride, sulfur and water are diamagnetic.

Copper, copper chloride, aluminium and sodium are paramagnetic.

Step by step solution

01

What is paramagnetic and diamagnetic material.

The diamagnetic material creates a field opposite to the external field and, in the absence of the external magnetic field, does not retain the magnetism.

These materials have weak and negative magnetic material susceptibility. These materials contain an even number of electrons.

The paramagnetic material produces a field in the direction of the external magnetic field. This material gets weakly magnetized in the external field and has positive but small susceptibility. These materials contain an even number of electrons.

02

Find the paramagnetic and diamagnetic material.

Carbon, lead nitrogen, sodium chloride, sulphur and water contain an even number of electrons; therefore, there are diamagnetic.

Copper, copper chloride, aluminium and sodium contain an odd number of electrons; therefore, there are paramagnetic.

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Most popular questions from this chapter

An infinitely long circular cylinder carries a uniform magnetization Mparallel to its axis. Find the magnetic field (due toM) inside and outside the cylinder.

Suppose the field inside a large piece of magnetic material is B0, so that H0=(1/渭0)B0-M, where M is a "frozen-in" magnetization.

(a) Now a small spherical cavity is hollowed out of the material (Fig. 6.21). Find the field at the center of the cavity, in terms of B0 and M. Also find H at the center of the cavity, in terms of H0 and M.

(b) Do the same for a long needle-shaped cavity running parallel to M.

(c) Do the same for a thin wafer-shaped cavity perpendicular to M.

Figure 6.21

Assume the cavities are small enough so M, B0, and H0 are essentially constant. Compare Prob. 4.16. [Hint: Carving out a cavity is the same as superimposing an object of the same shape but opposite magnetization.]

A coaxial cable consists of two very long cylindrical tubes, separated by linear insulating material of magnetic susceptibility 蠂m. A currentI flows down the inner conductor and returns along the outer one; in each case, the current distributes itself uniformly over the surface (Fig. 6.24). Find the magnetic field in the region between the tubes. As a check, calculate the magnetization and the bound currents, and confirm that (together, of course, with the free currents) they generate the correct field.

Figure 6.24

A current Iflows down a long straight wire of radius. If the wire is made of linear material (copper, say, or aluminium) with susceptibility Xm, and the current is distributed uniformly, what is the magnetic field a distances from the axis? Find all the bound currents. What is the net bound current flowing down the wire?

Notice the following parallel:

{鈭�路D=0鈭�脳E=0,蔚0E=D-P(Nofreecharge)鈭�路B=0鈭�脳H=0,渭0H=B-渭0M(Nofreecharge)

Thus, the transcription D鈫�B,E鈫�H,P鈫�渭0M,蔚0鈫�渭0,, turns an electrostatic problem into an analogous magnetostatic one. Use this, together with your knowledge of the electrostatic results, to rederive.

(a) the magnetic field inside a uniformly magnetized sphere (Eq. 6.16);

(b) the magnetic field inside a sphere of linear magnetic material in an otherwise uniform magnetic field (Prob. 6.18);

(c) the average magnetic field over a sphere, due to steady currents within the sphere (Eq. 5.93).
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