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Chapter 6: Q14P (page 284)

For the bar magnet of Problem. 6.9, make careful sketches of M, B, and H, assuming L is about 2a. Compare Problem. 4.17.

Short Answer

Expert verified

Draw the careful sketches of for the bar magnet.

Draw the careful sketches of for the bar magnet.

Draw the careful sketches of for the bar magnet.

Step by step solution

01

Write the given data from the question.

Reference as problem 6.9.

Assuming is about 2a.

02

Draw careful sketches of M, B, and H.

Draw the circuit diagram of M for the bar magnet.

Figure 1

Draw the circuit diagram of for the bar magnet.

Figure 2

Draw the circuit diagram of for the bar magnet.

Figure 3

We observe that the polarisation and the magnetization fields are similar (in problem 4.17).

Similar to the electric field, the auxiliary field H has a discontinuity at the top and bottom of the cylinder.

Last but not least, the magnetic field resembles the displacement field D鈫�, because the field lines in the electric case loop back on themselves because there are no free charges (like the magnetic field).

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Most popular questions from this chapter

Find the force of attraction between two magnetic dipoles, m1and m2, oriented as shown in Fig. 6.7, a distance r apart, (a) using Eq. 6.2, and (b) using Eq.6.3.

A sphere of linear magnetic material is placed in an otherwise uniform magnetic field B0. Find the new field inside the sphere.

(a)Show that the energy of a magnetic dipole in a magnetic field B is

U=鈭�m鈰�B.

[Assume that the magnitude of the dipole moment is fixed, and all you have to do is move it into place and rotate it into its final orientation. The energy required to keep the current flowing is a different problem, which we will confront in Chapter 7.] Compare Eq. 4.6.

Figure 6.30

(b) Show that the interaction energy of two magnetic dipoles separated by a displacement r is given by

U=渭04蟺1r3[m1鈰�m2鈭�3(m1鈰�r^)(m2鈰�r^)]

Compare Eq. 4.7.

(c) Express your answer to (b) in terms of the angles 胃1 and 胃2 in Fig. 6.30, and use the result to find the stable configuration two dipoles would adopt if held a fixed distance apart, but left free to rotate.

(d) Suppose you had a large collection of compass needles, mounted on pins at regular intervals along a straight line. How would they point (assuming the earth's magnetic field can be neglected)? [A rectangular array of compass needles aligns itself spontaneously, and this is sometimes used as a demonstration of "ferromagnetic" behaviour on a large scale. It's a bit of a fraud, however, since the mechanism here is purely classical, and much weaker than the quantum mechanical exchange forces that are actually responsible for ferromagnetism. 13]

At the interface between one linear magnetic material and another, the magnetic field lines bend (Fig. 6.32). Show that tan胃2/tan胃1=渭2/渭1 assuming there is no free current at the boundary. Compare Eq. 4.68.

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
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