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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

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

An infinitely long cylinder, of radius R, carries a "frozen-in" magnetization, parallel to the axis

M=ksz^,

Where is a constant and is the distance from the axis; there is no free current anywhere. Find the magnetic field inside and outside the cylinder by two different methods: (a) As in Sect. 6.2, locate all the bound currents, and calculate the field they produce. (b) Use Ampere's law (in the form of Eq. 6.20) to find, and then get from Eq. 6.18. (Notice that the second method is much faster, and avoids any explicit reference to the bound currents.)

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.

Imagine two charged magnetic dipoles (charge q, dipole moment m), constrained to move on the z axis (same as Problem 6.23(a), but without gravity). Electrically they repel, but magnetically (if both m's point in the z direction) they attract.

(a) Find the equilibrium separation distance.

(b) What is the equilibrium separation for two electrons in this orientation. [Answer: 4.72x10-13m.]

(c) Does there exist, then, a stable bound state of two electrons?

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.]
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