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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

Compare Eqs. 2.15, 4.9, and 6.11. Notice that if 蚁,P , and Mare uniform, the same integral is involved in all three:

鈭�r^r2d蟿'

Therefore, if you happen to know the electric field of a uniformly charged object, you can immediately write down the scalar potential of a uniformly polarized object, and the vector potential of a uniformly magnetized object, of the same shape. Use this observation to obtain Vinside and outside a uniformly polarized sphere (Ex. 4.2), andA inside and outside a uniformly magnetized sphere (Ex. 6.1).

How would you go about demagnetizing a permanent magnet (such as the wrench we have been discussing, at point in the hysteresis loop)? That is, how could you restore it to its original state, with M = 0 at / = 0 ?

A magnetic dipole m is imbedded at the center of a sphere (radius R) of linear magnetic material (permeability 渭). Show that the magnetic field inside the sphere 0<r鈮�R is

渭4蟺{1r3[3(m.r^r^-m)]+2(渭0-渭)m(2渭0+渭)R3}

What is the field outside the sphere?

A short circular cylinder of radius and length L carries a "frozen-in" uniform magnetization M parallel to its axis. Find the bound current, and sketch the magnetic field of the cylinder. (Make three sketches: one forL>>a, one forL<<a, and one forL鈮�a.) Compare this bar magnet with the bar electret of Prob. 4.11.

Starting from the Lorentz force law, in the form of Eq. 5.16, show that the torque on any steady current distribution (not just a square loop) in a uniform field B is m脳B.
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