Magnetic Fields in Matter Chapter 6

2  Magnetization

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4 Torques and Forces on Magnetic Dipoles rotation

5  Magnetization random paramagnetism Diamagnetism External B field Ferromagnetism

6  Magnetization Force on magnetic dipole Case of uniform field (B=constant): 0

7  Magnetization x y Case of nonuniform field (B ≠ constant): I B Fringing field

8  Magnetization I y z x

9 I y z x

10  Magnetization Electric dipole - + Magnetic dipole S N Gilbert model I Ampere model

11  Magnetization Effect of magnetic field on atomic orbits

12  Magnetization only electric force add magnetic field

13  Magnetization when B is turn on,the electron speeds up.

14  Magnetization

15  Bound Currents

16  Bound Currents

17  Bound Currents 0

18  Bound Currents --Using Biot-Savart law

19  Bound Currents Exp 1: Find the magnetic field at the center of a uniformly magnetized sphere.

20  Bound Currents Exp 1:

21  Bound Currents Exp 1: R θ

22  Bound Currents Exp 1: b

23  Bound Currents Find the magnetic field of point P. Find the magnetic field of point P.

24  Bound Currents    u R

25  Physical Interpretation of Bound Currents When the magnetization is uniform:

26 When the magnetization is nonuniform:  Physical Interpretation of Bound Currents

27  The Auxiliary Field H

28  The Auxiliary Field H Exp 2: A long copper rod of radius R carries a uniformly distributed (free) current I. Find H inside and outside the rod. current I. Find H inside and outside the rod.  The Auxiliary Field H

29 Exp 2:  The Auxiliary Field H

30  A Deceptive Parallel Ampere law in vacuum : Ampere law in magnetic materials : Whereas,the divergence of is not, in general, zero.

31  Boundary condition a

32  Boundary condition

33  Linear and Nonlinear Media 磁化率

34  Linear and Nonlinear Media 磁導率

35 For linear isotropic homogeneous media ElectricMagnetic  Linear and Nonlinear Media

36  Linear and Nonlinear Media Exp 3: An infinite solenoid (n turns per unit length, current I) is filled with linear material of susceptibility χ m. Find the magnetic field inside the solenoid. material of susceptibility χ m. Find the magnetic field inside the solenoid.

37  Ferromagnetism Ferromagnetic Materials : Fe, Co, Ni, Gd, Dy domain The domains range from about to m 3 in volume and contain to atoms. domain wall

38  Ferromagnetism Ferromagnetic domains. (photo courtesy of R. W. DeBlois)

39  Ferromagnetism Hysteresis loop saturation remanence coercive c a g b d f e

40 Hysteresis loop hard soft  Ferromagnetism

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56  In diamagnetic materials (bismuth 鉍 ): spin moments tend to be dominant and produce f ields that oppose the external field. Thus, the internal magnetic field is reduced slightly c ompared to the external field.  If diople moments dominate slightly, then the internal field is increase slightly over the external field and the material is paramagnetic (tungsten 鎢 ).  Large diople moments are produced in certain regions or domains for the ferromagnetic materials (iron). A random domain alignment exists for virgin ferromagnetic material. W hen an external field is applied and then removed, a net alignment occurs given permane nt magnetization and hysteresis effect. Alloys of some of the ferromagnetic materials are also ferromagnetic (alnico 磁性合金 )  In ferrimagnetic materials, adjacent atoms develop unequal, but oppositely directed mo ments, allowing a rather larger response to external fields. From the point of view of eng ineering applications, the ferrites are very important ferrimagnetic materials. Ferries poss ess a very high resistance, and hence give very little eddy current loss at higher frequenci es when used as transformer cores.  The magnetic tape used for audio and video recording is a superparamagnetic material and is composed of an array of small ferromagnetic particles.

57  The Auxiliary Field H