电磁场与电磁波第13讲磁化强度磁场强度和相对导磁率

1、Field and Wave Electromagnetic电磁场与电磁波电磁场与电磁波第第13讲讲2作业情况作业情况1班：人班：人合计：人合计：人情况情况:31. Introduction2. Fundamental Postulates of Magnetostatics in free spaceFqEquBLorentzs force equation0BJ0BDifferential form0SB ds0CB dlIIntegral formPostulates of Magnetostatics in Free SpaceReview43. Vector Magnetic Pot

2、ential4. The Biot-Savart Law and Applications0BBA20AJ ;020202zzyyxxJAJAJA0 (Wb/m)4VJAdvR0023 (T)44RCCCIIaRBd ld ldBRR5Main topic Steady Magnetic Fields3. Magnetic Field Intensity and Relative Permeability1. The Magnetic Dipole2. Magnetization and Equivalent Current Densities6Example 6-6 cylindrical

3、coordinatedla bdzrRopopzaba 2zrrzdlRbdazabaa bzda b d22003/23/22222 (T)42zzcIIbb dBaabzbz03 (T)4CIRBd lRxzyIbPPoara azazara - ar1. The Magnetic Dipole7EXAMPLE 6-7 Find the magnetic flux density at a distant point of a small circular loop of radius b that carries current I (a magnetic dipole).Spheric

4、al coordinatesRb014CId lAR( , , /2)P R xzyIbPoRR1 dl 1?dlRP8 sinc cos (sins o)xxyyyxyxd lbdadxd labdaabddyd labdaabdd ldxadyaabda sincos (sin cos)xxyyyxyxd lbdadxd labdaabddyd labdaabdd ldx ady aaabd ( , , /2)P R xzyIbPoRR1 dlP ara ara 9( , , /2)P R xzyIbPoRR1 dlP ara 2221222 1/221cossinsin22112(1si

5、nsin)RRbbRbbbbRRRRRR2222 1/21,01121(1sinsin)(1sinsin)bRbRbbRRRRR1020001200/20/22021(1sinsin)() sin44(1sinsin)sin4(1sinsin)sin2sin)4xxCIId lbAa bdRRRIbbdRRIbbdRRIbaaaR203(2cossin )4RIbBAaaR Magnetic dipole:202sin4IbAaR( , , /2)P R xzyIbPoRR1 dlP ara 11203(2cossin )4RIbBaaR30(2cossin )4RpEaaRElectric

6、dipole:Magnetic dipole:202sin4IbAaR2200cos44RP aqdVRRWhere is defined as the magnetic dipole moment, which is a vector whose magnitude is the product of the current in and the area of the loop and whose direction is the direction of the thumb as the fingers of the right hand follow the direction of

7、the current.22 (A m )zzzma I ba ISa m03(2cossin )4RmBaaR20022sin44RI bm aAaRR 12模型模型 极化，磁化极化，磁化产生的电场与磁场产生的电场与磁场电电偶偶极极子子磁磁偶偶极极子子mISpPpsnP amsnJMamJM电磁对偶性电磁对偶性pqd132. Magnetization and Equivalent Current DensitiescdbaFFBSanFdcbaFFFBSdcbaFFBBnBtFFSdFIdlB磁偶极子受磁场力而转动磁偶极子受磁场力而转动140BB15as where mk be the m

8、agnetic dipole moment of an atom，n is the number of atoms per unit volume and the numerator represents the vector sum of the magnetic dipole moments contained in a very small volume v. The vector M, is the volume density of magnetic dipole moment.To analyze the macroscopic effect of magnetic dipoles

9、 we define a magnetization vector, M, 10lim (A/m) n vkkvmMv The magnetic dipole moment dm of an elemental volume dv is dm=Mdv , will produce a vector magnetic potential02 4RMadAdvR16Integrating over the volume V of the dielectric, we obtain the vector magnetic potential due to the magnetized dielect

10、ricWhere R is the distance from the elemental volume dv to a fixed field point. 0021=() 44RVVVaAdAMdvMdvRRRecalling the vector identity,11()()MMMRRR we can rewrite as00()44VVMMAdvdvRR 17BecauseVSFdvF ds We have0044nVSMaMAdvdsRR 00 44sVSJJAd v AdsRR;SimilarThe effect of the magnetization vector is eq

11、uivalent to both a volume current density and a surface current density. A/mmsnJMa2 (A/m )mJMWhere an is the unit outward normal vector from ds and S is the surface bounding the volume V .183. Magnetic Field Intensity and Relative PermeabilityIn the magnetized medium, the magnetic field can be consi

12、dered as that produced by the conducting current I and the magnetizing current I in vacuum. In this way, 0B0 BJFundamental equation of magnetostatics in free space0000 1mBJJJMBMJBMJ Fundamental equation of magnetic material190 BMJWe now define a new fundamental field quantity, the magnetic field int

13、ensity H, such that0 (A/m).BHMHJ0B Differential form0SB dsCH dlIIntegral formPostulates of Magnetostatics in magnetic material20CH dlIwhere the path C for the line integral is the contour bounding the surface S, and I is the total free current through S. The sense of tracing C and the direction of c

14、urrent flow follow the right-hand rule. This equation is a form of Amperes circuital law, which states that the circulation of the magnetic field density around any closed path is equal to the total free current flowing through the surface bounded by the path. Amperes circuital law is very useful in

15、 determining the magnetic flux density H caused by a current I when there is a closed path C around the current such that the magnitude of H is constant over the path.21Substitution 02000 ()(1) (Wb/m )mrBHMBHMHHH Relative permeability1rm （Absolute） permeability0r When the magnetic properties of the

16、medium are linear and isotropic, the magnetization is directly proportional to the magnetic field intensitymMHWhere m is a dimensionless quantity called Magnetic susceptibility22 Nevertheless, whether it is the diamagnetic抗磁性抗磁性 or the paramagnetic顺磁性顺磁性 material, magnetization is very weak. Hence,

17、usually their relative permeability can be considered to be equal to 1. After a diamagnetic (抗磁性抗磁性) material is magnetized the composite magnetic field will be decreased, thus1 , , 0r 0 m A paramagnetic (顺磁性顺磁性)material is magnetized, the composite magnetic field will be increased, thus1 , , 0r 0 m

18、 The magnetization in ferromagnetic (铁磁性铁磁性) materials is very strong, so that the value of the relative permeability could be very large. 1rm 0r 23The relative permabilities of three kinds of magnetic materialsMaterialsrGold0.9996Silver0.9998Copper0.9999MaterialsrAluminum1.000021Magnesium1.000012Ti

19、tanium1.000180MaterialsrNickel250Iron4000Mu-metal105Diamagnetic 抗磁性抗磁性 Ferromagnetic铁磁性铁磁性Paramagnetic顺磁性顺磁性24 铁、钴、镍铁、钴、镍及一些及一些稀土元素稀土元素存在独特的磁性现象称为存在独特的磁性现象称为铁磁性铁磁性，这，这个名称的由来是因为铁是具有个名称的由来是因为铁是具有铁磁性铁磁性物质中最常见也是最典型的。物质中最常见也是最典型的。钐钐(Samarium)，钕钕(neodymium)与与钴钴的合金常被用来制造强磁铁。的合金常被用来制造强磁铁。 铁磁性材料存在铁磁性材料存在长程序长

20、程序，即，即磁畴磁畴(自发磁化的小区域称为磁畴自发磁化的小区域称为磁畴)内每内每个原子的未配对电子个原子的未配对电子自旋倾向于平行排列自旋倾向于平行排列。因此，在磁畴内磁性是非常。因此，在磁畴内磁性是非常强的，但材料整体可能并不体现出强磁性，因为不同磁畴的磁性取向可强的，但材料整体可能并不体现出强磁性，因为不同磁畴的磁性取向可能是随机排列的。如果我们外加一个能是随机排列的。如果我们外加一个微小磁场微小磁场，比如螺线管的磁场会使，比如螺线管的磁场会使本来随机排列的本来随机排列的磁畴取向一致磁畴取向一致，这时我们说材料被磁化。材料被磁化后，这时我们说材料被磁化。材料被磁化后，将得到很强的磁场，这就是电磁铁的物理原理。将得到很强的磁场，这就是电磁铁的物理原理。 当外加磁场去掉后，材料仍会剩余一些磁场，或者说材料当外加磁场去掉后，材料仍会剩余一些磁场，或者说材料记忆记忆了了它们被磁化的历史。这种现象叫作它们被磁化的历史。这种现象叫作剩磁剩磁，所谓，所谓永磁体永磁体就是被磁化后，剩就是被磁化后