电磁场与电磁波第13讲磁化强度磁场强度和相对导磁率-wb

1、1Field and Wave Electromagnetics电磁场与电磁波电磁场与电磁波2012. 4. 121. Introduction2. Fundamental Postulates of Magnetostatics in free spaceFqEquBLorentzs force equation0BJ0BDifferential form0SB ds0CB dlIIntegral formPostulates of Magnetostatics in Free SpaceReview33. Vector Magnetic Potential4. The Biot-Savar

2、t Law and Applications0BBA20AJ ;020202zzyyxxJAJAJA0 (Wb/m)4VJAdvR0023 (T)44RCCCIIaRBd ld ldBRR4Main topic Steady Magnetic Fields3. Magnetic Field Intensity and Relative Permeability1. The Magnetic Dipole2. Magnetization and Equivalent Current Densities5Example 6-6 cylindrical coordinatedla bdzrRopop

3、zaba 2zrrzdlRbdazabaa bzda b d22003/23/22222 (T)42zzcIIbb dBaabzbz03 (T)4CIRBdlRxzyIbPPoara azazara - ar1. The Magnetic Dipole6EXAMPLE 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).Spherical coordinatesRb014CIdlA

4、R( , , /2)P R xzyIbPoRR1 dl 1?dlR7 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 8( , , /2)P R xzyIbPoRR1 dlP ara 2221222 1/221cossinsin22112(1sinsin)RRbbRbbbbRRRRRR2222 1

5、/21,01121(1sinsin)(1sinsin)bRbRbbRRRRR920001200/20/22021(1sinsin)() sin44(1sinsin)sin4(1sinsin)sin2sin)4xxCIIdlbAa bdRRRIbbdRRIbbdRRIbaaaR203(2cossin )4RIbBAaaRMagnetic dipole:202sin4IbAaR( , , /2)P R xzyIbPoRR1 dlP ara 10203(2cossin )4RIbBaaR30(2cossin )4RpEaaRElectric dipole:Magnetic dipole:202sin

6、4IbAaR2200cos44Rp 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 the current.22 (A m )zzzma I

7、ba ISa m03(2cossin )4RmBaaR20022sin44RI bm aAaRR 11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pqd122. Magnetization and Equivalent Current DensitiescdbaFFBSanFdcbaFFFBSdcbaFFBBnBtFFSdFIdlB磁偶极子受磁场力而转动130BB14as where mk be the magnetic dipole moment of an atom，n is th

8、e 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 we define a magnetization vector, M, 10

9、lim (A/m) n vkkvmMv The magnetic dipole moment dm of an elemental volume dv is dm=Mdv , will produce a vector magnetic potential02 4RMadAdvR15Integrating over the volume V of the dielectric, we obtain the vector magnetic potential due to the magnetized dielectricWhere R is the distance from the elem

10、ental volume dv to a fixed field point. 0021=() 44RVVVaAdAMdvMdvRRRecalling the vector identity,11()()MMMRRR we can rewrite as00()44VVMMAdvdvRR 16BecauseVSFdvF ds We have0044nVVMaMAdvdsRR 00 44sVSJJAd v AdsRR;SimilarThe effect of the magnetization vector is equivalent to both a volume current densit

11、y and a surface current density. A/mmsnJM a2 (A/m )mJMWhere an is the unit outward normal vector from ds and S is the surface bounding the volume V .173. Magnetic Field Intensity and Relative PermeabilityIn the magnetized medium, the magnetic field can be considered as that produced by the conductin

12、g 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 material180 BMJWe now define a new fundamental field quantity, the magnetic field intensity H, such that0 (A/m).BHMHJ0BDiffe

13、rential form0SB dsCH dlIIntegral formPostulates of Magnetostatics in magnetic material19CH 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 current flow follow the right-hand rule.

14、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 determining the magnetic flux density H

15、 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.20Substitution 02000 ()(1) (Wb/m )mrBHMBHMHHH Relative permeability1rm （Absolute） permeability0r When the magnetic properties of the medium are linear and isotropic, the mag

16、netization is directly proportional to the magnetic field intensitymMHWhere m is a dimensionless quantity called Magnetic susceptibility21 Nevertheless, whether it is the diamagnetic or the paramagnetic material, magnetization is very weak. Hence, usually their relative permeability can be considere

17、d to be equal to 1. After a diamagnetic (抗磁质抗磁质) material is magnetized the composite magnetic field will be decreased, thus1 , , 0r 0 m A paramagnetic (顺磁质顺磁质)material is magnetized, the composite magnetic field will be increased, thus1 , , 0r 0 m The magnetization in ferromagnetic (铁磁性铁磁性) materia

18、ls is very strong, so that the value of the relative permeability could be very large. 1rm 0r 22The relative permabilities of three kinds of magnetic materialsMaterialsrGold0.9996Silver0.9998Copper0.9999MaterialsrAluminum1.000021Magnesium1.000012Titanium1.000180MaterialsrNickel250Iron4000Mu-metal105

19、Diamagnetic FerromagneticParamagnetic23 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

20、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，剩磁很大。磁很大。当温度很高时，由于无规则热运动的增强，磁性会消失，这个临界当