中国科学技术大学：《电磁学》课程教学资源（PPT课件讲稿）Chapter 14 Magnetic Fields：VII

Chapter 14 Magnetic Fields: VII a Magnetization M The equivalent Surface Current Density The equivalent Volume Current Denisity J Calculation of Magnetic Fields in Material Magnetic Field intensity H Ampere' s circuit Law Magnetic Susceptibility, permeability a Magnetization Curve a Hysterisis

Chapter 14 Magnetic Fields:VII ◼ Magnetization M ◼ The Equivalent Surface Current Density ◼ The Equivalent Volume Current Denisity J ◼ Calculation of Magnetic Fields in Material ◼ Magnetic Field Intensity H ◼ Ampere’s Circuit Law ◼ Magnetic Susceptibility, Permeability ◼ Magnetization Curve ◼ Hysterisis

14. 1 Magnetization M So far we have studied only those magnetic fields ue to tree charges. In fact, all bodies contain spinning electrons moving in orbits, and they also produce magnetic fields Magnetized: Magnetic materials are similar to di- electrICs, Charges can possess magnetic moments, and these together can produce a resultant magnetic moment in a macroscopic body. Such a body is said to be magnetized

n most atoms the magnetic moments associated with the orbital and spinning motions of electrons cancel Paramagnetic: If the cancellation is not complete the material is said to paramagnetic When such a substance is put into a magnetic field gmeD→mm0mm010m Diamagnetic: in diamagnetic materials the elemen tary magnetic moments are not permanent but are nduced

erromagnetIC: in ferromagnetic materialS, such as iron, the magnetization can be much larger than that ot para-or diamagnetIc substances Domain: in ferromagnetic materials there are re gions in which electron spins are aligned. The mag netization of one domain may be oriented at random w.r.t. that of a neighboring domain Remark: usually dielectric D O E, linear; but in ferromagnetic materials the magnetization is non linear and depends on history

14.1 The Magnetization The magnetization M is the magnetization moment per unit volume at a given point If m is the average magnetic dipole moment per atom and they are aligned in the same direction, then the magnetization M=Nm where N is the number density of atoms M has unit: ampere/meter

14.2 The equivalent Surface Current density ae Recall: a loop of area T R and of current I has a magnetic moment m=TR-I See fig. 14-1 I meter M x Figure 14-1 Ampere's model for the equivalent current in a cylinder of magnetized material

Each square cell has a cross-sectional area a" and a length l, and carries a surface current density a (ampere per meter) Each cell has a magnetic moment m ala Each cell has a magnetization M=m/volume=a Inside, all the currents cancel, except at the bound ary with the le surface curre ent density a=M Thus, taking into account of the direction, one gets le= M X n1 called the equivalent surface current density Recall the bound surface charge density ob=Pn

14.3 The equivalent Volume Current Density Je One molecule has a current I with an area a, so its magnetic dipole moment is m=lae Consider a small length dl Taking dl as the hight and a cos o as the cross sectional area, we get a small volume adl cos o a molecule in this volume will contribute a current ladl cos 6 All the molecules in this volume contribute a current N/ adl cos0=Nm·dl=M·dl

Integrating dl over the path C yields the equivalent current le going through M·dl=le or in the differential form V×M=Je, lere Is Je da with s being the surface bounded by the closed path C onclusion the magnetization m gives rise to the equivalent current densities ae or Je

14. 4 Magnetic Field Originating in Magnetized Ma- terial In magnetized material the equivalent current den sities Ce or je also generate its magnetic field B just as if they were situated in a vacuum V×B=u0Je