《Electromagnetism, principles and application》教学课件（PPT讲稿）Chapter 14 Magnetic Fields：VII

14.2 The Equivalent Surface Current density ae Recall: a loop of area tr and of current i has a magnetic moment m=TR I See Fig 14-1 .I meter M Figure 14-1 Ampere's model for the equivalent current in a cylinder of magnetized material

Each square cell has a cross-sectional area an 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 surface current density a=M Thus, taking into account of the direction, one gets e M×n 1 called the equivalent surface current densi Recall the bound surface charge density Ob=Pn

14. 3 The equivalent Volume Current Density Je One molecule has a current 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 lad cos o all the molecules in this volume contribute a current Nadl cos0= Nm.dl=m. dl

Integrating dl over the path C yields the equivalent current le going through 亿M:dl=le, or in the differential form Y×M=Je ere Te=s Je da with S being the e surface boun y the closed pa Conclusion: the magnetization M gives rise to the equivalent current densities ae or Je