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