Chapter 14 Magnetic Fields: VIl Magnetization M The equivalent surface Current densit The equivalent Volume Current Denisity J Calculation of Magnetic fields in materia Magnetic Field intensity H Amperes circuit Law Magnetic Susceptibility permeability a Magnetization curve ■ 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 due to free 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
In 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 gment→< E random motion Diamagnetic: in diamagnetic materials the elemen tary magnetic moments are not permanent, but are d induce
Ferromagnetic: in ferromagnetic materials such as iron the magnetization can be much larger than that of 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 DX 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 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