Section 4 3 TRƯỜNG ĐIỆN TỪ

4 3 Magnetic materials Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electromagnetics, Sixth Edition” by Nannapaneni Narayana Rao Edwa[.]

Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electromagnetics, Sixth Edition” by Nannapaneni Narayana Rao Edward C Jordan Professor of Electrical and Computer Engineering University of Illinois at Urbana-Champaign, Urbana, Illinois, USA Distinguished Amrita Professor of Engineering Amrita Vishwa Vidyapeetham, Coimbatore, Tamil Nadu, India 4.3 Magnetic Materials 4.3-3 Magnetic Materials are based upon the property of magnetization, which is the phenomenon of creation of magnetic dipoles within the material Diamagnetism: A net dipole moment is induced by changing the angular velocities of the electronic orbits I + A e I Dipole moment m = IA an 4.3-4 Paramagnetism Already existing dipoles are acted upon by a torque I dl × B I B I dl × B I 4.3-5 The phenomenon of magnetization results in a magnetization current in the material which produces a secondary B  J S 0a y z=d Ba m  m z=0 J S 0a y z=d J mS  J mS 0a y Bs z=0 J mS  J mS 0a y Bt Magnetization Current 4.3-6 4.3-7 To take into account the effect of magnetization, we define the magnetic field intensity vector, H, as H B  M 0 m B B     m  B   01  m  B   r B  A m    permeability, H m r  relative permeability r and  vary with the material, implicitly taking into account the effect of magnetization 4.3-8 As an example, consider  J S 0a y z m y x J S 0a y Then inside the material,   B = J S 0a y × az   J S 0a y  × az  2   J S ax B H   J S ax  4.3-9 D4.6  0.1 a y z=d z  100  z=0 0.1 a y For < z < d, (a) H  0.1 a y × a z  0.1 a x A m y x 4.3-10 (b) B =  H = 100  00.1 a x  10  0ax Wb m2  4 10 ax Wb m2 (c) M  B  H 0 = 10 ax  0.1 ax  9.9 ax A m