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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

Magnetic Materials

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

Dipole moment

m = IA a n

+

I A

Already existing dipoles are acted upon by a torque

I

I

B

I dl × B

I dl × B

z = d

z = 0

0

mS  J mS y

0

mS J mS y

Bs

Bt

The phenomenon of magnetization results in a magnetization

current in the material which produces a secondary B.

Ba

z = 0

z = d

0

  

0 y

J

0 y

J a

To take into account the effect of magnetization, we define the

magnetic field intensity vector, H, as

r and  vary with the material, implicitly taking into account the effect of magnetization

permeability, H m relative permeability

r









0

0

0

1 1

A m

m m

m

r





 



 

 











B

B B B

Then inside the material,

0

S x

J





a

0

S x

J



  B



0 y

J a

0 y

J

 a

z x y

D4.6

For 0 < z < d,

(a)

0

100

z = d

z = 0

z x y

2 0

x x

x





a

a

0

9.9 A m

x







B

a