1. Fields and Waves
Lesson 4.6
MAGNETIC MATERIALS
Darryl Michael/GE CRD

2. Magnetic Materials Today’s Lesson: linkage between H and B fields
M - magnetization
re-visit Ampere’s Law
boundary conditions
permanent magnets

3. Magnetic Materials
Vast majority of materials
Magnetic properties tend to either very strong or very weak
ferromagnets (Fe) and permanent magnets
Use simple, linear model
exhibit strong non-linear effects
demonstrate “memory” or hysterisis effects
Recall in electrostatics that most materials have moderate effect:
1 < e < 10

4. Magnetic Materials In Quantum mechanics, atoms have “spin”
In the classical picture:
electron orbits the nucleus
acts like a current loop
Usually in most materials, the loops has random orientation - so the net effect is small
In ferromagnets, neighboring atoms have spins that are aligned - strong effects

5. Magnetic Dipole Moment
The individual current loops can be thought of as having a dipole moment,

6. Relationship between & In general, one can write: magnetization
Sum over all atoms
-flux due to all sources
where,
-flux due to atomic sources
-flux due to free current
(e.g. conduction current, e-beam)

7. Relationship between & Maxwell’s equation:
these are free-currents
Maxwell’s equation:
we can determine H without determining M
In most general form:
If,
Values,
most materials
for iron

8. Curves for & Typical B-H Curve for materials
For course, use ideal curve: H B

9. Boundary Conditions Do problem 1a: use then apply Boundary Conditions:
Normal component: h a
Material 1
Material 2
TOP
BOTTOM
Take h << a (a thin disc)
ignore contribution from the sides

10. Boundary Conditions Boundary Conditions: Tangential component:
h << w
Material 1
Material 2 w h
Inet can only be due to surface currents = Js.w
Surface currents
- out of plane or
If non-conductor, Js = 0 ,then,
If conductor in 1 and

11. Magnetic Materials Do Problems 1b and 2
Problem 2 : Field lines exit normally in high m materials
Also, field lines like to travel through high m materials
Transformers :
use IRON to direct flux
primary and secondary windings intercept almost all the flux - no need for “smoothly-wound” coils
Noise reduction
increase Inductance with increasing m
Do Problem 3

12. Magnetic and Electric Dipole Moment
The current loop approximates the dipole moment,
E-field of electric dipole
B-field of magnetic dipole
Far-fields look the same for both types of dipoles