Transcript Sources of Magnetic Field

Chapter 27
Magnetism in
Matter
Topics
 Magnetization
 Saturation
 Types
magnetization
of materials
Magnetization
Atoms have magnetic dipole
moments due to
 orbital
motion of the electrons
 magnetic
electron
moment of the
Magnetization
Material placed in magnetic field 
magnetic dipole moments aligned 
material “magnetized”
Magnetization

magnetization = net magnetic dipole
moment per unit volume
d
M 
dV

magnetization contributes an
additional magnetic, Bm, given by
Bm  o M
Magnetic susceptibility
Magnetization M
depends on
applied field
Bapp and the
susceptibility
m of the
material
M  m
Bapp
o
Bm   m Bapp
Magnetic susceptibility
For paramagnets:
 For diamagnets:
 Total field:

m > 0
m < 0
B  Bapp  o M  Bapp (1  m )  Km Bapp

Km = relative permeability of the
material
Km  1   m
Magnetic moment and angular
momentum
Angular momentum L  r  p
 For circular motion L = rmv
 Magnetic moment of current loop
 = IA = Iπr2
 For single charge q on circular
orbit I = q/T = qv/(2πr)
=Iπr2 = qvπr2/(2πr)
q
= qvr/2 = qL/(2m)

L

2m
Saturation magnetization


Magnetization grows with applied
field until all magnetic moments
are aligned --“saturation”
At saturation, the magnetization
is Ms = n•μ, where n is number of
atoms per unit volume and μ is the
magnetic moment of each atom
Types of Materials
Materials exhibit three types of
magnetism:
 paramagnetic
 diamagnetic
 ferromagnetic
Paramagnetism
Paramagnetic materials
 have permanent magnetic
moments
 moments
randomly oriented at
normal temperatures
 adds
a small additional field to
applied magnetic field
Paramagnetism
 Small
effect (changes B by only
0.01%)

Example materials
 Oxygen (STP), aluminum,
tungsten, platinum
Diamagnetism
Diamagnetic materials
 no permanent magnetic
moments
 magnetic
moments induced by
applied magnetic field B
 applied
field creates magnetic
moments opposed to the field
Diamagnetism



Common to all materials.
Applied B field induces a magnetic
field opposite the applied field,
thereby weakening the overall
magnetic field
But the effect is very small:
Bm ≈ -10-4 Bapp
Diamagnetism
Example materials
 High temperature
superconductors
 copper
 silver
Ferromagnetism
Ferromagnetic materials
 have permanent magnetic
moments
 align
at normal temperatures
when an external field is
applied and strongly enhances
applied magnetic field
Ferromagnetism
Ferromagnetic materials
(e.g. Fe, Ni, Co, alloys)
have domains of randomly
aligned magnetization
(due to strong interaction
of magnetic moments of neighboring
atoms)
Ferromagnetism
Applying a magnetic field causes
domains aligned with the applied field
to grow at the expense of others
that shrink
Saturation magnetization is reached
when the aligned domains
have replaced all others
Ferromagnetism
In ferromagnets, some magnetization
will remain after the applied
field is reduced to zero,
yielding permanent magnets
Such materials exhibit
hysteresis
Material properties
Summary
The magnetism of materials is due
to the magnetic dipole moments
of atoms, which arise from:
 the orbital motion of electrons
 and
the intrinsic magnetic
moment of each electron
Summary
Three classes of materials
 Diamagnetic M = - const • Bext,
small effect (10-4)
 Paramagnetic M = + const • Bext
small effect (10-2)
 Ferromagnetic M ≠ const • Bext
large effect (1000)