12 Magnetism of Matter 磁 性
Electromagnetic Waves 電磁波
How can a clay- walled kiln reveal Earth’s magnetic field of the past?
The earth’s dipole field The mid-atlantic ridge
The Magnetic field of the Earth
Sections
1. 物質的磁性 Magnetism
2. 麥斯威爾方程式 Maxwell’s Equations
3. 電磁波 Electromagnetic Waves 4. 偏振 Polarization
12-1 Magnetic Materials
Diamagnetism (逆磁性)
Paramagnetism (順磁性)
Ferromagnetism (鐵磁性)
Magnetism and Electrons
•除電子的運動(電流)外,其自旋與軌道 運動亦可產生磁場
Orbital Magnetic Dipole Moment
,
2 2
0, 1, 2, , (limit)
orb orb
orb z l l
l
e L m
L m h m
m
orbital magnetic quantum number
Spin Magnetic Dipole Moment and Bohr magneton
J/T 10
27 .
4 9
4
2 ) ( 1
2 ,
24 B
,
m eh
m S eh
m e
h m m
S m S
e
z z
s
s s
z s
spin magnetic quantum number
Loop Model for Electron Orbits
2 2 /
2
/ 2
time charge ,
2
orb orb
orb orb orb
m L mrv e
L
r evr v
r e
v r
i e iA
Loop Model in a Nonuniform Field
downward and upward force
increase
upward and downward force
decrease When Bext is turned on:
Loop Model in a Nonuniform Field
A diamagnetic material placed in an external magnetic field Bext develops a magnetic dipole moment directed opposite Bext .
If the field is nonuniform, the diamagnetic material is repelled from a region of greater magnetic field toward a region of lesser field.
The Bohr magneton and paramagnetism
0
1
m
m m
K K
•permeability 導磁率
•susceptibility 磁化率
bismuth铋
pyrolytic graphite 熱解石墨
12-1.1 Diamagnetism
逆磁性材料產生之磁矩與外磁場逆向,
如外磁場非均勻,其將受到由強磁場區 到弱磁場區之斥力。
Diamagnetism and
ferromagnetism
12-1.2 Paramagnetism
•液態氧被吸在兩個磁極之間
•順磁性材料產生之磁矩與外磁場順 向,如外磁場非均勻,其將受到由 弱磁場區到強磁場區之吸力。
12-1.2.1 Curie’s Law
M:Magnetization
A magnetization curve for
potassium chromium sulfate硫酸铬钾
12-1.3 Ferromagnetism
•鎳的磁域(magnetic domain)
Ferrohydrodynamics
12-1.3.1 Rowland Ring
0 0
0 P
M
B i n
B B B
12-1.3.2 Magnetization Curve
12-1.3.3 Hysteresis (磁滯)
矯頑磁力 coercive force 殘餘磁通密度
Residual Flux Density
Hysteresis
• Read the text discussion of hysteresis using Figure 28.29 below.
• Follow Example 28.12.
12-2 Maxwell’s Equations
12-2.1
線積分與面積分 (安培迴路和高斯面)磁場環流量 (安培定律) 電場通量 電場環流量 磁場通量 法拉第定律
/ A
0 A
0
q d
E d B
E B
0 0
B
E
E ds d
dt B ds d
dt
高 斯 面
/ A
0 A
0
q d
E d B
E B
12-2.2 Magnets and magnetic flux (磁鐵和磁通量)
Magnetic dipole: north/south pole
12-2.3 Gauss’ Law for Magnetic Fields
The net magnetic flux thru any closed
Gaussian surface is zero.
/ A
0 A
0
q d
E
d B
E B
12-2.4 Gauss’ Law for electric Fields
Flux enclosed charge
qenc
A d E
0 0
12-2.5 Induced Magnetic Fields
inductin) of
Law s
(M axwell'
inductin) of
Law s
(Faraday'
0
0
dt s d
d B
dt s d
d E
E B
3 ways to produce a magnetic field:
by an electric current, by a magnetic material, and by induction.
Law) M axwell
- (Ampere
+
Law) s
(Ampere'
0 0
0 0
enc E
enc
dt i s d
d B
i s
d B
12-2.6 Ampere-Maxwell Law
induced B field induced E field
Both increasing
12-2.7 Find B(r)
R) r
(for
2
) (
2
R) r
(for
2
) (
2
2 0
0
2 0
0 2
0 0 0
0
2 0
0 2
0 0
0 0
dt dE r
B R
dt R dE
E dt R
r d B
dt dE B r
dt r dE
E dt r
r d B
dt s d
d
B E
12-2.8 Displacement Current
0 0 0
0
0 , 0
+
+
E
enc
E d
d enc enc
B ds d i
dt i d
dt
B ds i i
12-2.9 Maxwell’s Equations
12-3 Electromagnetic Waves
The oscillating E and B Fields
A Most Curious Wave –The ether (以太)
) sin(
) sin(
t kx
B B
t kx
E E
m m
The Traveling Electromagnetic Wave
hdE
Eh h
dE E
s d E
dt s d
d E
)
(
• The induced electric field:
dt dB dx
dE dt
hdx dB hdE
dt hdx dB
dt hdx d
B B
B
, ), )(
(
hdE
Eh h
dE E
s d E
dt s d
d E
)
(
B c E
t kx
B t
kx kE
t kx
t B B
t kx
x kE E
t B x
E dt
dB dx
dE
m m
m m
m m
) cos(
) cos(
) cos(
) cos(
․The induced magnetic field:
hdB
Bh h
dB B
s d B
dt s d
d
B E
) (
0 0
0 0 0
0 0
0
0 0
0 0 0
0
c 1 1 ,
) /
( 1
) cos(
) cos(
) (
), )(
(
c k
B E
t kx
kx kB
t E t
B dt
hdx dE hdB
dt hdx dE
dt hdx d
E
m m
m
E E
Light Electromagnetic Waves
Hertz (赫茲)– Radio Waves
The Electromagnetic Spectrum
The Relative Sensitivity of Human eyes 430nm – 690nm
12-3.1 Characteristics
12-3.2 Maxwell’s Rainbow
12-3.3
Comets
What shapes the curved dust tail of a comet?
12-3.3.1 Radiation Pressure
․Momentum Gain of an Object
) reflection (total
2
) absorption (total
c p U
c p U
Momentum change energy change
․The Force Exerted by Radiation
) reflection (total
2
2
) absorption (total
c p I
c F IA
c p I
c F IA
c t IA c
p U t
IA t U
F p
r r
GM m c
R P F
F
r
R GM
r
m F GM
cr R P c
R F I
c F IA
r I P
S S
g r
S S
g
S r
r S
7 2
3 2
2 2 2
2
10 7
. 16 1
3 3 4
4 4
․The size of comet particles
光壓 重力
αR2 αR312-4 Polarization (偏振)
Polarized Light
The Plane of Polarization
Linear, Circular and Elliptical polarization
偏振片
Polarization of Light
偏 振 與 太 陽 眼鏡
12-4.1
Liquid Crystal - ILiquid Crystal - II
Liquid Crystal - III
LCD –Liquid Crystal Display