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# 12 Magnetism of Matter 磁 性 Electromagnetic Waves 電磁波

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(1)

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?

(2)

The earth’s dipole field The mid-atlantic ridge

The Magnetic field of the Earth

(3)

### 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

(4)

12-1 Magnetic Materials

Diamagnetism (逆磁性)

Paramagnetism (順磁性)

Ferromagnetism (鐵磁性)

(5)

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

(6)

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

(7)

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

(8)

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

(9)

Loop Model in a Nonuniform Field

downward  and upward force

increase

upward  and downward force

decrease When Bext is turned on:

(10)

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.

(11)

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)

12-1.1 Diamagnetism

(13)

### ferromagnetism

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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。

(15)

12-1.2.1 Curie’s Law

M：Magnetization

A magnetization curve for

potassium chromium sulfate硫酸铬钾

(16)

12-1.3 Ferromagnetism

•鎳的磁域(magnetic domain)

Ferrohydrodynamics

(17)

12-1.3.1 Rowland Ring

0 0

0 P

M

B i n

B B B

(18)

12-1.3.2 Magnetization Curve

(19)

12-1.3.3 Hysteresis (磁滯)

Residual Flux Density

(20)

Hysteresis

Read the text discussion of hysteresis using Figure 28.29 below.

(21)

(22)

/ A

0 A

0

q d

E d B

E B

0 0

B

E

E ds d

dt B ds d

  dt

 

(23)

/ A

0 A

0

q d

E d B

E B

### 

(24)

12-2.2 Magnets and magnetic flux (磁鐵和磁通量)

Magnetic dipole: north/south pole

(25)

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

### 

(26)

12-2.4 Gauss’ Law for electric Fields

Flux  enclosed charge

qenc

A d E

## 

0 0

(27)

12-2.5 Induced Magnetic Fields

inductin) of

Law s

(M axwell'

inductin) of

Law s

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.

(28)

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

(29)

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

(30)

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

 

(31)

12-2.9 Maxwell’s Equations

(32)

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

(33)

The Traveling Electromagnetic Wave

hdE

Eh h

dE E

s d E

dt s d

d E

### 

)

(

• The induced electric field:

(34)

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

### 

)

(

(35)

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(

(36)

․The induced magnetic field:

hdB

Bh h

dB B

s d B

dt s d

d

B E

### 

) (

0 0

(37)

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

(38)

Light  Electromagnetic Waves

Hertz (赫茲)– Radio Waves

The Electromagnetic Spectrum

The Relative Sensitivity of Human eyes 430nm – 690nm

12-3.1 Characteristics

(39)

12-3.2 Maxwell’s Rainbow

(40)

12-3.3

### Comets

What shapes the curved dust tail of a comet?

(41)

․Momentum Gain of an Object

) reflection (total

2

) absorption (total

c p U

c p U

Momentum change energy change

(42)

․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

(43)

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

(44)

αR2 αR3

(45)

### 12-4 Polarization (偏振)

Polarized Light

The Plane of Polarization

Linear, Circular and Elliptical polarization

(46)

(47)

Polarization of Light

(48)

(49)

### 12-4.1

Liquid Crystal - I

(50)

Liquid Crystal - II

(51)

Liquid Crystal - III

(52)

LCD –Liquid Crystal Display

(53)

We explicitly saw the dimensional reason for the occurrence of the magnetic catalysis on the basis of the scaling argument. However, the precise form of gap depends

A diamagnetic material placed in an external magnetic field B ext develops a magnetic dipole moment directed opposite B ext. If the field is nonuniform, the diamagnetic material

The CME drastically changes the time evolution of the chiral fluid in a B-field. - Chiral fluid is not stable against a small perturbation on v

reveal Earth’s magnetic field of the past?... The earth’s dipole field The

10 Magnetism of Matter 磁 性 Electromagnetic Waves 電磁 波. How can a clay-walled kiln reveal

In section29-8,we saw that if we put a closed conducting loop in a B and then send current through the loop, forces due to the magnetic field create a torque to turn the loopÆ

for a uniform field, a point charge, and an electric

• Figure 21.31 below left shows the force on a dipole in an electric field. electric