磁性麥斯威爾方程式

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12 Magnetism of Matter

Maxwell’s Equations

磁性麥斯威爾方程式

How can a clay- walled kiln reveal Earth’s magnetic field of the past?

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The earth’s dipole field The mid-atlantic ridge

The Magnetic field of the Earth

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Sections

1. 物質的磁性 Magnetism

2. 麥斯威爾方程式 Maxwell’s Equations

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12-1 Magnetic Materials

 Diamagnetism (逆磁性)

 Paramagnetism (順磁性)

 Ferromagnetism (鐵磁性)

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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

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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

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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

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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

   







 



 

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Loop Model in a Nonuniform Field

for diamagnetic material

downward  and upward force

increase

upward  and downward force

decrease When B_ext is turned on:

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Loop Model in a Nonuniform Field

A diamagnetic material placed in an external magnetic field B_extdevelops a magnetic dipole moment directed opposite B_ext.

If the field is nonuniform, the diamagnetic material is repelled from a region of greater magnetic field toward a region of lesser field.

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Magnetic susceptibility

0

1

m

m m

K K

 





 

•permeability 導磁率

•susceptibility 磁化率

bismuth铋

pyrolytic graphite 熱解石墨

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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。

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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。

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12-1.2.1 Curie’s Law

M：Magnetization

A magnetization curve for

potassium chromium sulfate硫酸铬钾

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12-1.3 Ferromagnetism

•鎳的磁域(magnetic domain)

Ferrohydrodynamics

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12-1.3.1 Rowland Ring

0 0

0 P

M

B i n

B B B





 

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12-1.3.2 Magnetization Curve

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Magnetic domains of ferromagnetic materials

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12-1.3.3 Hysteresis (磁滯)

矯頑磁力 coercive force 殘餘磁通密度

Residual Flux Density

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Hysteresis

• Read the text discussion of hysteresis using Figure 28.29 below.

• Follow Example 28.12.

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12-2 Maxwell’s Equations

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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

   

  



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

Magnetic dipole: north/south pole

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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



















 



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12-2.4 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.

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Law) M axwell

- (Ampere

+

Law) s

(Ampere'

0 0

enc E

enc

dt i s d

d B

i s

d B









 







 

12-2.5 Ampere-Maxwell Law

induced B field induced E field

Both increasing

ε d ^B

Ε ds dt

     

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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













 





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







































 



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12-2.6 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

  



 

  

 

 



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12-2.7 Maxwell’s Equations

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磁 性 麥斯威爾方程式