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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?

(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

(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

for diamagnetic material

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)

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

(12)

12-1.1 Diamagnetism

(13)

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。

(14)

12-1.2.1 Curie’s Law

M：Magnetization

A magnetization curve for

potassium chromium sulfate硫酸铬钾

(15)

12-1.3 Ferromagnetism

•鎳的磁域(magnetic domain)

Ferrohydrodynamics

(16)

12-1.3.1 Rowland Ring

0 0

0 P

M

B i n

B B B

(17)

12-1.3.2 Magnetization Curve

(18)

Magnetic domains of ferromagnetic materials

(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)

12-2.1

/ A

0 A

0

q d

E d B

E B

0 0

B

E

E ds d

dt B ds d

  dt

 

(23)

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

Magnetic dipole: north/south pole

(24)

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



(25)

12-2.4 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.

(26)

Law) M axwell

- (Ampere

+

Law) s

(Ampere'

0 0

0 0

enc E

enc

dt i s d

d B

i s

d B

12-2.5 Ampere-Maxwell Law

induced B field induced E field

Both increasing

ε d B

Ε ds dt

 

(27)

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

(28)

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

 

(29)

12-2.7 Maxwell’s Equations

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The localization plays important role in supersymmetric (exact solvable) field theory. A special Wilson loop is also solvable by

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

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

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

Define instead the imaginary.. potential, magnetic field, lattice…) Dirac-BdG Hamiltonian:. with small, and matrix

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