2. §10.1 磁介质对磁场的影响
0E
v
• An insulator in an electric field
Relative permittivity
rEE ε0
rr
='EEE 0
vvv
+= 相对介电常数
1>rεhomogeneous isotropic dielectric material
均匀、各向同性的电介质
• homogeneous isotropic magnetic material in an
magnetic field 0B
v
0BB r
rr
µ=
Relative Permeabilityr
Experiment result
µ
相对磁导率 退出返回
3. Materials can be classified by how they respond to an
applied magnetic field 0B
r
0BB r
rr
µ=
•抗磁质 Diamagnetic (silver, copper, water,…)
(slightly less than 1)1<rµ 1≈rµ0BB <
•顺磁质 Paramagnetic (aluminum, tungsten, oxygen,…)
(slightly greater than 1) 1≈rµ1>rµ 0BB >
•铁磁质 Ferromagnetic (iron, cobalt, nickel,…)
1>>rµ )10~10( 42
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4. Atoms as Magnets
• Classical view of the atom: electron(s) in orbit around
nucleus
The orbital angular momentum
kvrmL e
ˆ=
r
轨道角动量
This is a current loop;
)()
2
( 2
kˆr
r
v
eorb −⋅⋅= π
π
µ
r 磁偶极矩
磁矩
L
m
e
e
r
2
−=
kˆevr
2
1
−=
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should have magnetic moment
轨道磁矩
5. L
m
e
e
orb
rr
2
−=µ
Quantum mechanics shows the orbital angular momentum
of an electron is quantized.
Its component in a particular direction is always an integer
multiple of h/2π.
(limit)210 ，，，， …±±== llLz h π2
h
=h
轨道角动量轨道磁矩
量子化
e
z,orb
m
e
l
2
h
−=µ Blµ−=
玻尔磁子
224
mA10279
2
⋅×== −
.
m
e
e
B
h
µ Bohr magneton
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6. • An electron has an intrinsic angular momentum called
its spin angular momentum (or just spin) ; associated
with this spin is an intrinsic spin magnetic dipole
moment
S
r
sµ
r
S
m
e
e
s
rr
−=µ 自旋角动量自旋磁矩
The component of intrinsic angular momentum is
quantized
2
1
h±=zS
量子化
B
e
z,s
m
e
µµ ±=±=
2
h
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7. Diamagnetism and Paramagnetism 抗磁质和顺磁质
the vector sum of magnetic dipole moment of all the
electrons in the molecular
∑=
i
iµµ
rr
Molecular magnetic dipole moment 分子磁矩
Diamagnetic material : In the absence of an external
magnetic field , the vector sum of magnetic dipole
moment of all the electrons in the molecular is zero.
Paramagnetic material : These materials contain
molecules with permanent magnetic dipole moments.
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固有磁矩
抗磁质
顺磁质
8. 1. Diamagnetism
0BM orb
rrr
×= µ
dtBdtMLd orb )( 0
rrrr
×== µ
LLd
rr
⊥ precession
L
m
e
orb
rr
2
−=µdtBL
m
e
)(
2
0
rr
×−=
orbµ∆
r
0B
r
orbµ
r
L
r
orbµ∆
r
0B//orb
rr
−µ∆
Additional magnetic moment
进动
附加磁矩 感应磁矩
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抗磁质
In the external magnetic field 0B
r
0B
r
orbµ
r
L
r
orbµ∆
r
Ld
r
电子轨道运动
10. 2. Paramagnetism
The permanent magnetic dipole moments tend to line
up , that is parallel to the direction of the external
field. But thermal motion randomizes their directions,
so only a small effect persists.
宏观小 微观大
These dipoles are randomly
oriented due to thermal motion
In the external magnetic field 0B
r
0BM i
rrr
×= µ
0B
v
'B
v
V∆ 0=∑i
iµ
r
0≠∑i
iµ
r
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顺磁质
0BB >
产生的附加磁场方向与外磁
场的方向相同
B//
i
i
rr
∑µ
13. Diamagnetic material 0B//M
rr
−(2) 00 ≠B
r
Paramagnetic material 0B//M
rr
Paramagnetic substances are
attracted to one pole of a
nearby bar magnet.
Diamagnetic substances are
repelled by one pole of a nearby
bar magnet.
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14. 0B
v
PM
0I
0I
Magnetization current
磁化电流
Consider a cylinder of
magnetized material.
Because of cancellation of
neighboring current loops,
the net current at any
point inside the material is
zero.
I'
0B
r
Leaving a net current on the surface of the material.I′
This surface current magnetization current.I′
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磁化电流
16. The relationship between andM
r
α′
r
IS
i
i
′=∑ d∆µ
r
θ
µ
cosd∆
d∆
∆ lS
IS
V
M
i
i
′
==
∑
r
ld
r
M
r
'dI S∆
θ
M
r
ld
r
neˆ
ϕ
l
I
d
d ′
=′α ϕsinM=θcosM=
neˆM ×=′
rr
α
∫ ⋅=′
L
ldMI
rr
lMlMI
rr
dcosdd ⋅==′ θ
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19. Gauss’s law in magnetic materials
'BBB
vvv
+= 0
In magnetic materials, the magnetic field lines also
form closed curves. For a closed surface,
§10.3 有磁介质时的高斯定理
0d0d0 =⋅′=⋅ ∫∫∫∫ SBSB
ss
rrrr
0)( 00 =⋅′+⋅=⋅′+=⋅ ∫∫∫∫∫∫∫∫ SdBSdBSdBBSdB
ssss
rrrrrrrrr
0d =⋅∫∫ SB
s
rr
磁介质1
磁介质2
1neˆ
2neˆ nn BB 21 =
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