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第十一章稳恒电流

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```									Chapter 11 Magnetic Field
in the Medium

(Magnetic Property of Matter)
§ 11-1 Classifications of magnetic media
Magnetic permeability

§ 11-2 Molecular theory of paramagnetism &
Diamagnetism

§ 11-3 Ampere’s Law in the magnetic matter
and magnetic intensity H

§ 11-4 Ferromagnetism
§ 11-1 Classifications of magnetic media
Magnetic permeability
1. Magnetization of Media
When a magnetic medium is brought into a
magnetic field,
(1)The matter will be magnetized;
(2) The magnetic field will also be influenced
and changed:
       
B  B  B      additional field due to the
magnetization of matter
External field
2.Classification of Magnetic Media

(1)Paramagnetic substance( 顺 磁 质 ): B  has

same direction of B , --- B  B .

(2) Diamagnetic substance(抗磁质）： B  is

opposite to B0, --- B  B0 .


(3)Ferromagnetic substance(铁磁质):
                  B has
the same direction of B0 and B  B .
3. Permeability（磁导率）
B ---relative permeability of
r 
B   the material.

       for vacuum
 
         for paramagnet ic subs tan ce
r 
       for diamagnetic subs tan ce
  
         for ferromagne tic subs tan ce

  r 0   ---Permeability
§ 11-2 Molecular Theory of Paramagnetism
& Diamagnetism
1. The basic theory:

Molecule               atom

Charged
and spin

electron
There are the elementary current loops
resulting from electron spinning （ 自 旋 ）
about their axes and revolving （轨道旋转）in
orbits around nuclei, --- Molecular Current.

        Paramagnetic substance
pm                     
pm  
Molecular magnetic dipole
Diamagnetic substance

pm  0

2. Paramagnetic substance:        pm  0
Mg, Al, W, Pt, O2 ,etc.
              
B0
pm

B0

In the external M-field,
           
Randomly due to
thermal motion，
pm turns to B0
 no magnetism           B>B0

Surface magnetized
current:

3. diamagnetic substance: pm  0
The electrons in the atom is in precession(进动）around

the direction of B because of the Lorentz force .
0

                                   axis
B0             B0


              B
B
§11-3    Ampere’s Law in a Medium
1. The extension of two laws:
Like the conduction current,molecular
current will produce the magnetic field. For the
magnetic medium, the Gauss’s magnetic law
 

S
B  dS  0 does not change;

however, the Ampere’s law
 
 B  d    0  I should be changed
                  into another form.
 
 B  dl   0 (  I c   I m )
l

molecular (or polarizing ) current

unknown

B
2. Ampere’s Law in a Medium
Example: the long solenoid

B0   0 nI

js

r

B   0 j s
B   r B0  nI
From
B  B0  B   0 nI   0 j s  nI
we have
  0
js         nI  (  r  1 )nI
0
Depend on r and conduction current I.
Taking the loop as                    r
shown in Fig., apply
Ampere’s law ,

 B  dl   0 (  I  I m )
   I    I m
Using
  0
js         nI  (  r  1 )nI
0

   I m    (  r   ) I    I     I
We have
 
 B  dl    I               r P

B 
   dl   I
Introduce a new quantity

     B                        (auxiliary
H        ---magnetic intensity parameter)

we have                 conduction currents
                               
 H  dl   I ---Ampere’s law for H
Example: A specimen of ferromagnetism with 
is formed in a toroidal ring, A wire carrying I is
uniformly close packed over the ring. The
number of winds per unit length is n. find B=?
d<<r
 
r            As  H  dl   I
l
d
2 rH  NI
NI
H      nI
r

B  H   nI    Here: n  N
r
§11-4       Ferromagnetic
1. Properties of Ferromagnetic material
            
(1) r >>1,   B  B  B  B
B      
 ferromagnetism
         B  0 H
 paramagnetism
               diamagnetism
O
H
B-H curve

(2) r is not a constant  B is not a linear

function of H , it is depends on the
magnetizing process.
    
B  H
(3) hysteresis (磁滞现象)
----B’s changing behinds the exterior field H);

(4) The temperature effect of ferromagnetism:
Curie temperature Tc
T < Tc , ferromagnetism
T > Tc , paramagnetism
2. Hysteresis Loop 磁滞回线
(1) Initial magnetization curve
Measure B
Magnetizing
current
BG
I
secondary coil
Primary coil

Ferromagnetic substance

H  nI
B
B～H

O                  H

Initial magnetization curve
(2)Hysteresis Loop
The process of magnetization;

B
B～H
H   H

O             H            磁滞回线


B depending on not only H but on the
magnetic history of sample ;
The B-H curve for decreasing H does not
coincide with that for increasing H, which is
called hysteresis(滞后）；

剩磁
Br

Hc            H
矫顽力

磁滞回线

RemanenceBr(剩磁）and Coercive force (矫顽

３. Hard & soft M-materials

B             B                B

H               H               H

a）soft       b）hard          c）矩磁铁氧体材料

The different material can be used for
different purpose.
H
Soft material： c is small, be suitable for
alternating M-field.
Hard material： c is large, be suitable for
H
permanent magnet.
矩磁铁氧体材料：反向磁场一超过矫顽力
磁化方向立即反转—只有两种磁
化状态，对应电流的开与关两种
状态，适用于做计算机的存储器
元件的环形磁芯。
４. Magnetic Domains 磁畴
The magnetism of ferromagnetic materials
result from spinning of the electrons.
The interactions between the atoms in the
ferromagnetic materials are intensive. 量子理论

４. Magnetic Domains 磁畴
The magnetism of ferromagnetic materials
result from spinning of the electrons.

The electronic spinning magnetic moments of
the adjacent atoms align spontaneously to
form many of small magnetization volume –
M-domain.
       

        
(1) H=0：M-domains are                 
randomly oriented.
--no magnetism in
macroscopic size.                    
(2) when the external M-field H
is supplied,
 the domains that are
oriented favorably with H
increase in size – the walls of
domains are moving.
 the orientation of the domains turn to the
direction of H.
(3) when the H is intensive, all dimains turn to
the direction of H.

(4) When the H is removed, the domains disrupt
again. But they can not restore their initial
states because of internal strain.
--Hysteresis

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