Chapter 11 Magnetic Field

in the Medium

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

When a magnetic medium is brought into a magnetic field,

§ 11-1 Classifications of magnetic media Magnetic permeability

(1)The matter will be magnetized;

(2) The magnetic field will also be influenced and changed:

BBB

External fieldExternal field

additional field due to the magnetization of matter

1. Magnetization of Media

2.Classification of Magnetic Media

(1)Paramagnetic substance( 顺磁质 ): has sa

me direction of , --- .

B

B

BB

(2) Diamagnetic substance( 抗磁质）： is opposite to , --- .

B

0B

0BB

(3)Ferromagnetic substance( 铁磁质 ): has the same direction of and .

B

0B

BB

3. Permeability （磁导率）

---relative permeability of

the material.

B

Br

cetansubsticferromagnefor

cetansubscdiamagnetifor

cetansubsicparamagnetfor

vacuumfor

r

0 r ---Permeability

§ 11-2 Molecular Theory of Paramagnetism & Diamagnetism

1. The basic theory:

atomMolecule

electron

Charged and spin

Diamagnetic substance0mp

Paramagnetic substancemp

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.

mp

Molecular magnetic dipole

2. Paramagnetic substance: 0mp

Mg, Al, W, Pt, O2 ,etc.

Randomly due to thermal motion ， no magnetism

0B

Surface magnetized current:

mp

0B

In the external M-field, turns to B>B0

0B

mp

3. diamagnetic substance: 0mp

The electrons in the atom is in precession( 进动） around t

he direction of because of the Lorentz force . 0B

axis0B

0B

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

0S

SdB

does not change;

IdB 0

however, the Ampere’s law

should be changed into another form.

)II(ldB mc

l

0

)II(ldB mc

l

0

BB

molecular (or polarizing ) current

unknown

2. Ampere’s Law in a Medium

Example: the long solenoid

nIB 00

nIBB r 0

rr

sj

sjB 0

nIjnIBBB s 000

From

we have

nI)(nIj rs 10

0

nI)(nIj rs 1

0

0

Depend on r and conduction current I.

Taking the loop as shown in Fig., apply Ampere’s law ,

)II(ldB m 0

mII

UsingnI)(nIj rs 1

0

0

III)(I rm III)(I rm

rr

IlB

d

IlB d

IlB d

We have

Introduce a new quantity

B

H

---magnetic intensity

rr PP

IldH

we have

---Ampere’s law forH

conduction currents

(auxiliary parameter)

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=?

NIrH 2

Here:r

Nn

nIr

NIH

nIHB

IldHl

Asr

dd

d<<r

§11-4 Ferromagnetic

1. Properties of Ferromagnetic material

(1) r >>1, BBBB

B-H curve

H

B

O

HB 0

ferromagnetism paramagnetism diamagnetism

ferromagnetism paramagnetism diamagnetism

(2) r is not a constant is not a linear

function of , it is depends on the magnetizing process.

B

H

HB

(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

nIH

Ferromagnetic substance

I

Primary coil

secondary coil

BGBG

Magnetizing Magnetizing currentcurrent

Determine Determine HH

Measure Measure BB

H

B

O

B～ H

Initial magnetization curve

(2)Hysteresis Loop

The process of magnetization;

B

depending on not only H but on the magnetic history of sample ;

H

磁滞回线

H

H

B

O

B～ H

The B-H curve for decreasing H does not coincide with that for increasing H, which is called hysteresis( 滞后）；

Remanence ( 剩磁） and Coercive force ( 矫顽力）

rBcH

磁滞回线

HcH

rB

剩磁

矫顽力

３ . Hard & soft M-materials

a） soft b） hard c）矩磁铁氧体材料

H

B

H

B

H

B

The different material can be used for different purpose.

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。

Soft material ： is small, be suitable for alternating M-field.

cH

Hard material ： is large, be suitable for permanent magnet.

cH

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. 量子理论证明，在这种作用下 , 铁磁质的内部形成了一些自发磁化的小区域－磁畴：

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

The electronic spinning magnetic moments of The electronic spinning magnetic moments of

the adjacent atoms align spontaneously to the adjacent atoms align spontaneously to

form many of small magnetization volume – form many of small magnetization volume –

M-domain.M-domain.

(1)(1) HH=0=0 ：： M-domains are M-domains are randomly oriented.randomly oriented.

--no magnetism in macroscopic size.

(2)(2) when the external M-field when the external M-field H H

is supplied, is supplied,

the domains that are the domains that are oriented favorably with oriented favorably with HH increase in size – increase in size – the walls of the walls of domainsdomains are moving. are moving.

the orientation of the domains turn to the dithe orientation of the domains turn to the direction ofrection of HH..

(3)(3) when thewhen the H H is intensive, all dimains turn to is intensive, all dimains turn to

the direction of the direction of H.H.

(4) (4) When the When the HH is removed, the domains disrupt is removed, the domains disrupt

again. But they can not restore their initial again. But they can not restore their initial

states because of internal strain.states because of internal strain.

--Hysteresis