32 Magnetism of Matter:Maxwell ’ s Equations
31
32 Magnetism of Matter:Max 32 Magnetism of Matter:Max well’s Equations well’s Equations 32-1 Magnets implest magnetic structure that ca magnetic dipole.Magnetic monopoles xist(as far as we know)
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32 Magnetism of Matter:Maxwell ’ s Equations. 32-1 Magnets. The simplest magnetic structure that can exit is a magnetic dipole.Magnetic monopoles do not exist(as far as we know). 32-2 Gauss ’ Law for Magnetic Fields. 32-3 The Magnetism of Earth. 32-4 Magnetism and Electrons. - PowerPoint PPT Presentation
Transcript of 32 Magnetism of Matter:Maxwell ’ s Equations
32 Magnetism of Matter:Maxwell’s 32 Magnetism of Matter:Maxwell’s EquationsEquations
32-1 Magnets
The simplest magnetic structure that can exitis a magnetic dipole.Magnetic monopoles donot exist(as far as we know)
32-2 Gauss’ Law for Magnetic Field32-2 Gauss’ Law for Magnetic Fieldss
0 AdBB
0 AdBB
0enc
E
qAdE
0enc
E
qAdE
32-3 The Magnetism of Earth32-3 The Magnetism of Earth
32-4 Magnetism and Electrons32-4 Magnetism and Electrons
Spin Magnetic Dipole Moment
Sm
es
Sm
es
TJm
ehB /1027.9
424
TJ
m
ehB /1027.9
424
extzsexts BBU ,
extzsexts BBU ,
Orbital Magnetic Dipole MomentOrbital Magnetic Dipole Moment
orborb Lm
eu
2
orborb L
m
eu
2
extzorbextorb BBU ,
extzorbextorb BBU ,
Loop Model for Electron OrbitsLoop Model for Electron OrbitsiAorb iAorb
vr
ei
/2
vr
ei
/2
2/22 evrr
vr
eorb
2/22 evrr
vr
eorb
mrvmrvLorb 090sin mrvmrvLorb 090sin
orborb Lm
e 2
orborb L
m
e 2
Loop Model in a Nonuniform FieldLoop Model in a Nonuniform Field
extBLidFd
extBLidFd
32-5 Magnetic Materials32-5 Magnetic Materials
Diamagnetism
Paramagnetism
Ferromagnetism
32-6 Diamagnetism32-6 Diamagnetism
A diamagnetic material placed in an externalmagnetic field develops a magnetic dipole moment directed opposite .If thefield is nonuniform,the diamagnetic materialis repelled from a region of greater magneticfield toward a region of lesser field.
extB
extB
32-7 Paramagnetism32-7 Paramagnetism
A paramagnetic material placed in an externalmagnetic field develops a magnetic dipolemoment in the direction of .If the field is nonuniform,the paramagnetic material is attracted toward a region of greater magnetic field from a region of lesser field.
extB
extB
T
BCM ext
T
BCM ext
Sample Problem 32-1Sample Problem 32-1
eVJ
KKJkTK
039.0102.6
300/1038.12
3
2
3
21
23
eVJ
KKJkTK
039.0102.6
300/1038.12
3
2
3
21
23
eVJ
TTJB
BBBU
B
B
00017.0108.2
5.1/1027.922
20cos180cos
23
24
00
eVJ
TTJB
BBBU
B
B
00017.0108.2
5.1/1027.922
20cos180cos
23
24
00
32-8 Ferromagnetism32-8 Ferromagnetism
niB p00
MBBB 0 MBBB 0
Magnetic DomainsMagnetic Domains
A ferromagnetic material placed in an externalmagnetic field develops a strong magneticdipole moment in the direction of If the field is nonuniform,the ferromagnetic materialis attracted toward a region of greater magneticfield from a region of lesser field.
extB
extB
Sample Problem 32-2Sample Problem 32-2
FeN 10.0FeN 10.0
Step one:Step one:N=
needle’s mass
iron’s atomic mass
Step two:Step two:
iron’s Atomic= mass
iron’s molar mass M
Acogadro’s number NA
Step three:Step three: N=mNA
M
Step four:Step four: needle’s mass m
=(needle’s density)(needle’s volume)=(7900kg/m3)(1.5×10 － 8m3)=1.185×10-4kg
Step five:Step five:
21
234
102774.1
/055847.0
)1002.6)(10185.1(
molekg
kgN
21
234
102774.1
/055847.0
)1002.6)(10185.1(
molekg
kgN
TJTJ
TJ
/107.2/10682.2
/101.2102774.110.033
2321
TJTJ
TJ
/107.2/10682.2
/101.2102774.110.033
2321
Step six:Step six:
HysteresisHysteresis
32-9 Induced Magnetic Fields32-9 Induced Magnetic Fields
dt
dsdE B
dt
dsdE B
dt
dsdB E
00
dt
dsdB E
00
Ampere-Maxwell LawAmpere-Maxwell Law
encisdB 0 encisdB 0
encE i
dt
dsdB 000
enc
E idt
dsdB 000
Sample Problem 32-3Sample Problem 32-3(a)
Step one:Step one:
dt
dsdB E
00
dt
dsdB E
00
Step two:Step two: BdsBdssdB 00cos
BdsBdssdB 00cos
Step three:Step three: dt
EAdrB 002
dt
EAdrB 002
dt
dEArB 002 dt
dEArB 002
Step four:Step four:
dt
dErB
200
dt
dErB
200
(b)
Tdt
dErB 8
00 1018.92
1 Tdt
dErB 8
00 1018.92
1
(c)
dr
dE
r
RB
2
200
dr
dE
r
RB
2
200
32-10 Displacement Current32-10 Displacement Current
dt
di Ed
0
dt
di Ed
0
encencd iisdB 0,0
encencd iisdB 0,0
Finding the Induced Magnetic Finding the Induced Magnetic FieldField
rR
iB d
20
2
rR
iB d
20
2
r
iB d
2
0r
iB d
2
0
Sample Problem 32-4Sample Problem 32-4(a)
encdisdB ,0
encdisdB ,0
Step one:Step one:
Step two:Step two:
2
2
, R
rii dencd
2
2
, R
rii dencd
Step three:Step three:
25
5/ 02
2
0
i
R
RisdB
25
5/ 02
2
0
i
R
RisdB
Step four:Step four:
25
5/ 02
2
0
i
R
RisdB
25
5/ 02
2
0
i
R
RisdB
(b)
Step one:Step one:
R
i
R
Rir
R
iB ddd
102
5/
20
20
20
R
i
R
Rir
R
iB ddd
102
5/
20
20
20
Step two:Step two:
R
iR
R
iB dd
220
20
max
R
iR
R
iB dd
220
20
max
32-11 Maxwell’s Equations32-11 Maxwell’s Equations
Gauss’ law for electricity
0/encqAdE
0/encqAdE
Gauss’ law for magnetism
0 AdB
0 AdB
Faraday’s law
dt
dsdE B
dt
dsdE B
Ampere-Maxwell law
encE i
dt
dsdB 000
enc
E idt
dsdB 000
