7. magnetostatic fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12...
TRANSCRIPT
![Page 1: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/1.jpg)
7. Magnetostatic Field
![Page 2: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/2.jpg)
1
Matrix, Cross Product, Determinant
4 0 10
14
132
212
102
a)BABA(
a)BABA(
a)BABA(
BBB
AAA
aaa
BA
)B,B,B(B
)A,A,A(A
zxyyx
yxzzx
xyzzy
zyx
zyx
zyx
zyx
zyx
![Page 3: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/3.jpg)
2
22
22
2
2
2
yx3
]x)yx[(xx
f
?x
f
x)z,y,x(f
xy2x
f
zyx)z,y,x(f
)8.2(
zz
siny
cosx
)7.2(
zz
x
ytan
yx
1
22
φ
z
x
y
z
ρ
az
aρ
aφ
dρ
ρdφ
dz
편미분 (Partial Derivative)
![Page 4: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/4.jpg)
3
)Spherical(A
sinr
1)sinA(
sinr
1)Ar(
rr
1A
)lCylindrica( z
AA1)A(
1A
(Catesian) z
A
y
A
x
AA
Divergence
)Spherical( aV
sinr
1a
V
r
1a
r
VV
)lCylindrica( az
Va
V1a
VV
)(Cartesian az
Va
y
Va
x
VV
Gradient
r2
2
z
zyx
r
z
zyx
Del Operator
![Page 5: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/5.jpg)
4
AsinrrAAr
asinrara
sinr
1A
AAAz
aaa
1A
AAA
zyx
aaa
A
Curl
r
r
2
z
z
zyx
zyx
zxyyx
yxzzx
xyzzy
zyx
zyx
zyx
a)BABA(
a)BABA(
a)BABA(
BBB
AAA
aaa
BA
![Page 6: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/6.jpg)
5dzddxddv
add
adzd
adzdSd
adzadadLd
coordinate ylindricalC
dzdxdyxddv
adS
adydx
adxdz
adzdy Sd
adzadyadxLd
coordinateCartesian
3
z
z
3
n
z
y
x
zyx
적분자 (Integrator)
φ
z
x
y
z
ρ
az
aρ
aφ
dρ
ρdφ
dz
dL dzaz
dxax
dyay
![Page 7: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/7.jpg)
6
ddrdsinrxddv
addr
addrsinr
addsinrSd
adsinrardadrLd
coordinate Spherical
23
r2
r
θ는 Zenith Angle이고φ는Azimuthal Angle.
φ
z
x
y
θ
rdφ
r
dr
r sinθdφ
rdθr sinθ
![Page 8: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/8.jpg)
7
v3
vS
S nL
xdAdvASdA
theorem)(Gauss theoremDivergence
Sda)A(LdA
theoremsStoke'
선적분, 면적분
![Page 9: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/9.jpg)
8
densitychargeVolume:
densityCurrent:J
)(ty Permittivi : m/F10854.8m/F36/10
)(tyPermeabili:m/H104
fieldElectric:E
densityfluxElectric:ED
fluxMagnetic:B
fieldMagnetic:/BH
EqAmperet
DJH
VE0EEqFaradayt
BE
EqGauss0B
EqGaussD
v
1290
70
v
유전율
투자율
Maxwell Equation
![Page 10: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/10.jpg)
9
Ex 3.7 G r = 10e−z(ρaρ + az)일때 ρ=1, 0 ≤ z ≤1 인원통밖으로
나오는 G의 Flux를구하라.
0
2
1102)e1(102
2
12e10
dd10dzde10dde10
)0z(dd)a()aa(e10
)1(dzda)aa(e10
)1z(dda)aa(e10
dSaG
11
1
0
2
0
1
0
2
0z1
0
2
01
b1
0
2
0 zzz
s1
0
2
0 zz
t1
0
2
0 zzz
bstS n
zadd
adzd
adzdSd
coordlCylindrica
Ψt
Ψs
Ψb
z
yx
![Page 11: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/11.jpg)
10
2014.1 학기 중간고사:
다음그림의 Closed Path에서 (zax + yay + yaz) ∙ dL 을구하라.
xy
z1
1
②
①
③
2
1
0)adzLd,0yx(
Ld)ayayaz(
02
11
2
1dz)z1(dy)y(
)adzadyLd,0x,y1z(
Ld)ayayaz(
2/1dy)y()adyLd,0zx(
Ld)ayayaz(
Ld)ayayaz(
z
3 zyx
1
0
0
1
zy
2 zyx
1
0y
1 zyx
L zyx
zyx adzadyadxLd
coordCartesian
dL dzaz
dxax
dyay
![Page 12: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/12.jpg)
11
2013. 1 학기 기말고사:
J = (x, 0,0)일때중심이원점에있고반지름이 a인구의표면을통과하여흐르는전류의양을구하라.
3
3
3
3zyx
3
n
a3
4
xd
xdz
0
y
0
x
x
xdz
J
y
J
x
J
xdJ
dSaJ
a
dS
an=ar
![Page 13: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/13.jpg)
12
2013. 1 학기 기말고사:
J = (x, 0,0)일때중심이원점에있고반지름이 a인구의표면을통과하여흐르는전류의양을구하라.
3
3
2
0
1
023
2
02
033
2
rx
n
a3
4
)(3
2a2
d2
)2cos(1dt)t1(a2
tcos
dcosdsina
)ddsinr)(cos)(sincossinr(
dSaax
dSaJ
)23.2(
asinacosa
acos
asincos
asinsina
asin
acoscos
acossina
)22.2(
cosrz
sinsinry
cossinrx
rz
ry
rx
addraddrsinraddsinrSd
coordinate Spherical
r2
![Page 14: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/14.jpg)
13
tan 1 cot
sin cos
cscsec
2
22
secd
tand
sind
cosd
cosd
sind
tantan1
tantan)tan(
sincos)2cos(
sinsincoscos)cos(
cossin2)2sin(
sincoscossin)sin(
![Page 15: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/15.jpg)
14ab
h1
b
1
a
1
ba
h1
zh
bab
ba
h1
dzzh
bab
1
zh
bab
dz1
dzz
S
LR
h/z)ba(b
h
0
1
h
0
2
h
0 2
h
0 22
2013. 1학기 기말고사:
전도율이 σ 인물질로만들어진다음그림의원뿔대의상하양단사이의저항R을구하라.
Δz ~ dzρ
a
b
hz
ρ
![Page 16: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/16.jpg)
15JA/VeqPoisson
2/HBw2/EDwdensityEnergy
dt/LdIVdt/CdVI
LICVQ
SdBSdDFlux
r4
LIdA
r4
dLVPotential
)0J(VHVEPotential
HBEDField
]m/Wb[S/B]m/C[S/DdensityFlux
]m/A[L/IH]m/volt[L/VEensityintField
LIdvQdQelementSource
BvQFEQFForce
ILdHQSdD
R4
aLIdBda
r4
QQFlawBasic
2v
2
mE
L
m
22
encenc
2r0
r221
관계
자장전장
표 7.1 전기장과 자기장의 상사성
t
DJH
t
BE
0B
D v
Maxwell
![Page 17: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/17.jpg)
16
7.2 BIOT-SAVART’S LAW
)4.7(R4
RLdI
R4
aLdIHd
)3.7(R4
sindLIdH
)2.7(R
sindLkIdH
)1.7(R
sindLIdH
32R
2
2
2
Fig 7.1 𝐈𝐝 𝐋에 의한 자기장 𝐝𝐇
𝐁~𝐇
𝐑
𝐝 𝐋 I
P
𝛂
![Page 18: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/18.jpg)
17
Fig 7.2 Determining of dH using
(a) the right-hand rule, or
(b) the right=handed screw rule.
H (or I) is out
⊙
(a)
H (or I) is in
⊗
(b)
Fig 7.3 Conventional representation
of H (or I)
![Page 19: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/19.jpg)
18
![Page 20: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/20.jpg)
19
J
Ld
dvJ
LdAJ
LdAJLId
J
na
A
K
a
1
IdL = K ∙ adL
= Ka ∙ dL
= KdS
dL
an
![Page 21: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/21.jpg)
20
𝐁
𝐑~𝐚𝐫
𝐝 𝐋 I
P
(7.8)current) (volume R4
advJH
(7.7)current) (surface R4
adSKH
(7.6)current) (line R4
aLdIH
)5.7( dvJdSKdLI
R4
RLdI
R4
aLdIHd)4.7(
V 2R
S 2R
L 2R
32R
![Page 22: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/22.jpg)
21
Line current
z
xy
Ld
R a
z
x y
aza
a
z
B
O
α2
α1
RI
H
ρ
aρ
d L
aφP
)11.7( a]z[4
dzIH
)10.7(adz)aza(adzRLd
)9.7( R4
RLIdHd
2/322
zz
3
![Page 23: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/23.jpg)
22
z
B
O
α2
α1
RI
H
ρ
aρd L = aLdL
aφP
Fig 7.5 직선선도체에의한 P 점의자기장
)12.7(a)cos(cos4
IH
a)cos(cos4
I
dsin4
aI
accs
dccs
4
I
dccsdz
cotz
)11.7(a]z[4
dzIH
12
12
33
22
2
2/322
2
1
2
1
dccsdz
sin
sin
coscossinsin
d
dz
sin
cos
tan
1z
cotz
2
2
2
![Page 24: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/24.jpg)
23
dccs
tan
dsec
tan
tan
dseczdz
0d
dsecztandz)tanz(d
tanz
dccsdz
cotz
2
2
2
2
2tan 1 cot
sin cos
cscsec
2
22
secd
tand
sind
cosd
cosd
sind
tantan1
tantan)tan(
sincos)2cos(
sinsincoscos)cos(
cossin2)2sin(
sincoscossin)sin(
![Page 25: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/25.jpg)
24
z
B
O
α2
α1
RI
H
ρ
aρd L = aLdL
aφP
Fig 7.5 직선 선도체에의한 P 점의 자기장
)15.7( aaa
0,
current line infinitefor )14.7(a
2
IH
0,2/
current line infinite-semifor )13.7(a
4
IH
a)cos(cos4
IH)12.7(
L
21
21
12
![Page 26: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/26.jpg)
25
예제 7.1 그림 7.6 과 같이 도체 Loop에 10 A 의 전류가 흐를 때 (0,0,5)에서
(1) 번 도선에 의한 𝐇 를 구하라.
x
z5
2
2
1)5,0,0(
1
그림 7.6 삼각형도체 Loop
②
①
③
1
1 2x
z
y
10 A
(0,0,5)
(a)
m/mAa1.59
)a)(029/2(54
10H
)cos(cos4
IH
a)cos(cos4
IH)12.7(
29
2
25
2cos
0cos
2/
5
y
y
12
12
222
1
1
![Page 27: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/27.jpg)
26
m/mAa65.28a2.38
)a5
3a
5
4)(01(
54
3H
)cos(cos4
IH)12.7(
yx
yx
12
yx a5
3a
5
4
예제 7.2 그림 7.7 에서 보여준 3 A 가 흐르는 도선전류에 의한
(3,4,0)에서의 𝐇 를 구하라.
1cos
0cos
5
2
1
(𝟏) 𝐇𝟏
![Page 28: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/28.jpg)
27
m/mAa88.23
a)5
31(
44
3H
)cos(cos4
IH)12.7(
z
z
12
za
m/mA)88.23,65.28,2.38(
HHH 21
1cos
5/3cos
4
2
1
(𝟐) 𝐇𝟐
![Page 29: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/29.jpg)
28
![Page 30: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/30.jpg)
29
예제 7.3 그림 7.8 (a)에서 𝐚φ 방향으로 10 A 의 전류가 흐른다. (0,0,4)와
(0,0,-4)에서 𝐇 를 구하라. Coil의 반경은 3 이다.
Fig 7.8 (a) circular current loop,
(b) flux lines due to the current loop.
x
y
z
dHz
dHρ
dL aρ
ρ𝜑
R
P(0,0,h)
I
(a) circular current loop. (b) flux lines due to the current loop.
𝐇
𝐈
![Page 31: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/31.jpg)
30
m/A)36.0,0,0()4,0,0(H
m/A)36.0,0,0()4,0,0(H
)h(2
aI
)h(4
a2I
)h(4
a2I
)h(4
d)asina(coshIH
)adahd()h(4
IHd
adahd
h0
0d0
aaa
RLd
aha
)0,y,x()h,0,0(R
adLd
R4
RLIdHd)9.7(
2/322z
2
2/322z
2
2/322z
22
0 2/322
yx
z2
2/322
z2
z
z
3
x
y
z
dHz
dHρ
dL aρ
ρ𝜑
R
P(0,0,h)
I
yx
z
asinacosa)10.2(
adzadadLd)5.3(
![Page 32: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/32.jpg)
31
)10.2(
aa
acosasina
asinacosa
)9.2(
aa
acosasina
asinacosa
zz
yx
yx
zz
y
x
![Page 33: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/33.jpg)
32
예제 7.4 길이 L, 반경 a, 권선수 N 인 solenoid에전류 I가흐른다.
다음을유도하라.
(a) 축상의임의의 P 점에서
H =nI
2(cosθ2 − cosθ1)az
where n=N/L
Fig 7.9 Cross section of solenoid.
θ2
θ
P
dz I
L
z
a θ1
![Page 34: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/34.jpg)
33
z12
12
z
2/322
2
2/322
2
2/322
2
z
2/322
2
z
a)cos(cos2
nIH
)cos(cos2
nI
dsin2
nIH
dsin2
nI
)za(2
dznIa
)za(2
a)Indz(
)za(2
dIadH
L/Nn
3.7from)h(2
IH
2
1
예제
dsina
)za(dz
2
2/322
θ2
θ
P
dz I
L
z
a θ1
![Page 35: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/35.jpg)
34
3.7from)h(2
IH
2/322
2
z 예제
x
y
z
dHz
dHρ
dL aρ
ρ𝜑
R
P(0,0,h)
I
![Page 36: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/36.jpg)
35
dsina
)za(
dsina
)za(a
dsincsca
dcscadz
sin
1a
sin
coscossinsina
d
dz
sin
cosaz
z/atan
2
2/322
32/122
3
2
22tan 1 cot
sin cos
cscsec
2
22
secd
tand
sind
cosd
cosd
sind
tantan1
tantan)tan(
sincos)2cos(
sinsincoscos)cos(
cossin2)2sin(
sincoscossin)sin(
θ2
θ
P
dz I
L
z
a θ1
![Page 37: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/37.jpg)
36
zz
zz
z22
z12
122
2
z
aL
NIanIH
aL
NIanI
a4/La2
InL
a)cos(cos2
nIH
cos)2/L(a
2/Lcos
P
aLforcenterataL
NIH)b(
중심에서가
θ2
θ
P
dz I
L
z
a θ1
![Page 38: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/38.jpg)
37
7.3 AMPERE’S CIRCUIT LAW – MAXWELL’S EQUATION
)19.7(JH
)18.7(SdJI
)17.7(Sd)H(
LdHI
)16.7()lawcircuits'Ampere(ILdH
Senc
S
Lenc
enc
HI
Ld
![Page 39: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/39.jpg)
38
7.4 APPLICATION OF AMPERE’S LAW
A. Infinite Line Current
Fig 7.10 Ampere’s law applied to
an infinite filamentary line current.
a2
IH
2
IH
I2H
ILdH)16.7(
a2
IH)14.7(
a)cos(cos4
IH)12.7(
)20.7(a2
IH
enc
12
![Page 40: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/40.jpg)
39
B. Infinite Sheet of Current
)c21.7(bH2
]b[]H[
]a[]0[
]b[]H[
]a[]0[
LdHLdH
)b21.7(0zaH
0zaHH
)a21.7(bKILdH
o
0
0
1
4
4
3
3
2
2
1
x0
x0
yenc
K
H
H0ax H0ax
-H0ax -H0ax
zx
![Page 41: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/41.jpg)
40
𝐝𝐇는 -𝐚𝐱 방향
𝐝 𝐋은 -𝐚𝐳 방향
𝐝𝐇는 𝐚𝐱 방향
𝐝 𝐋은 -𝐚𝐳 방향
![Page 42: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/42.jpg)
41
)23.7(aK2
1H
)22.7(
0zaK2
1
0zaK2
1
H
)c21.7(bH2LdH
)b21.7(0zaH
0zaHH
)a21.7(bKILdH
n
xy
xy
o
x0
x0
yenc
![Page 43: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/43.jpg)
42
C. Infinitely Long Coaxial Transmission Line
)26.7(ba2
IH
)25.7(a0a2
IH
)24.7(SdJILdH
2
L enc1
![Page 44: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/44.jpg)
43
)25.7(a2
IH
H2LdH
aISdJ
a0
)24.7(SdJILdH
2
L
2
2
enc
L enc
1
1
)26.7(2
IH
H2LdH
a
aISdJ
ba
1L
2
2
enc
![Page 45: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/45.jpg)
44
)27.7(bt2t
b1
2
IH
H2LdH
b)tb(
bIISdJ
tbb
2
22
L
22
22
encenc
1
)28.7(0H
tb
![Page 46: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/46.jpg)
45
)29.7(
tb0
tbbabt2t
b1
2
I
baa2
I
a0aa2
I
H
2
22
2
Fig 7.13 Plot of Hφ against ρ.
Hφ
1
2πa
1
2πb
ρ0 a b b+t
![Page 47: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/47.jpg)
46
예제 7.5 z=0, z=4 인 평면에 𝐊 = −𝟏𝟎𝐚𝐱 𝐀/𝐦, 𝐊 = 𝟏𝟎𝐚𝐱 𝐀/𝐦 인 전류가 흐른다.
다음 point에서 𝐇를구하라.(a) (1,1,1) (b) (0,-3,0)
an
z=4
(1,1,1)an
x y
z
z=0
Fig 7.14 Parallel infinite current sheets.
K
m/Aa10HHH
m/Aa5)a()a10(2
1aK
2
1H
m/Aa5a)a10(2
1aK
2
1H
aK2
1H)3.7(
)1,1,1()a(
y40
yzxn4
yzxn0
n
![Page 48: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/48.jpg)
47
anz=4
(0,-3,10)
an
x y
z
z=0
K
m/Aa0HHH
m/Aa5a)a10(2
1aK
2
1H
m/Aa5a)a10(2
1aK
2
1H
aK2
1H)3.7(
)10,3,0()b(
y40
yzxn4
yzxn0
n
![Page 49: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/49.jpg)
48
예제 7.6 toroid에서 권선수 N 이고 전류 I 가 흐른다.
toroid 안과 밖에서 𝐇를 구하라.
0H0SdJ
L
NI
)toroid(2
NI
2
NIH
NI2H
I2HLdH)a27.7(
S
00
enc
밖에서는
반지름중심
𝐋
𝐒
𝐈
![Page 50: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/50.jpg)
49
7.5 MAGNETIC FLUX DENSTY – MAXWELL’S EQUATION
E )(
)Law'Gaussor Eq sMaxwell'4th (the
)34.7(0B
)33.7(0SdB
]Gauss000,10Tesla1
Teslam/Wb[B
)32.7(]Wb[SdB
space) free ofity (Permeabil:
)31.7(m/H104
)30.7(]Tesla[HB
2
S
70
0
![Page 51: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/51.jpg)
50
N
S
I
MagneticFluxLine
Fig 7.16 magnetic flux line due to a
straight wire with current
coming out of the page
![Page 52: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/52.jpg)
51
![Page 53: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/53.jpg)
52
7.6 MAXWELL’S EQUATIONS FOR STATIC EM FIELD
Law sAmpere' SdJLdHJH
field ticelectrosta
of venessConservati 0LdE0E
monopole magnetic
of ceNonexisten 0SdB0B
Law sGauss' dxdydzSdDD
Remark formIntegralformPoint
SL
L
S
vSv
![Page 54: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/54.jpg)
53
dSaJLdHdSa)H(
JH
EqAmperet
DJ
B
LdEdSa)E(
0E
EqFaradayt
BE
0dSaB
dV)0B(
EqGauss0B
dVdSaD
dV)E(
EqGaussE
nn
n
n
vn
v
v
![Page 55: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/55.jpg)
54
7.7 MAGNETIC SCALAR AND VECTOR POTENTIALS
)a35.7(VE
0E0)V(
)b35.7(AB
0B0)A(
)36.7(VH
0J if0H0)V(
mm
)39.7(AB
EqAmperet
DJ
B
EqFaradayt
BE
EqGauss0B
EqGaussE v
![Page 56: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/56.jpg)
55
)36.7(0J if0HVH m
)38.7(0V
0VH
m2
m2
EqAmperet
DJ
B
EqFaradayt
BE
EqGauss0B
EqGaussE v
![Page 57: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/57.jpg)
56
(7.43)current for volumeR4
dvJA
(7.42)current surfacefor R4
dSKA
(7.41)current linefor R4
LdIA
)40.7(r4
dQV
v0
S0
L0
0
![Page 58: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/58.jpg)
57
K
a
1
IdL = K ∙ adL
= Ka ∙ dL
= KdS
dL
an
J
Ld
dvJ
LdAJ
LdAJLId
J
na
A
![Page 59: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/59.jpg)
58
유도
L0
R4
LdIA)41.7(
L0
L0
L0
L0
L 30
L 30
3
RR
LId
4A
ARR
LId
4
RR
LId
4
RR
1LId
4
RR
)RR(LId
4B
R
RLId
4B
R
RLdkIBd
RR
1f
LIdu
ufuf)uf(
)i(장뒷
)ii(장뒷
R
R
R R
R
R
vd 𝐁
𝐑~𝐚𝐫
𝐝 𝐋 I
P
![Page 60: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/60.jpg)
59
3
2/3222
zyx
z2/32222/1222
z
y2/32222/1222
y
x2/3222
2/3222x
2/1222x
2/1222zyx
R
R
R
1
)zyx(
azayax
R
1
)az()zyx()zyx(z
a
)ay()zyx()zyx(y
a
)ax()zyx(
)x2()zyx(2
1a)zyx(
xa
)zyx(z
ay
ax
aR
1
)dzzd,dyyd,dxxd
)zz,yy,xx()z,y,x(
RRR
3
L0
L 30
RR
RR
RR
1
RR
1LId
4
RR
)RR(LId
4B
(i)
![Page 61: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/61.jpg)
60
RR
LId
RR
1LId
RR
LId
4
RR
1LId
4B
L0
L0
RR
1)LId(
RR
LId
RR
1)LId(
)LId(RR
1
)LId(RR
1
)LId(RR
1LId
RR
1
RR
1f
LIdu
ufuf)uf(
(ii)
![Page 62: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/62.jpg)
61
)51.7(LdA
SdA
SdB
L
S
S
![Page 63: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/63.jpg)
62
Wb75.3
dzd2
1
SdB)32.7(
a2
AB
1Method
5
0z
2
1
S
뒷장
뒷장
a2
AAA
z
aaa
1A
z
z
예제 7.7 A = −(ρ2/4)az 일 때 φ=π/2, 1≤ρ≤2 m, 0≤z≤5 m 인면을 통과하는 자속 ψ를 구하라.
Fig 7.20 For example 7.7
3
2 4
11
2
3
4
5
ρ
z
2
L
B A
3
⊗
S
⊗
1
![Page 64: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/64.jpg)
63
a2
a4
1
4/00
00
aaa
1
AAA
z
aaa
1A
2
2
z
z
z
![Page 65: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/65.jpg)
64Wb75.3
dz4
0
dz4
0
LdA
SdA
SdB
2Method
0
5
2
2
5
0
1
2
4321
L
S
S
예제 7.7 A = −(ρ2/4)az 일 때 φ=π/2, 1≤ρ≤2 m, 0≤z≤5 m 인면을 통과하는 자속 ψ를 구하라.
3
2 4
11
2
3
4
5
ρ
z
2
L
A
Fig 7.20 For example 7.7
3
1
![Page 66: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/66.jpg)
65
0zaK2
1
0zaK2
1
H)22.7(
xy
xy
예제 7.8 z=0 인면에 K = Kyay 의 면전류가 흐를 때 다음을 유도하라.
![Page 67: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/67.jpg)
66
x0
2
0 2/322
y0
x2/3222
y0
2/3222
xy0
xy
222
yy0
0
S0
a)z(4
)dd(zK
a)zyx(4
)ydxd(zKB
)zyx(4
a)ydxd(zK
)adA(z
AdAdBd
zyx4
)ydxd(aK
R4
dSKAd
R4
dSKA)42.7(
xy
zyxy
y
zyx
a)dA(z
a)dA(x
a)dA(z
0dA0
zyx
aaa
Ad
![Page 68: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/68.jpg)
67
x0
2
0 2/322
y0
x2/3222
y0
a)z(4
)dd(zK
a)zyx(4
)ydxd(zKB
![Page 69: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/69.jpg)
68
0zfor2
aK
z
1
2
azK
0zfor2
aK
z
1
2
azK
z
10
2
azK
)zt(24
azK
dt)zt(4
azK
dtd2
ta
)zt(8
zdtK2
a)z(4
dzK2
a)z(4
)dd(zKB
xy0xy0
xy0xy0
2
xy0
02/12xy0
0t2/32xy0
2
x0t 2/32
y0
x0 2/322
y0
x0
2
0 2/322
y0
![Page 70: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/70.jpg)
69
7.8 Biot-Savart 법칙과 Ampere 법칙유도
전선에 전류 I가 흐르면 Point P에 전선에 수직인 방향으로 자장이 발생한다.
30
3
x
xLId
4
x
xLdkIBd
Biot와 Savart가 정교하고 철저한 실험에 의해 전류가 흐르는 전선에 의해point P에서 발생하는 자장은 전선과point P의 거리의 제곱에 역 비례하고전선과 𝐱 에 수직인 방향으로 발생한다는 것을 알았다.
𝐁
𝐱
𝐝 𝐋 I
P
![Page 71: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/71.jpg)
70
xdxx
)x(J
4
)x(JA
xx
1f
AfAf)Af(
xdxx
)x(J
4
xd)x(Jxx
1
4
xdxx
1)x(J
4
xd)x(J
LAd)x(JLIdxd
xx
)xx()x(J
4)x(B
x
xLId
4Bd
30
30
30
30
3
3
30
30
장뒷
x
x
x
x
![Page 72: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/72.jpg)
71
3
2/3222
zyx
z2/32222/1222
z
y2/32222/1222
y
x2/3222
2/3222x
2/1222x
2/1222zyx
R
R
R
1
)zyx(
azayax
R
1
)az()zyx()zyx(z
a
)ay()zyx()zyx(y
a
)ax()zyx(
)x2()zyx(2
1a)zyx(
xa
)zyx(z
ay
ax
aR
1
)dzzd,dyyd,dxxd
)zz,yy,xx()z,y,x(
RRR
3
L0
L 30
RR
RR
RR
1
RR
1LId
4
RR
)RR(LId
4B
![Page 73: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/73.jpg)
72
RR
LId
RR
1LId
RR
LId
4
RR
1LId
4B
L0
L0
RR
1)LId(
RR
LId
RR
1)LId(
)LId(RR
1
)LId(RR
1
)LId(RR
1LId
RR
1
RR
1f
LIdu
ufuf)uf(
![Page 74: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/74.jpg)
73xd)xx()x(J
)xx(4xx
1xd)]xx(4[)x(J
4
xdxx
1)x(J
4
xdxx
)x(J
4Sd
xx
)x(J
4
xdxx
)x(J
4xd
xx
)x(J
4
xdxx
)x(J
4xd
xx
)x(J
4
A)A()A(xdxx
)x(J])([
4
xdxx
)x(J
4)x(B
xdxx
)x(J
4)x(Axd
xx
)x(J
4)x(B
30
230
320
3200
32030
32030
2320
30
3030
![Page 75: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/75.jpg)
74
tJ
0Jt
E
Jt
EB
Jt
EB
?0J
JB
)(
)x(f)xx()x(f)x(J)x(B
xd)xx()x(J)x(B
)xx(4xx
1xd)]xx(4[)x(J
4)x(B
v
0
00
00
0
000
30
230
![Page 76: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/76.jpg)
75
0r
1
0r)1(
r
1
rr
rr
1
r
1
r
1
xx
1
)xx(4xx
1:
2
2
2
2
22
2
경우인
유도
![Page 77: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/77.jpg)
76
0 2/522
22
0a
230
2
2/522
2
0a
2
2
23
2/522
2
0a
3
22
2
0a
3
22
2
0a
32
)ar(
drra12
drr4xd)drr4()ar(
1a3
rr
rr
1xd
)ar(
1a3
xdar
1
xdar
1
xdr
1
0r)2(
lim
lim
lim
lim
lim
경우인
![Page 78: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/78.jpg)
77
4
dcosdt
sintdtt12
dcossin12
sec
dtan12
dsecadr
tanar
)1(tan
dsectan12
)ar(
drra12
xdr
1
1
02
2/
02
2/
0 3
2
2
2/
0 2/52
22
0 2/522
22
0a
32
lim
tan 1 cot
sin cos
cscsec
2
22
secd
tand
sind
cosd
cosd
sind
tantan1
tantan)tan(
sincos)2cos(
sinsincoscos)cos(
cossin2)2sin(
sincoscossin)sin(
![Page 79: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/79.jpg)
78
δ(x-x0)
x0 x0+Δx
x
1/Δx
Δx
)x(fdx)xx()x(f 00
0r
1
0r)1(
2
경우인
4xdr
1
0r)2(
32
경우인
)xx(4xx
12
![Page 80: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/80.jpg)
79
)x(fdx)xx()x(f
)x(f
xx
)x(f
dxx
1)x(flim
dx0)x(fdxx
1)x(fdx0)x(flim
dx)xx()x(fdx)xx()x(fdx)xx()x(f
dx)xx()x(f
)x(fdx)xx()x(f
00
0
0
xx
x0x
xx 0xx
x
x
0x
xx 0xx
x 0x
0
0
00
0
0
0
0
0
0
0
0
0
0
유도
δ(x-x0)
x0 x0+Δx
x
1/Δx
Δx
![Page 81: 7. Magnetostatic Fieldiirc.khu.ac.kr/uploads/6/3/4/3/63434825/sadiku_ch07.pdf · 2019-11-23 · 12 2013. 1 학기기말고사: J =(x,0,0)일때중심이원점에있고반지름이a인구의표면을통과하여](https://reader033.vdocuments.site/reader033/viewer/2022042018/5e760a71dd29b34f4168dbc3/html5/thumbnails/81.jpg)
80
0t/where
)60.7(JA
Jt
EA
1
A
A)A(
AB
AB)39.7(0B
Jt
EB
02
02
0
2
2
00
)59.7(0)x(A
xx
Sd)x(J
4
xdxx
)x(J
4
xdxx
)x(J)(
4
xdxx
)x(J
4
xdxx
)x(J
4)x(A
xdxx
)x(J
4)x(A
0
30
30
30
30
30
(7.59) & (7.60) 유도