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Study of electromagnetics is for electric and magnetic fields. To understand those fields, we need to know the concept of vector and differential operators.
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Electromagnetics
Antenna Antenna EngineeringEngineering
CHO, Yong HeuiCHO, Yong Heui
Antenna Antenna EngineeringEngineering
EM Wave LabEM Wave Lab2
1. Maxwell’s equations
Basic equations (기본방정식 )
: Gauss(가우스 )’s law
: Faraday(패러데이 )’s law
: Biot-Savart(비오 -사바르 )’s law
: Ampere(앙뻬르 )’s law
D
0 B
Bt
E
Dt
JH
Antenna Antenna EngineeringEngineering
EM Wave LabEM Wave Lab3
1. Maxwell’s equations
Explanations
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EM Wave LabEM Wave Lab4
2. Explanations
Vector (벡터 )
Vector: magnitude + direction- Coordinate (좌표계 ): -
Scalar: magnitude- Real number (실수 )-
Temperature Velocity
E
),,( zyx
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EM Wave LabEM Wave Lab5
Electric field (전기장 )
2. Explanations
: electric field [V/m]- Force:
: electric flux (전속 ) density [C/m2]-
: electric potential [V]- (static) , gradient (경사 )- Energy:
: permittivity (유전율 ) [F/m]-
E
D
EqF
CVQED ,
r 0
EqVW
Electricity
Antenna Antenna EngineeringEngineering
EM Wave LabEM Wave Lab6
Magnetic field (자기장 )
: magnetic field intensity [A/m]
: magnetic flux (자속 ) density [Wb/m2]- - Force:
: vector potential [Wb/m]- , curl (회전 )- Energy
: permeability (투자율 ) [H/m]-
H
B
A
BvqF LIHB ,
r 0
AB Magnet
2. Explanations
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EM Wave LabEM Wave Lab7
Product (곱 )
Dot product, inner product-
Cross product, outer product-
zzyyxx BABABABA
zBABABA xyyx ˆ)(
Right screwProjection
2. Explanations
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EM Wave LabEM Wave Lab8
Gradient (경사 , 구배 )
Nabla (del), -
(static field)
Peak detector
zz
yy
xx
ˆˆˆ
Map
xx
xEx ˆˆ
E
2. Explanations
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EM Wave LabEM Wave Lab9
Divergence (발산 )
Source detector, hole detector
D
0 B
zyx Dz
Dy
Dx
2. Explanations
Tap
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EM Wave LabEM Wave Lab10
Divergence (발산 )
Electric field Magnetic field
2. Explanations
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EM Wave LabEM Wave Lab11
Principle of divergence
2. Explanations
Antenna Antenna EngineeringEngineering
EM Wave LabEM Wave Lab12
Curl (회전 )
Rotation detector
,Bt
E
Dt
JH
zBt
zEy
Ex
z
xy
ˆ
ˆ
2. Explanations
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EM Wave LabEM Wave Lab13
Principle of curl
2. Explanations
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EM Wave LabEM Wave Lab14
Boundary conditions (경계조건 )
: continuity of normal D
: continuity of tangential E
: continuity of normal B
: continuity of tangential H
21 ˆˆ DnDn
21 ˆˆ BnBn
21 ˆˆ EnEn
21 ˆˆ HnHn
Sourceless system
2. Explanations
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EM Wave LabEM Wave Lab15
Continuity of E fields
: continuity of normal D
: continuity of tangential E
21 ˆˆ HnHn
0C LdE
QSdDS
Gauss’ divergence theorem
D
Bt
E
Stokes’ theorem
2. Explanations
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EM Wave LabEM Wave Lab16
Continuity of H fields
: continuity of normal B
: continuity of tangential HILdHC
0S SdB
Biot-Savart’s law
0 B
JH Ampere’s law
2. Explanations