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Electromagnetics

Antenna Antenna EngineeringEngineering

CHO, Yong HeuiCHO, Yong Heui


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



1. Maxwell’s equations

Explanations



2. Explanations

Vector (벡터 )

Vector: magnitude + direction- Coordinate (좌표계 ): -

Scalar: magnitude- Real number (실수 )-

Temperature Velocity

E

),,( zyx



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



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



Product (곱 )

Dot product, inner product-

Cross product, outer product-

zzyyxx BABABABA

zBABABA xyyx ˆ)(

Right screwProjection

2. Explanations



Gradient (경사 , 구배 )

Nabla (del), -

(static field)

Peak detector

zz

yy

xx

ˆˆˆ

Map

xx

xEx ˆˆ

E

2. Explanations



Divergence (발산 )

Source detector, hole detector

D

0 B

zyx Dz

Dy

Dx

2. Explanations

Tap



Divergence (발산 )

Electric field Magnetic field

2. Explanations



Principle of divergence

2. Explanations



Curl (회전 )

Rotation detector

,Bt

E

Dt

JH

zBt

zEy

Ex

z

xy

ˆ

ˆ

2. Explanations



Principle of curl

2. Explanations



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



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



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