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Electromagnetic Field and Waves

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Presentation on theme: "Electromagnetic Field and Waves"— Presentation transcript:

1 Electromagnetic Field and Waves
Gi-Dong Lee Outline: Electrostatic Field Magnetostatic Field Maxwell Equation Electromagnetic Wave Propagation

2 Vector Calculus Basic mathematical tool for electromagnetic field solution and understanding.

3 Line, Surface and Volume Integral
Line Integral : Circulation of A around L ( ) Perfect circulation : Surface Integral : Path L Net outward flux of A

4 Del operator : Volume Integral : Gradient Divergence Curl
Laplacian of scalar

5 dV = potential difference btw the scalar field V
Gradient of a scalar → V1 V2 dV = potential difference btw the scalar field V

6 Divergence, Gaussian’s law
It is a scalar field

7 Curl, Stoke’s theorem ds Closed path L

8 Practical solution method
Laplacian of a scalar Practical solution method

9 Classification of the vector field

10 Electrostatic Fields Time-invariant electric field in free space

11 Coulomb’s law and field intensity Experimental law
Coulomb’s law in a point charge Q1 Q2 Vector Force F12 or F21 Q1 Q2 F21 F12 r1 r2

12 E : Field intensity to the normalized charge (1)
Electric Field E r r’ 1 Q R E : Field intensity to the normalized charge (1)

13 Electric Flux density D
Flux density D is independent on the material property (0) Maxwell first equation from the Gaussian’s law

14 From the Gaussian’s law
From this From the Gaussian’s law

15 In case of a normalized charge Q
Electric potential Electric Field can be obtained by charge distribution and electric potential E A Q B In case of a normalized charge Q + : work from the outside - : work by itself

16 Second Maxwell’s Equ. From E and V
Absolute potential E r O : origin point Q=1 Second Maxwell’s Equ. From E and V

17 Relationship btn. E and V
Second Maxwell’s Equ Relationship btn. E and V 3,4,5 : EQUI-POTENTIAL LINE E 3 4 5

18 Energy density We

19 E field in material space ( not free space)
Conductor Non conductor Insulator Dielctric material Material can be classified by conductivity   << 1 : insulator  >> 1 : conductor (metal :  ) Middle range of  : dielectric

20 Convection current ( In the case of insulator)
Current related to charge, not electron Does not satisfy Ohm’s law

21 Conduction current (current by electron : metal)

22 Displacement can be occurred
Polarization in dielectric + - After field is induced Displacement can be occurred Equi-model -Q +Q Dipole moment Therefore, we can expect strong electric field in the dielectric material, not current

23 Multiple dipole moments
- + 0 : permittivity of free space : permittivity of dielectric r : dielectric constant

24 Linear, Isotropic and Homogeneous dielectric
D  E : linear or not linear When (r) is independent on its distance r : homogeneous When (r) is independent on its direction : isotropic  anisotropic (tensor form)

25 Continuity equation Qinternal time

26 Boundary condition Dielectric to dielectric boundary
Conductor to dielectric boundary Conductor to free space boundary

27 Poisson eq. and Laplacian
Practical solution for electrostatic field

28 Magnetostatic Fields Electrostatic field : stuck charge distribution
E, D field to H, B field Moving charge (velocity = const) Bio sarvart’s law and Ampere’s circuital law

29 Independent on material property
Bio-Savart’s law I dl H field R Experimental eq. Independent on material property

30 The direction of dH is determined by right-hand rule
Independent on material property Current is defined by Idl (line current) Kds (surface current) Jdv (volume current) Current element I K

31 By applying the Stoke’s theorem
Ampere’s circuital law I H dl I enc : enclosed by path By applying the Stoke’s theorem

32 Magnetic flux density From this Magnetic flux line always has
same start and end point

33 Electric flux line always start isolated (+) pole to isolated (-) pole :
Magnetic flux line always has same start and end point : no isolated poles

34 Maxwell’s eq. For static EM field
Time varient system

35 Magnetic scalar and vector potentials
Vm : magnetic scalar potential It is defined in the region that J=0 A : magnetic vector potential

36 Magnetic force and materials Magnetic force
Q E B u Q Fm : dependent on charge velocity does not work (Fm dl = 0) only rotation does not make kinetic energy of charges change

37 Magnetic torque and moment
Lorentz force Magnetic torque and moment Current loop in the magnetic field H D.C motor, generator Loop//H  max rotating power

38 Slant loop an B F0

39 A bar magnet or small current loop
Magnetic dipole A bar magnet or small current loop N S m I m A bar magnet A small current loop

40 Magnetization in material
Similar to polarization in dielectric material Atom model (electron+nucleus) Ib B Micro viewpoint Ib : bound current in atomic model

41 Material in B field B

42 Magnetic boundary materials
Two magnetic materials Magnetic and free space boundary

43 Magnetic energy

44 Maxwell equations Maxwell equations
In the static field, E and H are independent on each other, but interdependent in the dynamic field Time-varying EM field : E(x,y,z,t), H(x,y,z,t) Time-varying EM field or waves : due to accelated charge or time varying current

45 Electric field can be shown by emf-produced field
Faraday’s law Time-varying magnetic field could produce electric current Electric field can be shown by emf-produced field

46 Motional EMFs E and B are related B(t):time-varying I E

47 Stationary loop, time-varying B field

48 Time-varying loop and static B field

49 Time-varying loop and time-varyinjg B field

50 Displacement current → Maxwell’s eq. based on Ampere’s
circuital law for time-varying field In the static field In the time-varying field : density change is supposed to be changed

51 Displacement current density
Therefore, Displacement current density

52 Maxwell’s Equations in final forms
Point form Integral form Gaussian’s law Nonexistence of Isolated M charge Faraday’s law Ampere’s law

53 In the tme-varying field ?
Time-varying potentials stationary E field In the tme-varying field ?

54  Coupled wave equation
Poisson’s eqation in time-varying field poisson’s eq. in stationary field poisson’s eq. in time-varying field ?  Coupled wave equation

55 Relationship btn. A and V ?

56 From coupled wave eq. Uncoupled wave eq.

57 Explanation of phasor Z
Time-harmonic fields Fields are periodic or sinusoidal with time Time-harmonic solution can be practical because most of waveform can be decomposed with sinusoidal ftn by fourier transform. Im Re Explanation of phasor Z Z=x+jy=r 

58 Phasor form If A(x,y,z,t) is a time-harmonic field
Phasor form of A is As(x,y,z) For example, if

59 Maxwell’s eq. for time-harmonic EM field
Point form Integral form

60 EM wave propagation Most important application of Maxwell’s equation
→ Electromagnetic wave propagation First experiment → Henrich Hertz Solution of Maxwell’s equation, here is General case

61 Waves in general form Sourceless u : Wave velocity

62 Special case : time-harmonic
Solution of general Maxwell’s equation Special case : time-harmonic

63 Solution of general Maxwell’s equation
A, B : Amplitude t - z : phase of the wave : angular frequency  : phase constant or wave number

64 Plot of the wave E A /2 3/2 z A T/2 T 3T/2 t

65 EM wave in Lossy dielectric material
Time-harmonic field

66 Propagation constant and E field
If z-propagation and only x component of Es

67 Propagation constant and H field

68 E field plot of example x z t=t0 t=t0+t

69 EM wave in free space

70 E field plot in free space
x z ak aE aH y TEM wave (Transverse EM) Uniform plane wave Polarization : the direction of E field

71 Reference Matthew N. O. Sadiku, “Elements of electromagnetic” Oxford University Press,1993 Magdy F. Iskander, “Electromagnetic Field & Waves”, prentice hall

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