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Display Device Lab Dong-A University Electromagnetic Field and Waves Gi-Dong Lee Outline: Electrostatic Field Magnetostatic Field Maxwell Equation Electromagnetic.

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Presentation on theme: "Display Device Lab Dong-A University Electromagnetic Field and Waves Gi-Dong Lee Outline: Electrostatic Field Magnetostatic Field Maxwell Equation Electromagnetic."— Presentation transcript:

1 Display Device Lab Dong-A University Electromagnetic Field and Waves Gi-Dong Lee Outline: Electrostatic Field Magnetostatic Field Maxwell Equation Electromagnetic Wave Propagation

2 Display Device Lab Dong-A University Vector Calculus Basic mathematical tool for electromagnetic field solution and understanding.

3 Display Device Lab Dong-A University Line, Surface and Volume Integral –Line Integral : Circulation of A around L ( ) Perfect circulation : –Surface Integral : Path L Net outward flux of A

4 Display Device Lab Dong-A University Volume Integral : Del operator : Gradient Divergence Curl Laplacian of scalar

5 Display Device Lab Dong-A University Gradient of a scalar → V1 V2  dV = potential difference btw the scalar field V

6 Display Device Lab Dong-A University Divergence, Gaussian’s law It is a scalar field

7 Display Device Lab Dong-A University Curl, Stoke’s theorem ds Closed path L

8 Display Device Lab Dong-A University Laplacian of a scalar Practical solution method

9 Display Device Lab Dong-A University Classification of the vector field

10 Display Device Lab Dong-A University Time-invariant electric field in free space Electrostatic Fields

11 Display Device Lab Dong-A University Coulomb’s law and field intensity –Experimental law –Coulomb’s law in a point charge Q1Q2 – Vector Force F 12 or F 21 Q1Q2 F21 r1 r2 F12

12 Display Device Lab Dong-A University Electric Field E E : Field intensity to the normalized charge (1) r r’ 1 Q R

13 Display Device Lab Dong-A University Electric Flux density D  Flux density D is independent on the material property (  0 ) Maxwell first equation from the Gaussian’s law

14 Display Device Lab Dong-A University From this From the Gaussian’s law

15 Display Device Lab Dong-A University 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 Display Device Lab Dong-A University Absolute potential E r O : origin point  Q=1 Second Maxwell’s Equ. From E and V

17 Display Device Lab Dong-A University Second Maxwell’s Equ Relationship btn. E and V E 345 3,4,5 : EQUI-POTENTIAL LINE

18 Display Device Lab Dong-A University Energy density We

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

20 Display Device Lab Dong-A University Convection current ( In the case of insulator) –Current related to charge, not electron –Does not satisfy Ohm’s law

21 Display Device Lab Dong-A University Conduction current (current by electron : metal)

22 Display Device Lab Dong-A University Polarization in dielectric Therefore, we can expect strong electric field in the dielectric material, not current After field is inducedDisplacement can be occurred – Equi-model Q+Q Dipole moment

23 Display Device Lab Dong-A University Multiple dipole moments -+  0 : permittivity of free space  : permittivity of dielectric  r : dielectric constant

24 Display Device Lab Dong-A University 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 Display Device Lab Dong-A University Continuity equation Q internal time

26 Display Device Lab Dong-A University Boundary condition  Dielectric to dielectric boundary  Conductor to dielectric boundary  Conductor to free space boundary

27 Display Device Lab Dong-A University Poisson eq. and Laplacian Practical solution for electrostatic field

28 Display Device Lab Dong-A University 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 Magnetostatic Fields

29 Display Device Lab Dong-A University Bio-Savart’s law  I dl  H field Experimental eq. Independent on material property R

30 Display Device Lab Dong-A University 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 Display Device Lab Dong-A University Ampere’s circuital law I H dl I enc : enclosed by path By applying the Stoke’s theorem

32 Display Device Lab Dong-A University Magnetic flux density From this Magnetic flux line always has same start and end point

33 Display Device Lab Dong-A University Electric flux line always start isolated (+) pole to isolated (-) pole : Magnetic flux line always has same start and end point : no isolated poles

34 Display Device Lab Dong-A University Maxwell’s eq. For static EM field Time varient system

35 Display Device Lab Dong-A University Magnetic scalar and vector potentials Vm : magnetic scalar potential It is defined in the region that J=0 A : magnetic vector potential

36 Display Device Lab Dong-A University Magnetic force and materials Magnetic force Q E Bu Q Fm : dependent on charge velocity does not work (Fm  dl = 0) only rotation does not make kinetic energy of charges change

37 Display Device Lab Dong-A University Lorentz force Magnetic torque and moment Current loop in the magnetic field H D.C motor, generator Loop//H  max rotating power

38 Display Device Lab Dong-A University Slant loop   anan B F0F0 F0F0 

39 Display Device Lab Dong-A University Magnetic dipole A bar magnet or small current loop I m N S m A bar magnetA small current loop

40 Display Device Lab Dong-A University Magnetization in material Similar to polarization in dielectric material Atom model (electron+nucleus) IbIb B Micro viewpoint I b : bound current in atomic model

41 Display Device Lab Dong-A University Material in B field B

42 Display Device Lab Dong-A University Magnetic boundary materials  Two magnetic materials  Magnetic and free space boundary

43 Display Device Lab Dong-A University Magnetic energy

44 Display Device Lab Dong-A University 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 Maxwell equations

45 Display Device Lab Dong-A University Faraday’s law –Time-varying magnetic field could produce electric current Electric field can be shown by emf-produced field

46 Display Device Lab Dong-A University Motional EMFs E and B are related B(t):time-varying I E

47 Display Device Lab Dong-A University Stationary loop, time-varying B field

48 Display Device Lab Dong-A University Time-varying loop and static B field

49 Display Device Lab Dong-A University Time-varying loop and time-varyinjg B field

50 Display Device Lab Dong-A University 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 Display Device Lab Dong-A University Therefore, Displacement current density

52 Display Device Lab Dong-A University Maxwell’s Equations in final forms Gaussian’s law Nonexistence of Isolated M charge Faraday’s law Ampere’s law Point formIntegral form

53 Display Device Lab Dong-A University Time-varying potentials  stationary E field  In the tme-varying field ?

54 Display Device Lab Dong-A University  Poisson’s eqation in time-varying field  poisson’s eq. in stationary field  poisson’s eq. in time-varying field ?  Coupled wave equation

55 Display Device Lab Dong-A University Relationship btn. A and V ?

56 Display Device Lab Dong-A University → From coupled wave eq. Uncoupled wave eq.

57 Display Device Lab Dong-A University 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 Display Device Lab Dong-A University 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 Display Device Lab Dong-A University Maxwell’s eq. for time-harmonic EM field Point formIntegral form

60 Display Device Lab Dong-A University 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 Display Device Lab Dong-A University Waves in general form Sourceless 0 u : Wave velocity

62 Display Device Lab Dong-A University Solution of general Maxwell’s equation Special case : time-harmonic

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

64 Display Device Lab Dong-A University Plot of the wave E z t 0 0 /2 3 /2 T/2T3T/2 A A

65 Display Device Lab Dong-A University EM wave in Lossy dielectric material Time-harmonic field 0

66 Display Device Lab Dong-A University Propagation constant and E field If z-propagation and only x component of Es

67 Display Device Lab Dong-A University Propagation constant and H field

68 Display Device Lab Dong-A University E field plot of example x z t=t 0 t=t 0 +  t

69 Display Device Lab Dong-A University EM wave in free space

70 Display Device Lab Dong-A University E field plot in free space y x z akak aEaE aHaH TEM wave (Transverse EM) Uniform plane wave Polarization : the direction of E field

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


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