Download presentation

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

Similar presentations

Presentation is loading. Please wait....

OK

Chapter 7 Electrodynamics

Chapter 7 Electrodynamics

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on pin diode switches Ppt on power sharing in democracy your vote Free ppt on types of houses Ppt on autonomous car Ppt on area of trapezium rectangle Ppt on delhi metro rail corporation Jit ppt on manufacturing process Ppt on mars one art Ppt on point contact diode application Ppt on chromosomes and chromatin are both made