Electromagnetic Field and Waves

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

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

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

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

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

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

7. ds Closed path L • Curl, Stoke’s theorem

8. Practical solution method • Laplacian of a scalar

9. Classification of the vector field

10. Electrostatic Fields • Time-invariant electric field in free space

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

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

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

14. From this From the Gaussian’s law

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

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

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

18. Energy densityWe

19. Conductor Material Insulator Non conductor Dielctric material • E field in material space ( not free space) 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. After field is induced - - - - - - - - - - - + + - - - - - - - - - Displacement can be occurred - - - - - • Equi-model - + Dipole moment - -Q +Q + • Polarization in dielectric 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 distancer :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. dl  I H field  • Bio-Savart’s law R Experimental eq. Independent on material property

30. I K • 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

31. I H dl • Ampere’s circuital law 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. u B Q Q E • Magnetic force and materials • Magnetic force Fm : dependent on charge velocity does not work (Fm dl = 0) only rotation does not make kinetic energy of charges change

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

38. F0  B   an F0 • Slant loop

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

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

41. B • Material in B field

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

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

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