1. EMLAB 1 Introduction to electromagnetics

2. EMLAB 2 Electric phenomena

3. EMLAB 3 +q 1 +q 2 Coulomb force This law is discovered by Coulomb experimentally. In the free space, the force between two point charges is proportional to the charges of them, and is inversely proportional to the square of the distance between those charges. If q 1, q 2 have the same polarity, the force is repulsive. Otherwise, the force is attractive.

4. EMLAB 4 The electrostatic forces between two isolated charges are simple enough to calculate. In practical cases, however, numerous charges are clustered on objects, which complicates the calculation of forces. Difficulties of electrostatic problems

5. EMLAB 5 + - Electron energy level -- - - -- 1 atom Electrons in an isolated atom Tightly bound electron Energy levels and the radii of the electron orbit are quantized and have discrete values. For each energy level, two electrons are accommodated at most. - - More freely moving electron

6. EMLAB 6 + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - Atoms in a solid are arranged in a lattice structure. The electrons are attracted by the nuclei. The amount of attractions differs for various material. Electrons in a solid Freely moving electron Tightly bound electron - Electron energy level External E-field

7. EMLAB 7 - Energy level of insulator atoms + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - - Energy level of conductor atom + - + - + - + - + - + - + - + - Insulator and conductor Insulator atomsConductor atoms Occupied energy level Empty energy level External E-field

8. EMLAB 8 Movement of electrons in a conductor The electrons can move freely in conductor atoms. External E-field

9. EMLAB 9 The electrons in conducting objects move freely, which means the positions of electrons changes easily. In a conductor, the density of electrons and positions of them are difficult to find, which complicates the prediction of electrostatic phenomena. Difficulties due to conductor

10. EMLAB 10 Charges in an insulator 1.If an electric field problem contains a physical media, it is difficult to predict electric field in the space due to the charges contained on it. 2.If the positions of the charges are unknown, Coulomb’s law cannot be applied. molecule Molecules in a solid are aligned in the direction of the external electric field.

11. EMLAB 11 Generation of charges : friction charging

12. EMLAB 12 Electrons “lost” Electrons “gained” Contact Separation Friction charging

13. EMLAB 13 (a) A negatively charged rubber rod suspended by a thread is attracted to a positively charged glass rod. (b) A negatively charged rubber rod is repelled by another negatively charged rubber rod.

14. EMLAB 14 Induction charging Metallic sphere

15. EMLAB 15 Electrons(-) are absorbed. (+) charges are generated Electrons(-) are generated. (+) charges are absorbed. Generation of charges : battery Electrons are generated via electro-chemical reaction. An amount of positive charges are generated such that the terminal voltage is sustained.

16. EMLAB 16 Current flow The globe lights up due to the work done by electric current (moving charges). Steady state current (simple DC circuit)

17. EMLAB 17 Charge transport example : battery with open wire Positive charges are plenty. Charges in a wire are moved by diffusion and electromagnetic laws. Charge movement by diffusion Negative charges are plenty. Diffusion

18. EMLAB 18 Field concept To facilitate description of electric phenomena, field concept is introduced. Electric phenomena can be explained in terms of electric fields.

19. EMLAB 19 Mathematics -Glossary Scalar : a quantity defined by one number (eg. Temperature, mass, density, voltage,... ) Vector : a quantity defined by a set of numbers. It can be represented by a magnitude and a direction. (velocity, acceleration, …) Field : a scalar or vector as a function of a position in the space. (scalar field, vector field, …) Scalar field Vector field

20. EMLAB 20 Example of a vector field +q Magnitudes and directions of vectors change with positions. Electric field generated by a charge (+q 1 ) The electric field is a field quantity because its magnitude and direction changes with positions.

21. EMLAB 21 +q Usefulness of the field concept -q +q-q This equation states only the forces between the two charges +q and –q. It does not state about the interactions that occur between them. It is misleading that this equation may imply that the interaction occurs instantaneously. The electric field due to +q spread into the space. Then (–q) feels the attractive force by way of the electric field.

22. EMLAB 22 Analogy to the mechanical law Newton’s law of gravity : Point-to-point reaction (action at a distance)

23. EMLAB 23 Gravitational field Earth (M) Moon (m) Gravitational field mediates interactions between the earth and the moon.

24. EMLAB 24 This law is discovered by Coulomb experimentally. In the free space, the force between two point charges is proportional to the charges of them, and is inversely proportional to the square of the distance between those charges. +q 1 +q 2 O If q 1, q 2 have the same polarity, the force is repulsive. Coulomb’s law only states that the force between two charge is related to the distance between them and their charges. It does not tells us how the interaction occurs. Coulomb’s law ε 0 : permittivity of vacuum.

25. EMLAB 25 Definition of electric field +q 1 +q 2 Electric field is measured by the force divided by charge quantity with the amount infinitesimally small. This limit process is necessary for not disturbing the original electric field by q 1.

26. EMLAB 26

27. EMLAB 27 Magnetic phenomena

28. EMLAB 28 Magnetic field A charged particle in motion generates magnetic field nearby. In the same way, currents generate magnetic field nearby.

29. EMLAB 29

30. EMLAB 30 Biot-Savart law Direction of H-field Current segment The generated magnetic field can be predicted by Biot-Savart’s law

31. EMLAB 31 Permeability Magnetic flux density Magnetic material

32. EMLAB 32 (a) A wire suspended vertically between the poles of a magnet. (b) The setup shown in part (a) as seen looking at the south pole of the magnet, so that the magnetic field (blue crosses) is directed into the page. When there is no current in the wire, it remains vertical. (c) When the current is upward, the wire deflects to the left. (d) When the current is downward, the wire deflects to the right. Motion of a charge in a magnetic field Lorentz force

33. EMLAB 33 Motion of a charge in a magnetic field Charged particles in motion are influenced by magnetic fields

34. EMLAB 34 Electro-magnetic phenomena

35. EMLAB 35 Electromagnetic law – Maxwell equations 1.Electromagnetic phenomena are explained by the four Maxwell equations. 2.Through the equations, electric field and magnetic field are coupled to each other. 3.Quantities on the right hand side are the source terms. 4.Quantities on the left side are the resulting phenomena. J  5.The independent variables are current density vector J and charge density . Maxwell equations E: electric field D: electric displacement flux density H: magnetic field B: magnetic flux density

36. EMLAB 36 Ampere’s law Current or increase of electric field strength E, J H

37. EMLAB 37 E H Increase of magnetic field Faraday’s law

38. EMLAB 38 Faraday’s law The time-varying magnetic field generates electric field nearby.

39. EMLAB 39 Gauss’ law +Q -Q E E Electric field lines emanate from positive charges and sink into negative charges.

40. EMLAB 40 Magnetic field lines always form closed loops

41. EMLAB 41 Example – Hertzian dipole antenna Heinrich Hertz (1857-1894) spheres for storing electric charges arc monitoring

42. EMLAB 42 Schematic diagram of Hertz experiment Transformer for high voltage generation

43. EMLAB 43 Electric field : red Magnetic field : blue Propagation of electromagnetic wave

44. EMLAB 44 Radio communication

45. EMLAB 45 V Reception of EM wave current Transmitting antenna Receiving antenna The charges on the receiving antenna move toward the antenna terminal, which causes voltage drop across them.

46. EMLAB 46 Radiation by oscillating charges

47. EMLAB 47 Oscillator circuit Output voltage Oscillating voltage source forces electrons to be accelerated, which generates electromagnetic wave Generation of electromagnetic wave

48. EMLAB 48 Electromagnetic wave : radio communication Moving charges on the antenna generate electromagnetic waves.

49. EMLAB 49 Electromagnetic wave : automotive radar Moving charges on the antenna generate electromagnetic waves.

50. EMLAB 50 Electromagnetic wave : ground penetrating radar The EM wave from the transmitter refracts into the ground and is reflected back by the underground facilities.

51. EMLAB 51 Electromagnetic wave generation : antennas Many kinds of antennas are built and utilized.

52. EMLAB 52 Electromagnetic wave : signal propagation The electrical signal propagate along the line trace at the speed of light.

53. EMLAB 53 E ZLZL        H-field due to moving charges Example – Signal propagation over a line trace H

54. EMLAB 54 EM theory helps understand how electrical signals propagate along conductors as well as free space. Predicts voltages and currents using the concept of electric and magnetic field. Importance of electromagnetic theory

55. EMLAB 55 Electromagnetic theory Electric field (E) Magnetic field (H) Electro-magnetic field (E,H ) Sources (q, J) Material (ε, μ) Mathematics Coordinate systems Vector calculus (divergence, curl, gradient) EM-theory Material

56. EMLAB 56 Contents 1.Electric field ① Coulomb’s law ② Gauss’s law (divergence) ③ Electric potential (gradient) ④ Capacitance ⑤ Ohm’s law 2.Magnetic field ① Biot-Savart law ② Ampere’s law (curl) ③ Inductance 1.Sources ① Charge ② Current 2.Material ① Conductor (semi-conductor, lossy material) ② Dielectric (insulator) ③ Magnetic material

57. EMLAB 57 3.Electro-magnetic field ① Faraday’s law ② Displacement current ③ Maxwell’s equations ④ Plane wave ⑤ Reflection/transmission 4.Transmission lines ① Impedance matching ② Smith chart ③ Waveguides 5.Radiation