Introduction to wave theory & propogation

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Introduction to wave theory & propogation

  1. 1. Introduction to Wave Theory and Propagation
  2. 2. Outline • Introductory Concepts • Vector Fields • Co-ordinate Systems Awab Sir (www.awabsir.com) 8976104646
  3. 3. Class Description Prerequisites by Topic: – University physics – Complex numbers – Partial differentiation – Multiple Integrals – Vector Analysis – Fourier Series Awab Sir (www.awabsir.com) 8976104646
  4. 4. Why Study Electromagnetics? Awab Sir (www.awabsir.com) 8976104646
  5. 5. Examples of Electromagnetic Applications Awab Sir (www.awabsir.com) 8976104646
  6. 6. Examples of Electromagnetic Applications Awab Sir (www.awabsir.com) 8976104646
  7. 7. Examples of Electromagnetic Applications Awab Sir (www.awabsir.com) 8976104646
  8. 8. Examples of Electromagnetic Applications Awab Sir (www.awabsir.com) 8976104646
  9. 9. Research Areas of Electromagnetics • Antenas • Microwaves • Computational Electromagnetics • Electromagnetic Scattering • Electromagnetic Propagation • Radars • Optics • etc … Awab Sir (www.awabsir.com) 8976104646
  10. 10. Why is Electromagnetics Difficult? Awab Sir (www.awabsir.com) 8976104646
  11. 11. What is Electromagnetics? Awab Sir (www.awabsir.com) 8976104646
  12. 12. What is a charge q? Awab Sir (www.awabsir.com) 8976104646
  13. 13. Fundamental Laws of Electromagnetics Awab Sir (www.awabsir.com) 8976104646
  14. 14. Steps in Studying Electromagnetics Awab Sir (www.awabsir.com) 8976104646
  15. 15. SI (International System) of Units Awab Sir (www.awabsir.com) 8976104646
  16. 16. Units Derived From the Fundamental Units Awab Sir (www.awabsir.com) 8976104646
  17. 17. Fundamental Electromagnetic Field Quantities Awab Sir (www.awabsir.com) 8976104646
  18. 18. Three Universal Constants Awab Sir (www.awabsir.com) 8976104646
  19. 19. Scalar and Vector Fields • A scalar field is a function that gives us a single value of some variable for every point in space. • Examples: voltage, current, energy, temperature • A vector is a quantity which has both a magnitude and a direction in space. • Examples: velocity, momentum, acceleration and force Awab Sir (www.awabsir.com) 8976104646
  20. 20. Example of a Scalar Field Awab Sir (www.awabsir.com) 8976104646
  21. 21. 21 Scalar Fields e.g. Temperature: Every location has associated value (number with units)Awab Sir (www.awabsir.com) 8976104646
  22. 22. 22 Scalar Fields - Contours • Colors represent surface temperature • Contour lines show constant temperaturesAwab Sir (www.awabsir.com) 8976104646
  23. 23. 23 Vector Fields Vector (magnitude, direction) at every point in space Example: Velocity vector field - jet streamAwab Sir (www.awabsir.com) 8976104646
  24. 24. Examples of Vector Fields Awab Sir (www.awabsir.com) 8976104646
  25. 25. Examples of Vector Fields Awab Sir (www.awabsir.com) 8976104646
  26. 26. VECTOR REPRESENTATION 3 PRIMARY COORDINATE SYSTEMS: • RECTANGULAR • CYLINDRICAL • SPHERICAL Choice is based on symmetry of problem Examples: Sheets - RECTANGULAR Wires/Cables - CYLINDRICAL Spheres - SPHERICAL Awab Sir (www.awabsir.com) 8976104646
  27. 27. Orthogonal Coordinate Systems: (coordinates mutually perpendicular) Spherical Coordinates Cylindrical Coordinates Cartesian Coordinates P (x,y,z) P (r, Θ, Φ) P (r, Θ, z) x y z P(x,y,z) θ z r x y z P(r, θ, z) θ Φ r z y x P(r, θ, Φ) Page 108 Rectangular Coordinates Awab Sir (www.awabsir.com) 8976104646
  28. 28. Cartesian Coordinates P(x,y,z) Spherical Coordinates P(r, θ, Φ) Cylindrical Coordinates P(r, θ, z) x y z P(x,y,z) θ z r x y z P(r, θ, z) θ Φ r z y x P(r, θ, Φ) Awab Sir (www.awabsir.com) 8976104646
  29. 29. VECTOR NOTATION VECTOR NOTATION: zzyyxx aAaAaAA ˆˆˆ   Rectangular or Cartesian Coordinate System x z y zzyyxx BABABABA   Dot Product zyx zyx zyx BBB AAA aaa BA ˆˆˆ   Cross Product  2 1 222 zyx AAAA   Magnitude of vector (SCALAR) (VECTOR) Awab Sir (www.awabsir.com) 8976104646
  30. 30. VECTOR REPRESENTATION: CYLINDRICAL COORDINATES Cylindrical representation uses: r ,f , z zzrr aAaAaAA ˆˆˆ  ff  zzrr BABABABA  ff  UNIT VECTORS:  zr aaa ˆˆˆ f Dot Product (SCALAR) r f z P x z y Awab Sir (www.awabsir.com) 8976104646
  31. 31. VECTOR REPRESENTATION: SPHERICAL COORDINATES r f P x z y q Spherical representation uses: r ,q , f UNIT VECTORS:  fq aaar ˆˆˆ ffqq aAaAaAA rr ˆˆˆ   ffqq BABABABA rr   Dot Product (SCALAR) Awab Sir (www.awabsir.com) 8976104646
  32. 32. x z y VECTOR REPRESENTATION: UNIT VECTORS yaˆxaˆ zaˆ Unit Vector Representation for Rectangular Coordinate System xaˆ The Unit Vectors imply : yaˆ zaˆ Points in the direction of increasing x Points in the direction of increasing y Points in the direction of increasing z Rectangular Coordinate System Awab Sir (www.awabsir.com) 8976104646
  33. 33. r f z P x z y VECTOR REPRESENTATION: UNIT VECTORS Cylindrical Coordinate System zaˆ faˆ raˆ The Unit Vectors imply : zaˆ Points in the direction of increasing r Points in the direction of increasing j Points in the direction of increasing z raˆ faˆ Awab Sir (www.awabsir.com) 8976104646
  34. 34. VECTOR REPRESENTATION: UNIT VECTORS Spherical Coordinate System r f P x z y q qaˆ faˆ raˆ The Unit Vectors imply : Points in the direction of increasing r Points in the direction of increasing j Points in the direction of increasing q raˆ faˆ qaˆ Awab Sir (www.awabsir.com) 8976104646
  35. 35.  zr aaa ˆˆˆ f  fq aaar ˆˆˆ zyx aaa ˆˆˆ RECTANGULAR Coordinate Systems CYLINDRICAL Coordinate Systems SPHERICAL Coordinate Systems NOTE THE ORDER! r,f, z r,q ,f VECTOR REPRESENTATION: UNIT VECTORS Summary Awab Sir (www.awabsir.com) 8976104646
  36. 36. METRIC COEFFICIENTS 1. Rectangular Coordinates: When you move a small amount in x-direction, the distance is dx In a similar fashion, you generate dy and dz Unit is in “meters” Awab Sir (www.awabsir.com) 8976104646
  37. 37. Cartesian Coordinates Differential quantities: Length: Area: Volume: dzzdyydxxld ˆˆˆ   dxdyzsd dxdzysd dydzxsd z y x ˆ ˆ ˆ       dxdydzdv  Page 109 Awab Sir (www.awabsir.com) 8976104646
  38. 38. METRIC COEFFICIENTS 2. Cylindrical Coordinates: Distance = r df x y df r Differential Distances: ( dr, rdf, dz ) Awab Sir (www.awabsir.com) 8976104646
  39. 39. 3. Spherical Coordinates: Distance = r sinq df x y df r sinq Differential Distances: ( dr, rdq, r sinq df ) r f P x z y q METRIC COEFFICIENTS Awab Sir (www.awabsir.com) 8976104646

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