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S J P N Trust's Hirasugar Institute of Technology, Nidasoshi.

S J P N Trust's Hirasugar Institute of Technology, Nidasoshi. Inculcating Values, Promoting Prosperity Approved by AICTE, Recognized by Govt. of Karnataka and Affiliated to VTU Belagavi. Department of Electronics & Communication Engg.

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S J P N Trust's Hirasugar Institute of Technology, Nidasoshi.

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  1. S J P N Trust's Hirasugar Institute of Technology, Nidasoshi. Inculcating Values, Promoting Prosperity Approved by AICTE, Recognized by Govt. of Karnataka and Affiliated to VTU Belagavi Department of Electronics & Communication Engg. Course : Engineering Electromagnetics -15EC36. Sem.: 3rd(2017-18) Course Coordinator: Prof. S. S. KAMATE

  2. Vector Analysis • Scalars and Vectors • Scalar Fields (temperature) • Vector Fields (gravitational, magnetic) • Vector Algebra

  3. There are three co-ordinate systems • Cartesian or rectangular co-ordinate system • Cylindrical co-ordinate System • Spherical co-ordinate System

  4. The Cartesian Coordinate System : vertices are x,y,z

  5. Vector Components and Unit Vectors

  6. Constant planes

  7. Contd… Distance vector - dl Differential surfaces - dv =

  8. The Dot product B in the direction of A You need to normalize a before the dot product. A.B = |A||B| cos qAB

  9. The Cross Product A x B = aN|A||B| sin qAB Example

  10. Circular Cylindrical Coordinate System

  11. Differential volume

  12. Circular Cylindrical Coordinate System Dot Product

  13. Spherical co-ordinate system

  14. The Spherical Coordinate System

  15. Sperical Co-ordinate System

  16. The Spherical Coordinate System

  17. The Experimental Law of Coulomb

  18. Electric Field Intensity

  19. Electric Field Intensity

  20. Field of a Line Charge

  21. Field of a Line Charge (neglect symmetry)

  22. Field of a Line Charge (neglect symmetry)

  23. Field of a Sheet of Charge This is a very interesting result. The field is constant in magnitude and direction. It is as strong a million miles away from the sheet as it is right of the surface.

  24. Streamlines and Sketches of Fields Cross-sectional view of the line charge. Lengths proportional to the magnitudes of E and pointing in the direction of E

  25. Streamlines and Sketches of Fields

  26. 3.1 Electric Flux Density • Faraday’s Experiment

  27. Electric Flux Density, D • Units: C/m2 • Magnitude: Number of flux lines (coulombs) crossing a surface normal to the lines divided by the surface area. • Direction: Direction of flux lines (same direction as E). • For a point charge: • For a general charge distribution,

  28. D3.1 Given a 60-uC point charge located at the origin, find the total electric flux passing through: • That portion of the sphere r = 26 cm bounded by • 0 < theta < Pi/2 and 0 < phi < Pi/2

  29. Gauss’s Law • “The electric flux passing through any closed surface is equal to the total charge enclosed by that surface.”

  30. The integration is performed over a closed surface, i.e. gaussian surface.

  31. We can check Gauss’s law with a point charge example.

  32. Symmetrical Charge Distributions • Gauss’s law is useful under two conditions. • DS is everywhere either normal or tangential to the closed surface, so that DS.dS becomes either DSdS or zero, respectively. • On that portion of the closed surface for which DS.dS is not zero, DS = constant.

  33. Gauss’s law simplifies the task of finding D near an infinite line charge.

  34. Infinite coaxial cable:

  35. Differential Volume Element • If we take a small enough closed surface, then D is almost constant over the surface.

  36. Divergence Divergence is the outflow of flux from a small closed surface area (per unit volume) as volume shrinks to zero.

  37. Water leaving a bathtub • Closed surface (water itself) is essentially incompressible • Net outflow is zero • Air leaving a punctured tire • Divergence is positive, as closed surface (tire) exhibits net outflow

  38. Mathematical definition of divergence Surface integral as the volume element (v) approaches zero D is the vector flux density - Cartesian

  39. Divergence in Other Coordinate Systems Cylindrical Spherical

  40. 4.1 Energy to move a point charge through a Field • Force on Q due to an electric field • Differential work done by an external source moving Q • Work required to move a charge a finite distance

  41. Line Integral • Work expression without using vectorsEL is the component of E in the dL direction • Uniform electric field density

  42. Potential • Measure potential difference between a point and something which has zero potential “ground”

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