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Electricity and Magnetism INEL 4151

Electricity and Magnetism INEL 4151. Sandra Cruz-Pol, Ph. D. ECE UPRM Mayagüez, PR. Electricity => Magnetism. In 1820, Prof. Oersted discovered that a steady current produces a magnetic field while teaching a physics class. . http://micro.magnet.fsu.edu/electromag/java/faraday/index.html.

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Electricity and Magnetism INEL 4151

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  1. Electricity and MagnetismINEL 4151 Sandra Cruz-Pol, Ph. D. ECE UPRM Mayagüez, PR

  2. Electricity => Magnetism • In 1820, Prof. Oersted discovered that a steady current produces a magnetic field while teaching a physics class. http://micro.magnet.fsu.edu/electromag/java/faraday/index.html

  3. Would magnetism would produce electricity? Eleven years later, and at the same time, • Mike Faraday in London and • Joe Henry in New York discovered that a time-varying magnetic field produces an electric current!

  4. Electromagnetics was born! • This is the principle of motors, hydro-electric generators and transformers operation. This is what Oersted discovered accidentally: *Mention some examples of em waves

  5. http://ece.uprm.edu/~pol/cursos

  6. Some terms • E = electric field intensity [V/m] • D = electric field density • H = magnetic field intensity, [A/m] • B = magnetic field density, [Teslas]

  7. Maxwell Equations in General Form

  8. Moving loop in static B field When a conducting loop is moving inside a magnet (static B field), there’s a force on the charges. http://www.walter-fendt.de/ph14e/electricmotor.htm http://micro.magnet.fsu.edu/electromag/java/generator/dc.html Encarta®

  9. Who was NikolaTesla? • Find out what inventions he made • His relation to Thomas Edison • Why is he not well know?

  10. Vector Analysis Review: • What is a vector? • How to add them, multiply, etc,? • Coordinate systems • Cartesian, cylindrical, spherical • Vector Calculus review

  11. Vector • A vector has magnitude and direction. • In Cartesian coordinates (x,y,z):

  12. Vector operations

  13. Example Given vectors A=ax+3az and B=5ax+2ay-6az • (a) |A+B| • (b) 5A-B • (c) the component of A along y • (d) a unit vector parallel to 3A+B Answers:(a)7(b)(0,-2,21)(c)0(d) ± (0.9117,.2279,0.3419)

  14. Vector Multiplications Note that: • Dot product • Cross product

  15. Also… • Multiplying 3 vectors: • Projection of vector A along B: Scalar: Vector:

  16. Coordinates Systems • Cartesian (x,y,z) • Cylindrical (r,f,z) • Spherical (r,q,f)

  17. Cylindrical coordinates

  18. Spherical coordinates

  19. Vector calculus review

  20. Theorems • Divergence • Stokes’ • Laplacian Scalar: Vector:

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