1. Electricity and Magnetism INEL 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. *Mention some examples of em waves This is what Oersted discovered accidentally:

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 Differential form Integral Form Gauss’s Law for E field. Gauss’s Law for H field. Nonexistence of monopole Faraday’s Law Ampere’s Circuit Law

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 Cartesian, cylindrical, spherical  Vector Calculus review

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

12. Vector operations Commutative Associative Distributive

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

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

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

16. Coordinates Systems  Cartesian (x,y,z)  Cylindrical ( ,z)  Spherical (r,  )

17. Cylindrical coordinates

18. Spherical coordinates

19. Vector calculus review Del (gradient) Divergence Curl Laplacian (del 2 )

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