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Electricity and Magnetism INEL 4151 Sandra Cruz-Pol, Ph. D. ECE UPRM Mayagüez, PR
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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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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!
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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:
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http://ece.uprm.edu/~pol/cursos
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Some terms E = electric field intensity [V/m] D = electric field density H = magnetic field intensity, [A/m] B = magnetic field density, [Teslas]
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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
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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®
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Who was NikolaTesla? Find out what inventions he made His relation to Thomas Edison Why is he not well know?
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Vector Analysis Review: What is a vector? How to add them, multiply, etc,? Coordinate systems Cartesian, cylindrical, spherical Cartesian, cylindrical, spherical Vector Calculus review
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Vector A vector has magnitude and direction. In Cartesian coordinates (x,y,z):
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Vector operations Commutative Associative Distributive
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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)
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Vector Multiplications Dot product Cross product Note that:
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Also… Multiplying 3 vectors: Projection of vector A along B: Scalar: Vector:
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Coordinates Systems Cartesian (x,y,z) Cylindrical ( ,z) Spherical (r, )
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Cylindrical coordinates
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Spherical coordinates
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Vector calculus review Del (gradient) Divergence Curl Laplacian (del 2 )
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Theorems Divergence Stokes’ Laplacian Scalar: Vector:
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