Electromagnetic Fields ELC205B-Spring 2012 Department of Electronics and Electrical Communications Engineering Faculty of Engineering Cairo University Outline Mathematical Operators Fundamental Laws of Electro and Magneto Statics Faradays Experiment Lenzs Law Faradays Law Induced Electric Field Electric Field in terms of Potential Functions Amperes Law and the Continuity Equation Retarded Potentials Mamdouh Hassan Abbas,2012 Outline Mathematical Operators Fundamental Laws of Electro and Magneto Statics Faradays Experiment Lenzs Law Faradays Law Induced Electric Field Electric Field in terms of Potential Functions Amperes Law and the Continuity Equation Retarded Potentials Mamdouh Hassan Abbas,2012 Mathematical Operators Mamdouh Hassan Abbas,2012 Positive Source Negative Sink Zero No charge S S S n n n Mathematical Operators n Always Zero Circulating quantity S Mamdouh Hassan Abbas,2012 Mathematical Operators Always Zero Flowing quantity Non-zero Circulating quantity E B Mamdouh Hassan Abbas,2012 Outline Mathematical Operators Fundamental Laws of Electro and Magneto Statics Faradays Experiment Lenzs Law Faradays Law Induced Electric Field Electric Field in terms of Potential Functions Amperes Law and the Continuity Equation Retarded Potentials Mamdouh Hassan Abbas,2012 Fundamental Laws of Electro and Magneto Statics Mamdouh Hassan Abbas,2012 Fundamental Laws of Electro and Magneto Statics Mamdouh Hassan Abbas,2012 Fundamental Laws of Electro and Magneto Statics Mamdouh Hassan Abbas,2012 Outline Mathematical Operators Fundamental Laws of Electro and Magneto Statics Faradays Experiment Lenzs Law Faradays Law Induced Electric Field Electric Field in terms of Potential Functions Amperes Law and the Continuity Equation Retarded Potentials Mamdouh Hassan Abbas,2012 Faradays Experiment battery switch toroidal iron core compass primary coil secondary coil Mamdouh Hassan Abbas,2012 Faradays Experiment battery switch toroidal iron core compass primary coil secondary coil Mamdouh Hassan Abbas,2012 Faradays Experiment battery switch toroidal iron core compass primary coil secondary coil Mamdouh Hassan Abbas,2012 Outline Mathematical Operators Fundamental Laws of Electro and Magneto Statics Faradays Experiment Lenzs Law Faradays Law Induced Electric Field Electric Field in terms of Potential Functions Amperes Law and the Continuity Equation Retarded Potentials Mamdouh Hassan Abbas,2012 Lenzs Law Mamdouh Hassan Abbas,2012 Outline Mathematical Operators Fundamental Laws of Electro and Magneto Statics Faradays Experiment Lenzs Law Faradays Law Induced Electric Field Electric Field in terms of Potential Functions Amperes Law and the Continuity Equation Retarded Potentials Mamdouh Hassan Abbas,2012 Faradays Law Mamdouh Hassan Abbas,2012 Faradays Law Illustrative examples Mamdouh Hassan Abbas,2012 Faradays Law Mamdouh Hassan Abbas,2012 Faradays Law Mamdouh Hassan Abbas,2012 Faradays Law B(Outward flux) Conducting path Conducting rod Mamdouh Hassan Abbas,2012 Faradays Law - - B(Outward flux) U F Induced (inward flux) Mamdouh Hassan Abbas,2012 Faradays Law Mamdouh Hassan Abbas,2012 Faradays Law Mamdouh Hassan Abbas,2012 Outline Mathematical Operators Fundamental Laws of Electro and Magneto Statics Faradays Experiment Lenzs Law Faradays Law Induced Electric Field Electric Field in terms of Potential Functions Amperes Law and the Continuity Equation Retarded Potentials Mamdouh Hassan Abbas,2012 Induced Electric Field Mamdouh Hassan Abbas,2012 Induced Electric Field Faradays law states that a changing magnetic field induces an electric field. The induced electric field is non- conservative. Mamdouh Hassan Abbas,2012 Outline Mathematical Operators Fundamental Laws of Electro and Magneto Statics Faradays Experiment Lenzs Law Faradays Law Induced Electric Field Electric Field in terms of Potential Functions Amperes Law and the Continuity Equation Retarded Potentials Mamdouh Hassan Abbas,2012 Electric Field in terms of Potential Functions Electric scalar potential Mamdouh Hassan Abbas,2012 Electric Field in terms of Potential Functions Mamdouh Hassan Abbas,2012 Outline Mathematical Operators Fundamental Laws of Electro and Magneto Statics Faradays Experiment Lenzs Law Faradays Law Induced Electric Field Electric Field in terms of Potential Functions Amperes Law and the Continuity Equation Retarded Potentials Mamdouh Hassan Abbas,2012 Amperes Law and the Continuity Equation Q S n J Mamdouh Hassan Abbas,2012 Amperes Law and the Continuity Equation Mamdouh Hassan Abbas,2012 Amperes Law and the Continuity Equation Conduction current Displacement current Mamdouh Hassan Abbas,2012 Amperes Law and the Continuity Equation Continuity equation is satisfied Mamdouh Hassan Abbas,2012 Amperes Law and the Continuity Equation Mamdouh Hassan Abbas,2012 Amperes Law and the Continuity Equation Displacement current is the type of current that flows between the plates of a capacitor. Displacement current is the mechanism which allows electromagnetic waves to propagate in a non-conducting medium. Mamdouh Hassan Abbas,2012 Amperes Law and the Continuity Equation Current in a capacitor Mamdouh Hassan Abbas,2012 Outline Mathematical Operators Fundamental Laws of Electro and Magneto Statics Faradays Experiment Lenzs Law Faradays Law Induced Electric Field Electric Field in terms of Potential Functions Amperes Law and the Continuity Equation Retarded Potentials Mamdouh Hassan Abbas,2012 Retarded Potentials The retarded potential formula describes the potentials due to time varying currents or charges distributions. Mamdouh Hassan Abbas,2012 Retarded Potentials Mamdouh Hassan Abbas,2012 Retarded Potentials Mamdouh Hassan Abbas,2012 Retarded Potentials Mamdouh Hassan Abbas,2012 Retarded Potentials Mamdouh Hassan Abbas,2012 Retarded Potentials Mamdouh Hassan Abbas,2012 Retarded Potentials Mamdouh Hassan Abbas,2012 Retarded Potentials Mamdouh Hassan Abbas,2012 Retarded Potentials Mamdouh Hassan Abbas,2012 Retarded Potentials Mamdouh Hassan Abbas,2012 Retarded Potentials Modeling Source Observer (Origin) Mamdouh Hassan Abbas,2012 Retarded Potentials Retarded potentials Variable Constant Mamdouh Hassan Abbas,2012