EE 307 Chapter 9 - Maxwells Eqns

EE 307 Chapter 9 - Maxwells Eqns - ECE 307 Electricity and...

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Unformatted text preview: ECE 307: Electricity and Magnetism Spring 2010 Instructor: J.D. Williams, Assistant Professor Electrical and Computer Engineering University of Alabama in Huntsville 406 Optics Building, Huntsville, Al 35899 Phone: (256) 824-2898, email: [email protected] Course material posted on UAH Angel course management website Textbook: M.N.O. Sadiku, Elements of Electromagnetics 4 th ed . Oxford University Press, 2007. Optional Reading: H.M. Shey, Div Grad Curl and all that: an informal text on vector calculus, 4 th ed . Norton Press, 2005. All figures taken from primary textbook unless otherwise cited. 8/11/2010 2 Chapter 9: Maxwell’s Equations • Topics Covered – Faraday’s Law – Transformer and Motional Electromotive Forces – Displacement Current – Magnetization in Materials – Maxwell’s Equations in Final Form – Time Varying Potentials (Optional) – Time Harmonic Fields (Optional) • Homework: All figures taken from primary textbook unless otherwise cited. 8/11/2010 3 Faraday’s Law (1) • We have introduced several methods of examining magnetic fields in terms of forces, energy, and inductances. • Magnetic fields appear to be a direct result of charge moving through a system and demonstrate extremely similar field solutions for multipoles, and boundary condition problems. • So is it not logical to attempt to model a magnetic field in terms of an electric one? This is the question asked by Michael Faraday and Joseph Henry in 1831. The result is Faraday’s Law for induced emf • Induced electromotive force (emf) (in volts) in any closed circuit is equal to the time rate of change of magnetic flux by the circuit where, as before, λ is the flux linkage, Ψ is the magnetic flux, N is the number of turns in the inductor, and t represents a time interval. The negative sign shows that the induced voltage acts to oppose the flux producing it . • The statement in blue above is known as Lenz’s Law: the induced voltage acts to oppose the flux producing it . • Examples of emf generated electric fields: electric generators, batteries, thermocouples, fuel cells, photovoltaic cells, transformers. dt d N dt d V emf Ψ − = − = λ 8/11/2010 4 Faraday’s Law (2) • To elaborate on emf, lets consider a battery circuit. • The electrochemical action within the battery results and in emf produced electric field, E f • Acuminated charges at the terminals provide an electrostatic field E e that also exist that counteracts the emf generated potential • The total emf generated in the between the two open terminals in the battery is therefore • Note the following important facts • An electrostatic field cannot maintain a steady current in a close circuit since • An emf-produced field is nonconservative • Except in electrostatics, voltage and potential differences are usually not equivalent IR l d E l d E V P N e P N f emf = ⋅ − = ⋅ = ∫ ∫ ∫ = = ⋅ L e IR l d E ∫ ∫ ∫ ⋅ = + ⋅ = ⋅...
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This note was uploaded on 12/14/2011 for the course EE 307 taught by Professor Williams during the Spring '10 term at University of Alabama - Huntsville.

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EE 307 Chapter 9 - Maxwells Eqns - ECE 307 Electricity and...

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