EE 307 Chapter 7 - Magnetostatic Fields

EE 307 Chapter 7 - Magnetostatic Fields - ECE 307:...

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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 7: Magnetostatic Fields • Topics Covered – Biot-Savart’s Law – Ampere’s Circuit Law – Applications of Ampere’s Law – Magnetic Flux Density – Maxwell’s Eqns. For Scalar Fields – Magnetic Scalar and Vector Potentials – Derivation of Biot-Savart’s Law and Ampere’s Law • Homework: All figures taken from primary textbook unless otherwise cited. Introduction to Magnetic Fields • For the next two and a half chapters we focus our attention on magnetic fields • In electrostatics we studied divergent potential fields • In magnetostatics, we will examine solenoid rotational fields • Also whereas, electrostatic fields are generated by static charges, magnetostatic fields are generated by static currents (charges that move with constant velocity in a particular direction) • There are several similarities between electrostatic and magnetostatic fields • For example, as we had E and D for electrostatics, we now use B and H to examine magnetic systems • Our study of these fields allows us to evaluate and solve for a tremendous number of electric and electromechanical devices. • Furthermore this study, will provide the basis for formulating an universal theory of Electromagnetic Fields that is utilized in almost every aspect of electrical engineering 8/11/2010 3 Analogy Between Electric and Magnetic Fields • Basic Laws • Force Law • Source Element • Field intensity • Flux density • Relationship Between Fields • Potentials • Flux • Energy Density • Poisson’s Eqn. 4 Electric Magnetic ( ) ε ρ ψ ψ πε ρ ε ψ πε v E L enc r V E D w dt dV C I CV Q S d D r dl V V E E D m C S D m V l V E dQ E Q F Q S d D a r Q Q F − = ∇ ⋅ = = = = ⋅ = = −∇ = = = = = = ⋅ = ∫ ∫ ∫ 2 2 2 1 1 2 1 4 / ) / ( ˆ 4 ( ) J A H B w dt dI L I LI S d B R l Id A J V H H B m Wb S B m A l I H l Id u Q B u Q F I l d H R a Idl B d E m enc r µ ψ ψ π µ µ ψ π µ − = ∇ ⋅ = = = ⋅ = = = −∇ = = = = = × = = ⋅ × = ∫ ∫ ∫ 2 2 2 2 1 4 ) ( , / ) / ( 4 ˆ Biot-Savart’s Law • The differential magnetic field intensity, d H , produced at a point P, by the differential current element, Id l , is proportional to the product Id l and the sine of the angle between...
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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 7 - Magnetostatic Fields - ECE 307:...

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