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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) 8242898, 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 6: Electrostatic Boundary Value Problems • Topics Covered – Poisson’s and Laplace’s Equations – Uniqueness Theorem – General procedures for solving Poisson’s or Laplace’s equations – Resistance and Capacitance – Method of Images (quick look re look into Coulomb’s law) • Homework: All figures taken from primary textbook unless otherwise cited. 8/11/2010 3 Resistance • Recall from Chapter 5, that we defined Resistance as R = ρ L/S • We can also define it using Ohm’s law as • The actual resistance in a conductor of nonuniform cross section can be solved as a boundary value problem using the following steps – Choose a coordinate system – Assume that Vo is the potential difference between two conductor terminals – Solve Laplaces Eqn. to obtain V. Then Determine E =  V and solve I from – Finally, R = Vo/I ∫ ∫ ⋅ ⋅ = = S d E l d E I V R σ ∫ ⋅ = S d E I σ 8/11/2010 4 Capacitance • Capacitance is the ratio of the magnitude of charge on two separated plates to the potential difference between them • Note that The negative sign is dropped in the definition above because we are interested in the absolute value of the voltage drop • Capacitance is obtained by one of two methods – Assuming Q, and determine V in terms of Q – Assuming V, and determine Q in terms of V • If we use method 1, take the following steps – Choose a suitable coordinate system – Let the two conducting plates carry charges +Q and –Q – Determine E using Coulomb’s or Gauss’s Law and find the magnitude of the voltage, V, via integration – Obtain C=Q/V ∫ ⋅ − = l d E V ∫ ∫ ⋅ ⋅ = = l d E S d E V Q C ε 8/11/2010 5 Parallel Plate Capacitor • Assume to parallel plates separated by a distance d with +Q and –Q on them • The charge density on each plate is ˆ ˆ ˆ ε ε ε ε ε ε ε ε ρ ρ = = = = = − − = ⋅ − = − = − = − = ∫ ∫ = C C d S V Q C S Qd dx S Q l d E V a S Q a E a D r d x x x S x S S Q S = ρ QV C Q S d Q S Sd Q dv S Q W C Q QV CV W v E E 2 1 2 2 2 2 1 2 2 1 2 1 2 2 2 2 2 2 2 2 2 2 = = = = = = = = ∫ ε ε ε ε ε 8/11/2010 6 Coaxial Capacitor • Assume to cylindrical plates of inner radius a and outer radius b with +Q and –Q on them • The charge density on each plate is...
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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.
 Spring '10
 Williams

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