EE 307 Chapter 6 - Electrostatic Boundary Value Problems

EE 307 Chapter 6 - Electrostatic Boundary Value Problems -...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 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...
View Full Document

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.

Page1 / 36

EE 307 Chapter 6 - Electrostatic Boundary Value Problems -...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online