Lect05Cond - ECE 3030 Electromagnetic Fields and Waves Fall...

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1 ECE 3030 Electromagnetic Fields and Waves Fall 2009 Lecture 5 2009/9/7 Electrical Conduction More on Electric Field Boundary Conditions Electrical Conduction in Materials 1 Rana and Swartz 06/5/23 Electromagnetic Fields and Waves – Fall 2009 Lecture 5: Instructor: Dr. Wesley E. Swartz The Concept of Perfect Conductors Electroquasitatics Problems with Perfect Metals Method of Images V + - + + + + + + + + - - - - - - - - + + + - + - - - + + + + + + + + - - - -- - - - V + - Problem Assignments Demo 2 (Tuesday, September 8) : Trig reminders Vector fields and position vectors Taylor’s series Boundary conditions Problem 3.5 (Charged disk – more complicated geometry) Example 3.11 (Separation of Variables) NOTE! Workshop 2 (Thursday, September 10) : 2 Rana and Swartz 06/5/23 Electromagnetic Fields and Waves – Fall 2009 Lecture 5: Problem 3.13 (Superpostion) Problem 3.16 (Simplification using Divergence Theorem) Start Homework 2 as time permits Homework 2 (due Tuesday, September 15 by 1pm) : Problem 3.3 (Infinite length line charge) Problem 3.4 (Finite length line charge) Problem 3.19 (Separation of variables, MATLAB solution) Modify MATLAB code that plots Figures 3.27 and 3.28 in the text to create figures for your solution. Electric Field Boundary Conditions There are two boundary conditions for the electric field at a material interface: The discontinuity of the normal component of the E-field at an interface is related to the surface charge density at the interface σ 1 E 2 E ( ) σ ε = 1 2 o E E We have seen this before! 3 Rana and Swartz 06/5/23 Electromagnetic Fields and Waves – Fall 2009 Lecture 5: The parallel component of the E-field at an interface is always continuous at the interface 0 E E 1 2 = σ 1 E 2 E **For formal proofs see the Appendix at the end of these lecture notes** Electrical Conductivity When E-field is present inside a material, it forces the charges inside the material to move causing an electric current. The current density (units: Amps/m 2 ) is related to the E-field by the relation: where σ is the material conductivity (units: 1/( -m) or S/m ) ( ) ( ) r E r J σ = J 4 Rana and Swartz 06/5/23 Electromagnetic Fields and Waves – Fall 2009 Lecture 5: Material ( ) S/m σ Rubber Water Alcohol Gold Aluminum Copper Silver 10 - 15 2X10 - 4 3X10 - 4 4X10 7 3X10 7 5X10 7 6X10 7 Perfect Conductors (1) A perfect conductor has infinite conductivity (i.e. σ = ). Of course, no real metal has infinite conductivity. However, some metals like Silver, Copper, and Gold have high enough conductivity that they may be considered “perfect conductors” or “perfect metals” for simplicity in many calculations A perfect conductor cannot have any E-field inside it. The current density and E field are related by: 5 Rana and Swartz 06/5/23 Electromagnetic Fields and Waves – Fall 2009 Lecture 5: The current density and E-field are related by: An infinite conductivity implies that for any non-zero E- field one would get an infinite current density – and this is physically impossible.
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