Lect05Cond

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

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1 1 Swartz 06/5/23 ECE 303 – Electromagnetic Fields and Waves – Fall 2008 Lecture 5: ECE 3030 Electromagnetic Fields and Waves Instructor: Dr. Wesley E. Swartz Fall 2008 Lecture 5 2008/6/8 Electrical Conduction More on Electric Field Boundary Conditions Electrical Conduction in Materials The Concept of Perfect Conductors Electroquasitatics Problems with Perfect Metals Method of Images V + - + + + + + + + + - - - - - - - - + + + - + - - - + + + + + + + + - - - -- - - - V + - 3 Swartz 06/5/23 ECE 303 – Electromagnetic Fields and Waves – Fall 2008 Lecture 5: Demo and Homework Problems Demo problems: Some trig Position vectors Taylor’s Series Boundary Conditions Misc. Problem 3.5: Charged disk. Problem 4.3: Charge images Homework: Problem 3.13 Problem 3.16 Problem 4.5 4 Swartz 06/5/23 ECE 303 – Electromagnetic Fields and Waves – Fall 2008 Lecture 5: 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 The parallel component of the E-field at an interface is always continuous at the interface σ 1 E 2 E ( ) σ ε = 1 2 o E E 0 E E 1 2 = σ 1 E 2 E **For formal proofs see the Appendix at the end of these lecture notes** We have seen this before! 5 Swartz 06/5/23 ECE 303 – Electromagnetic Fields and Waves – Fall 2008 Lecture 5: 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 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 6 Swartz 06/5/23 ECE 303 – Electromagnetic Fields and Waves – Fall 2008 Lecture 5: 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: An infinite conductivity implies that for any non-zero E- field one would get an infinite current density – and this is physically impossible. The only way such a catastrophe is avoided is to never have an E- field inside a perfect conductor. (More on this later …) ( ) ( ) r E r J σ = 7 Swartz 06/5/23 ECE 303 – Electromagnetic Fields and Waves – Fall 2008 Lecture 5: Perfect Conductors (2) Perfect conductors are always “equipotentials” (i.e. the electric potential inside a perfect conductor has the same value everywhere) The potential difference between any two points is given as:

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