lecture5 - Lecture 5 Electrical Conduction and Perfect...

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1 ECE 303 – Fall 2005 – Farhan Rana – Cornell University Lecture 5 Electrical Conduction and Perfect Metals in Electroquasistatics In this lecture you will learn: • Some More on Electric Field Boundary Conditions • Electrical Conduction in Materials • The Concept of Perfect Metals • Electroquasistatics Problems with Perfect Metals • Method of Images ECE 303 – Fall 2005 – Farhan Rana – Cornell University Electric Field Boundary Conditions σ 1 E 2 E ( ) ε = 1 2 E E o (1) The discontinuity of the normal component of the E- field at an interface is related to the surface charge density at the interface ( ) 0 1 2 = E E (1) The parallel component of the E-field at an interface is always continuous at the interface 1 E 2 E **For formal proofs see the Appendix at the end of these lecture notes**
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2 ECE 303 – Fall 2005 – Farhan Rana – Cornell University Electrical Conductivity 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: ( ) ( ) r E r J r r r r σ = J r where is the material conductivity ( units: 1/( -m) or S/m ). Don’t confuse the conductivity with sheet charge density σ (both have the same symbol) Material ( ) S/m Rubber Water Alcohol Gold Aluminum Copper Silver 10 -15 2X10 -4 3X10 4X10 7 3X10 7 5X10 7 6X10 7 ECE 303 – Fall 2005 – Farhan Rana – Cornell University Perfect Metals - I A perfect metal has infinite conductivity (i.e. = ) 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 metals” for simplicity in many calculations A perfect metal 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 if there is never an E-field inside a perfect metal. (More on this later …) ( ) ( ) r E r J r r r r =
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3 ECE 303 – Fall 2005 – Farhan Rana – Cornell University Perfect Metals - II Perfect metals are always “equipotential” (i.e. the electric potential inside a perfect metal has the same value everywhere) perfect metal 1 r r 2 r r The potential difference between any two points is given as: If the E-field is zero inside a perfect metal then the potential difference between any two points inside a perfect metal must also be zero () () = 2 1 . 2 1 r r s d E r r r r r r r r φ ECE 303 – Fall 2005 – Farhan Rana – Cornell University Perfect Metals - III At the surface of a perfect metal the component of E-field parallel to the surface must be zero (in other words, there cannot be a component of E- field at the surface of a perfect metal that is parallel to the surface) perfect metal E r The argument goes in two steps: If there were a non-zero parallel component of E-field just outside the metal there
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This note was uploaded on 02/02/2008 for the course ECE 3030 taught by Professor Rana during the Fall '06 term at Cornell.

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lecture5 - Lecture 5 Electrical Conduction and Perfect...

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