Lect04ElectPoten - ECE 303 Electromagnetic Fields and Waves...

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1 ECE 303 Electromagnetic Fields and Waves Fall 2009 Lecture 4 2009/9/4 Electric Potential Electric Scalar Potential 1 Swartz and Rana 06/5/20 Electromagnetic Fields and Waves – Fall 2009 Lecture 4: Instructor: Dr. Wesley E. Swartz Laplace’s and Poisson’s Equations Potentials of Some Simple Charge Distributions Conservative or Irrotational Fields Irrotational or Conservative Fields: Vector fields for which are called “irrotational” or “conservative” fields. This implies that the line integral of around any closed loop is zero. 0 = × F F 0 s d F = F 2 Swartz and Rana 06/5/20 Electromagnetic Fields and Waves – Fall 2009 Lecture 4: Equations of Electrostatics: Recall the equations of electrostatics from a previous lecture: In electrostatics or electroquasistatics , the E-field is conservative or irrotational. ρ ε = E o 0 = × E (But this is not true in electrodynamics.) Conservative or Irrotational Fields More on Irrotational or Conservative Fields: If the line integral of around any closed loop is zero … … then the line integral of between any two points is independent of any specific path (i e the line integral is the same for all possible paths 0 s d F = F F 3 Swartz and Rana 06/5/20 Electromagnetic Fields and Waves – Fall 2009 Lecture 4: specific path (i.e. the line integral is the same for all possible paths between the two points): B r r A r r B r r A r r B r r A r r 2 1 2 1 2 1 2 1 1 2 2 1 s d F s d F 0 s d F s d F 0 s d F s d F path path path path path path = = = + 1 r 2 r path A path B 0 s d F = The scalar potential: Any conservative field can always be written as the gradient of some scalar quantity. This is because the curl of a gradient is always zero. For the conservative E-field one writes: (The negative sign is just a convention) Where is the scalar electric potential . The Electric Scalar Potential (1) Φ −∇ = E ( ) () 0 F = × = × then = F If 4 Swartz and Rana 06/5/20 Electromagnetic Fields and Waves – Fall 2009 Lecture 4: The scalar potential is defined only up to a constant: If the scalar potential gives a certain electric field, then the scalar potential will also give the same electric field (where c is a constant). Remember that the derivative of a constant is zero. The absolute value of potential in a problem is generally fixed by some physical reasoning that essentially fixes the value of the constant c .
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This note was uploaded on 11/26/2009 for the course ECE 3030 at Cornell University (Engineering School).

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Lect04ElectPoten - ECE 303 Electromagnetic Fields and Waves...

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