{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lect04ElectPoten

# Lect04ElectPoten - ECE 303 Electromagnetic Fields and Waves...

This preview shows pages 1–2. Sign up to view the full content.

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 .

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

Lect04ElectPoten - ECE 303 Electromagnetic Fields and Waves...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online