{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ECE340_L2_S14_Distribution

# Pstccedudepartmentsnaturalbehavioralsciencesweb20physi

This preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: : Curl and Divergence •  Curl: A measure of the magnitude of rota[on in a vector ﬁeld at a given point •  Divergence: A measure of the ﬂux into or out of a given point http://apollo.lsc.vsc.edu/classes/met130/notes/chapter12/graphics/divergence.free.gif http://en.wikipedia.org/wiki/Curl_(mathematics) 15 Review: Gradient •  Gradient: A vector ﬁeld that provides a measure of the slope and direc[on of greatest change of a scalar ﬁeld (func[on) at a given point Scalar function f(x,y) Cartesian Coordinates: ∂ f ( x, y, z ) ∂ f ( x, y, z ) ∂ f ( x, y, z ) ˆ ˆ ˆ ∇f ( x, y, z ) = x+ y+ z ∂x ∂y ∂z Vector field http://upload.wikimedia.org/wikipedia/commons/3/31/Gradient99.png Cylindrical Coordinates: ∂ f ( ρ ,φ , z ) 1 ∂ f ( ρ ,φ , z ) ˆ ∂ f ( ρ ,φ , z ) ˆ ˆ ∇f ( ρ,φ , z ) = ρ+ φ+ z ∂ρ ρ ∂φ ∂z Spherical Coordinates: ∇f (r,θ ,φ ) = ∂ f (r ,θ ,φ ) 1 ∂ f (r ,θ ,φ ) ˆ 1 ∂ f (r ,θ ,φ ) ˆ ˆ r+ θ+ φ ∂r r ∂θ r sin θ ∂φ 16 Key Points: Fields & Waves Charge creates divergence in the electric displacement field: ∇i D = ρ The electric field is related to the electric displacement field through the permittivity: D = εE The electric field is the negative of the gradient of the scalar potential field: E = −∇V dV ( x ) In one dimesion: E ( x ) = − dx V ( x ) = − ∫ E ( x ) dx http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/E2020D0103.gif 17 Gauss’ Law ∇•D = ρ ρ is the charge density with units of Coulombs m3 •  The divergence of the electric displacement ﬂux density is equal to the charge density •  Can be derived from Ampere’s Law using the Con[nuity Equa[on http://www.ibiblio.org/links/devmodules/Gauss/graphics/blob1.gif 18 Key Points: Circuit Con...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online