Lecture 3

Lecture 3 - ∂ ∂ × ∇ A z y x A A A right hand rule low velocity Flow velocity vorticity agnetic field Magnetic field current xyz xy x u u u A

Info iconThis preview shows pages 1–16. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

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

View Full DocumentRight Arrow Icon
ivergence divergence ven a vector field the divergence given a vector field, the divergence operation tells if there is a source or sink useful for relating electric fields to charges vector field ==> scalar A A = div ds A lim v v Δ Δ 0
Background image of page 2
Cartesian Coordinates z A y A x A z y x + + = A
Background image of page 3

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

View Full DocumentRight Arrow Icon
source
Background image of page 4
ample example
Background image of page 5

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

View Full DocumentRight Arrow Icon
Gauss’s law or divergence theorem ds A lim v v Δ Δ 0 A = ds A Δ dv v A A onvert from volume integral to Δ v convert from volume integral to surface integral
Background image of page 6
Background image of page 7

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

View Full DocumentRight Arrow Icon
= ds A A dv Δ v x u A = x dv A ( ) ( ) 1 1 1 = = 0 1 x Δ v ds A 1 = [ ] 1 1 =
Background image of page 8
Curl place paddle wheel in a river o rotation at no rotation at the center rotation at the dges edges
Background image of page 9

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

View Full DocumentRight Arrow Icon
dl A u n lim s s Δ Δ 0 A A × = curl the vector u n is out of e screen the screen right hand rule ± Δ s is surface enclosed within loop s Δ closed line integral
Background image of page 10
artesian coordinates Cartesian coordinates z y x u u u z y x
Background image of page 11

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

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13

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

View Full DocumentRight Arrow Icon
Background image of page 14
Background image of page 15

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

View Full DocumentRight Arrow Icon
Background image of page 16
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ∂ ∂ × ∇ A z y x A A A right hand rule low velocity Flow velocity vorticity agnetic field Magnetic field current xyz xy x u u u A + + = z y x z y x u u u ∂ ∂ ∂ = × ∇ A z z y x ∂ ∂ ∂ xyz xy x x u A xz = × ∇ y yz u − z y u + • ∫ dl A u n lim s s Δ ⇒ Δ ≡ × ∇ A • ≈ Δ • × ∇ dl A u u A n n s ∫ • l s ∫ ∫ × ∇ dl A u u A n n ds ∫ ∫ • = • × ∇ dl A A ds ∫ ∫ • = • × ∇ dl A u u A n n ds xyz xy x u u u A + + = z y x y yz xz u u u A + − = × ∇ x u x z y x 1 1 ∫ • dl A ∫ = xdx ( ) ∫ = + 1 ydy x ∫ + 1 xdx ( ) ∫ = + 1 ydy x 2 1 2 1 2 1 − − + = 2 1 = ∫ • × ∇ dxdy A ∫ = dxdy y 2 1 =...
View Full Document

This note was uploaded on 02/04/2010 for the course EEGR 304 taught by Professor Craigscott during the Spring '08 term at Morgan.

Page1 / 16

Lecture 3 - ∂ ∂ × ∇ A z y x A A A right hand rule low velocity Flow velocity vorticity agnetic field Magnetic field current xyz xy x u u u A

This preview shows document pages 1 - 16. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online