lec03 - Northeastern Illinois University c circlecopyrt...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

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

Unformatted text preview: Northeastern Illinois University c circlecopyrt 2004-2009 G. Anderson Electricity & Magnetism I – slide 1 / 34 Electricity & Magnetsim I Vector Calculus III Greg Anderson Department of Physics & Astronomy Northeastern Illinois University Spring 2010 Northeastern Illinois University Overview c circlecopyrt 2004-2009 G. Anderson Electricity & Magnetism I – slide 2 / 34 Maxwell’s Equations Div & Gauss’s Thm. Curl & Stokes Thm. More Vector Calculus Curvilinear Coordinates Northeastern Illinois University Previously Previously Outline Maxwell’s Equations Div & Gauss’s Thm. Curl & Stokes Thm. More Vector Calculus Curvilinear Coordinates c circlecopyrt 2004-2009 G. Anderson Electricity & Magnetism I – slide 3 / 34 Lecture 02: Vector Calculus II Northeastern Illinois University Outline Previously Outline Maxwell’s Equations Div & Gauss’s Thm. Curl & Stokes Thm. More Vector Calculus Curvilinear Coordinates c circlecopyrt 2004-2009 G. Anderson Electricity & Magnetism I – slide 4 / 34 ◆ Integral Theorems ■ Gauss’s Theorem ■ Stokes’s Theorem ◆ More Identities ◆ The Laplacian ◆ Curvilinear Coordinates ■ General Derivations ■ Cylindrical Coordinates ■ Spherical Coordinates Northeastern Illinois University Maxwell’s Equations Previously Outline Maxwell’s Equations Maxwell’s Equations In Pictures Div & Gauss’s Thm. Curl & Stokes Thm. More Vector Calculus Curvilinear Coordinates c circlecopyrt 2004-2009 G. Anderson Electricity & Magnetism I – slide 5 / 34 Northeastern Illinois University Maxwell’s Equations in Vacuum c circlecopyrt 2004-2009 G. Anderson Electricity & Magnetism I – slide 6 / 34 Maxwell’s Equation in vacuum (Differential form) ∇ · E = 1 ǫ ρ, ∇ · B = 0 ∇ × E = − ∂ B ∂t , ∇ × B = μ ( J + ǫ ∂ E ∂t ) Maxwell’s Equations in vacuum (Integral form) contintegraltext S E · d A = 1 ǫ integraltext V d 3 xρ ( x ) , contintegraltext S B · d A = 0 contintegraltext C E · dℓ = − ∂ ∂t integraltext B · d A , contintegraltext C B · dℓ = μ integraltext S ( J + ǫ ∂ E ∂t ) · d A Northeastern Illinois University Maxwell’s Equations in Vacuum Previously Outline Maxwell’s Equations Maxwell’s Equations In Pictures Div & Gauss’s Thm. Curl & Stokes Thm. More Vector Calculus Curvilinear Coordinates c circlecopyrt 2004-2009 G. Anderson Electricity & Magnetism I – slide 7 / 34 Q Gauss’s Law Φ E = 1 ǫ Q No magnetic monopoles: Φ B = 0 Faraday’s Law: e.g. , increasing B E E = H E · d s = − d Φ B dt Amp´ere-Maxwell Law: e.g. , I , increasing E B H B · d s = μ ( I + ǫ d Φ E dt ) Northeastern Illinois University Divergence & Gauss’s Theorem Previously Outline Maxwell’s Equations Div & Gauss’s Thm....
View Full Document

This document was uploaded on 02/10/2010.

Page1 / 34

lec03 - Northeastern Illinois University c circlecopyrt...

This preview shows document pages 1 - 9. Sign up to view the full document.

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