lec03 - Northeastern Illinois University Electricity...

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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
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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
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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
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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
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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
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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 0 ρ, ∇ · B = 0 ∇ × E = B ∂t , ∇ × B = μ 0 ( J + ǫ 0 E ∂t ) Maxwell’s Equations in vacuum (Integral form) contintegraltext S E · d A = 1 ǫ 0 integraltext V d 3 ( x ) , contintegraltext S B · d A = 0 contintegraltext C E · dℓ = ∂t integraltext B · d A , contintegraltext C B · dℓ = μ 0 integraltext S ( J + ǫ 0 E ∂t ) · d A
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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 0 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 0 ( I + ǫ 0 d Φ E dt )
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Northeastern Illinois University Divergence & Gauss’s Theorem Previously Outline Maxwell’s Equations Div & Gauss’s Thm. Divergence Divergence & Flux Gauss’s Thm. Pf. Gauss’s Theorem Curl & Stokes Thm. More Vector Calculus Curvilinear Coordinates c circlecopyrt 2004-2009 G. Anderson Electricity & Magnetism I slide 8 / 34
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Northeastern Illinois University Divergence of a Vector Function Previously Outline Maxwell’s Equations Div & Gauss’s Thm.
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