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lec02 - Northeastern Illinois University c circlecopyrt...

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Unformatted text preview: Northeastern Illinois University c circlecopyrt 2004-2009 G. Anderson Electricity & Magnetism I – slide 1 / 34 Electricity & Magnetsim I Vector Calculus II 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 Tensor Algebra Rotation of Vectors Grad & Div Curl & Stokes’ Thm. More Vector Calculus Northeastern Illinois University Outline Outline Maxwell’s Equations Tensor Algebra Rotation of Vectors Grad & Div Curl & Stokes’ Thm. More Vector Calculus c circlecopyrt 2004-2009 G. Anderson Electricity & Magnetism I – slide 3 / 34 ◆ Recap. Vectors ◆ Transformations of Scalars, Vectors & Tensors ◆ Vector Differential Operators ■ Gradient ■ Divergence ■ Curl ◆ Integral Theorems ■ Gauss’s Theorem ■ Stokes’ Theorem Northeastern Illinois University Maxwell’s Equations Outline Maxwell’s Equations Electromagnetism Maxwell’s Equations In Pictures Tensor Algebra Rotation of Vectors Grad & Div Curl & Stokes’ Thm. More Vector Calculus c circlecopyrt 2004-2009 G. Anderson Electricity & Magnetism I – slide 4 / 34 Northeastern Illinois University Electromagnetism Outline Maxwell’s Equations Electromagnetism Maxwell’s Equations In Pictures Tensor Algebra Rotation of Vectors Grad & Div Curl & Stokes’ Thm. More Vector Calculus c circlecopyrt 2004-2009 G. Anderson Electricity & Magnetism I – slide 5 / 34 With the exception gravity, almost every force that you experience in everyday life is electro-magnetic in origin. ◆ EM forces bind electrons and nuclei into atoms. ◆ EM forces bind atoms into molecules. O H H ◆ EM forces bind atoms & molecules into solids. Electric forces are produced by electric charges. 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 Outline Maxwell’s Equations Electromagnetism Maxwell’s Equations In Pictures Tensor Algebra Rotation of Vectors Grad & Div Curl & Stokes’ Thm. More Vector Calculus 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 Tensor Algebra...
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