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lec01 - Northeastern Illinois University Electricity...

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Northeastern Illinois University c circlecopyrt 2004-2010 G. Anderson Electricity & Magnetism I slide 1 / 31 Electricity & Magnetsim I Vector Calculus I Greg Anderson Department of Physics & Astronomy Northeastern Illinois University Spring 2010
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Northeastern Illinois University Overview c circlecopyrt 2004-2010 G. Anderson Electricity & Magnetism I slide 2 / 31 Maxwell’s Equations Vector Algebra Rotation of Vectors
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Northeastern Illinois University Outline Outline Maxwell’s Equations Vector Algebra Rotation of Vectors c circlecopyrt 2004-2010 G. Anderson Electricity & Magnetism I slide 3 / 31 Maxwell’s Equations Vector Algebra Definitions Addition & Multiplication Vector Product Identities Geometric Interpretation Transformations of Vectors Vector Differential Operators Gradient, Curl, Divergence Identities
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Northeastern Illinois University Maxwell’s Equations Outline Maxwell’s Equations Electromagnetism Maxwell’s Equations In Pictures Vector Algebra Rotation of Vectors c circlecopyrt 2004-2010 G. Anderson Electricity & Magnetism I slide 4 / 31
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Northeastern Illinois University Electromagnetism Outline Maxwell’s Equations Electromagnetism Maxwell’s Equations In Pictures Vector Algebra Rotation of Vectors c circlecopyrt 2004-2010 G. Anderson Electricity & Magnetism I slide 5 / 31 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.
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Northeastern Illinois University Maxwell’s Equations in Vacuum c circlecopyrt 2004-2010 G. Anderson Electricity & Magnetism I slide 6 / 31 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 Outline Maxwell’s Equations Electromagnetism Maxwell’s Equations In Pictures Vector Algebra Rotation of Vectors c circlecopyrt 2004-2010 G. Anderson Electricity & Magnetism I slide 7 / 31 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 Vector Algebra Outline Maxwell’s Equations Vector Algebra Scalars & Vectors Vectors Vector Addition Active Learning Vector Subtraction Vector Multiplication Dot Product Dot Product II Active Learning Determinants Cross Product Anti-Commutative Levi-Civita Tensor Active Learning A · ( B × C ) Kronecker Delta Vec. Triple Prod.
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