华工电磁场与电磁波全英课Lecture 1

Field and Wave ElectromagneticsField and Wave ElectromagneticsField and Wave ElectromagneticsChapter 1Lecture 1李融林 R.L. LiMaxwell’s Theory ofField and Wave Electromagnetics李融林 R.L. Li1.1 Maxwell Equations in Integral FormOutline¾ Maxwell’s Equations in ¾ Maxwell’s Equations in1.1.1 Gauss' Law for the Electric FieldIntegral Form Differential Form Displacement Current Constitutive Relations∫ D ⋅ ds = ∫SvvVρ v dvC / m2 C / m3¾ Continuity Equation and ¾ Material Parameters and ¾ Boundary Conditions ¾ Summaryρ v is the volume charge density, inV is bounded i the th volume l b d d by b S. 1 e=-1.602×10 C In free space,-19v D is the electric flux density, inFigure 1.1.1 Illustration of Gauss’ law for the electric field.v v 1 ε 0 = 8.854 ×10 −12 F / m ≅ × 10 −9 F / m D = ε0E 36π v E is the electric field intensity, in V / m. is the permittivity of free-space.Gauss’ law for the electric field states that electric charges give rise to electric field. Specifically, the electric flux emanating from a closed surface S is equal to the charge enclosed by that surface.1.1.2 Gauss' Law for the Magnetic Field1.1.3 Faraday's LawS v B is the magnetic flux density, inor in a newer SI unit, tesla (T).v v B ∫ ⋅ ds = 0Wb / m2v v v ∂B v ∫CE ⋅ dl = − ∫S ∂t ⋅ dsA older unit for magnetic flux density is the gauss (G). 1 T=1 Wb/m =10,000 G MRI: 0.2-3 T, Earth: 0.3-0.6 GFigure 1.1.2 Illustration of Gauss’ law for the magnetic field.2S is any surface bounded by C.Figure 1.1.3 Illustration of Faraday’s law.Gauss’ law for the magnetic field states that the magnetic flux emanating from a closed surface S is equal to zero.Faraday’s law is a consequence of the experimental finding by Michael Faraday in 1831 that a time-varying magnetic field gives rise to an electric field. Specifically, the electromotive force around a closed path C is equal to the negative of the time rate of increase of the magnetic flux enclosed by that path.11.1.4 Ampere’s Law1.2 Maxwell Equations in differential Form● Gauss' divergence theoremv v v v v ∂D v ∫CH ⋅ dl = ∫SJ ⋅ ds + ∫S ∂t ⋅ dsv H is the magnetic field intensity, in A / m v J is the electric current density, in A / m 2 v v In free space, B = μ0 H . μ0 = 4π ×10−7 H / mis the permeability of free-space.v v v G ⋅ d s = ∇ ⋅ G ∫ ∫ dvS VFigure 1.1.4 Illustration of Ampere’s circuital law.● Stokes’ theoremε 0 μ0 Ampere’s circuital law is a combination of an experimental finding of Oersted that electric currents generate magnetic fields and a mathematical contribution of Maxwell that time-varying electric fields give rise to magnetic fields. Specifically, the magnetomotive force (mmf) around a closed path C is equal to the sum of the current enclosed by that path due to actual flow of charges and the displacement current due to the time rate of increase of the electric flux (or displacement flux) enclosed by that path.The speed of light: c =1≅ 3.0 ×108 m / sv v v v G ∫ ⋅ dl = ∫ ∇ × G ⋅ dsC SThe del operator ∇ is defined as a vector operator,∇=∂ ∂ ∂ ˆ+ ˆ+ z ˆ x y ∂x ∂y ∂z1.2.1 Gauss’ Law for the Electric Field1.2.2 Gauss' Law for the Magnetic Fieldv v ∫ D ⋅ ds = ∫ ρv dvS VUsing Gauss' divergence theorem,v v B ∫ ⋅ ds = 0SUsing Gauss' divergence theorem,d =∫ ∫ ∇ ⋅ DdvVvVρ v dv dd =0 ∫ ∇ ⋅ BdvVvv ∇ ⋅ D = ρvv ∇⋅B = 01.2.3 Faraday's Lawv v v ∂B v ∫CE ⋅ dl = − ∫S ∂t ⋅ ds1.2.4 Ampere’s Lawv v v v v ∂D v ∫CH ⋅ dl = ∫SJ ⋅ ds + ∫S ∂t ⋅ dsUsing Stokes’ theorem,Using Stokes’ theorem,v v v ∂B v ∫S∇ × E ⋅ ds = −∫S ∂t ⋅ ds v v ∂B ∇×E = − ∂tv v v v v ∂D v ∫S∇ × H ⋅ ds = ∫SJ ⋅ ds + ∫S ∂t ⋅ dsv v v ∂D ∇× H = J + ∂t21.3 Continuity Equation and Displacement Current● Conservation of charge and continuity equation● Ampere’s law and continuity equationS Using Gauss' divergence theorem, we have∫ J ⋅ ds = − dt ∫vvvdVρ v dvdvv Using vector identity ∇ ⋅ ∇ × G ≡ 0v v v ∂D ∇× H = J + ∂t∫ ∇ ⋅ Jdv = −∫V∂ρ v V ∂tr v ∇ ⋅∇× H = ∇ ⋅ J = 0Continuity equation:v ρv ∇ ⋅ J = − ∂∂ tThe law of conservation of charge states that the current due to flow of charges emanating from a closed surface S is equal to the time rate of decrease of the charge inside the volume V bounded by that surface.v ρv ∇ ⋅ J = − ∂∂ tThe principle of conservation of charge requires● Generation of interdependent electric and magnetic fields Maxwell equations:v v v ∇× H = J + JDv Using vector identity, ∇ ⋅ ∇ × G ≡ 0r v v ∇ ⋅ ∇ × H = ∇ ⋅ (J + J D ) = 0r v v ∂ρ ∂ ∇ ⋅ J = −∇ ⋅ J D = − v = − ∇ ⋅ D ∂t ∂tDisplacement current:v v ∂B ∇×E = − ∂t v v v ∂D ∇× H = J + ∂t v ∇ ⋅ D = ρv(1) (2) (3) (4)Continuity equation:v ρv ∇ ⋅ J = − ∂∂ t(5)v ∇⋅B = 0v J(5)Interdependence:(2)v v ∂D JD = ∂tv v H, B(1)ρv(3)v v D, EReferences & Acknowledgements1. N. Narayana Rao’s Book Chapter “Fundamentals of Engineering Electromagnetics Revisited”, Fundamentals of Engineering g g Electromagnetics g , Taylor y & Francis Group, p, LLC, 2006. 2. U. S. Inan, A. S. Inan, Engineering Electromagnetics, Addison Wesley Longman, 2000.3。