Lec21 - cture 21 cture 21 1 Maxwell’s Equations(so far Gauss’s law inside S Q E d A ε = ur ur g Ñ Gauss’ law for magnetism S B d A =

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Unformatted text preview: cture 21- cture 21- 1 Maxwell’s Equations (so far) Gauss’s law inside S Q E d A ε = ∫ ur ur g Ñ Gauss’ law for magnetism S B d A = ∫ ur ur g Ñ Faraday’s law B C d E dl dt Φ = - ∫ ur r g Ñ Ampere’s law * C B d l I μ = ∫ ur r g Ñ cture 21- cture 21- 2 Parallel-Plate Capacitor Revisited S S B d l I μ ∂ = ∫ ur r g Ñ For surface S 1 , I s = I , but for surface S 2 , I s = 0 ?? Wait, LHS is the same (because C is the same)! You could make this work if a fictitious current I d is added to I s in such a way that I d is zero for S 1 but is equal to I for S 2 . E dQ dV A dV I C dt dt d dt dE d A dt dt ε ε ε = = = Φ = = E d d I dt ε Φ ≡ will work. Q-Q E ur E = ur B=0 ? Not experimentally! cture 21- cture 21- 3 Displacement Current James Clerk Maxwell proposed that a changing electric field induces a magnetic field , in analogy to Faraday’s law: A changing magnetic field induces an electric field. Ampere’s law is revised to become Ampere-Maxwell law 0 0 ( ) E d C d B dl I I I dt μ μ μ ε Φ = + ≡ + ∫ ur r g Ñ is the displacement current . E d d I dt ε Φ ≡ where cture 21- cture 21- 4 MAXWELL’S EQUATIONS “COMPLETED” The equations are often written in slightly different (and more convenient) forms when dielectric and/or magnetic materials are present. Basis for electromagnetic waves! inside S Q E d A ε = ∫ ur ur g Ñ S B d A = ∫ ur ur g Ñ B C d E dl dt Φ = - ∫ ur r g Ñ 0 0 C E B l I d dt d μ ε μ Φ + = ∫ ur r g Ñ cture 21- cture 21- 5 ©2008 by W.H. Freeman and Company cture 21- cture 21- 6 The extended Amperes law involves a displacement current which was added to the real currents as a source of the magnetic (B) fields.added to the real currents as a source of the magnetic (B) fields....
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This note was uploaded on 12/07/2011 for the course PHYS 241 taught by Professor Wei during the Fall '08 term at Purdue University-West Lafayette.

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Lec21 - cture 21 cture 21 1 Maxwell’s Equations(so far Gauss’s law inside S Q E d A ε = ur ur g Ñ Gauss’ law for magnetism S B d A =

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