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# Lec21 - ture 21-1 ture Maxwells Equations(so far Gausss law...

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cture 21- cture 21-1 Maxwell’s Equations (so far) Gauss’s law 0 inside S Q E d A ε = ur ur g Ñ Gauss’ law for magnetism 0 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 * 0 C B dl I μ = ur r g Ñ

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cture 21- cture 21-2 Parallel-Plate Capacitor Revisited 0 S S B dl 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 . 0 0 0 E dQ dV A dV I C dt dt d dt dE d A dt dt ε ε ε = = = Φ = = 0 E d d I dt ε Φ will work. Q -Q E ur 0 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 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 . 0 E d d I dt ε Φ where

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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! 0 inside S Q E d A ε = ur ur g Ñ 0 S B d A = ur ur g Ñ B C d E dl dt Φ = - ur r g Ñ 0 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

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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.
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