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Chapter%2010

# Chapter%2010 - Chapter 10 Time-Varying Fields and Maxwell's...

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Dr. Ray Chen© Chapter 10 Time-Varying Fields and Maxwell’s Equations

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Dr. Ray Chen© 10.1 Faraday’s Law A time-varying magnetic field produces an electromotive force(emf) which may establish a current in a suitable closed circuit. ) t ( Φ emf Faraday’s law is represented by dt d emf Φ = (1) ( ) ( ) ( ) 4 turns N for 3 L d E emf 2 flux magnetic S d B dt d N emf , Φ = = = Φ v v v v
Dr. Ray Chen© 10.1 Farady’s Law From Eqa. 1 to 3, if B is the only time-varying quantity , we have: = = = S S dt S d B S d B dt d - L d E emf v v v v v v (5) Applying Stoke’s theorem to the closed line integral, we have: S d B = × S S dt S d ) E ( v v v v dt E B v v = × case tic electrosta the is which 0 then 0 B If , E , dt = × = v v

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Dr. Ray Chen© 10.1 Farady’s Law z kt a ˆ e I Case 0 B B(t) = a B 2 0 2 a e kB t B aE emf kt π π φ = = = ρ φ kt e kB E 0 2 1 point any At = ) ) E ( ( e kB ) E ( kt z ρ ρ ρ ρ = = × 1 0 v = ) E ( d d e kB Integrate kt ρ ρ ρ ρ 0 ρ ρ ρ φ φ kt kt e kB E E e kB 0 2 0 2 1 2 1 = =
Dr. Ray Chen© 10.1 Farady’s Law II Case y(t) d B S d B (t) 0 = = Φ = v v , t B Fig. 10.1 bar of velocity the is v , Bvd dt dy Bd dt d emf = = Φ = ( ) = Φ Φ S d B varying - time or B varying - time either by induced be can emf : Conclusion v v v

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Dr. Ray Chen© 10.1 Farady’s Law B v E field electric
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Chapter%2010 - Chapter 10 Time-Varying Fields and Maxwell's...

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