ece107_set7_nbg

# ece107_set7_nbg - ECE 107 Electromagnetism Set 7 Dynamic...

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1 ECE 107: Electromagnetism Set 7: Dynamic fields Instructor: Prof. Vitaliy Lomakin Department of Electrical and Computer Engineering University of California, San Diego, CA 92093

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2 Maxwell s equations Maxwell s equations Goals of this chapter To close the loop between dynamics and statics To explain effects introduced by time variations To extend some results from static to dynamics t ∇× = B E t ∇× = + D H J ρ ∇⋅ = D 0 ∇⋅ = B 12 2 1 12 2 1 12 2 1 12 2 1 ˆ ( ) 0 ˆ ( ) ˆ ( ) ˆ ( ) 0 s s ρ × = = × = = n E E n D D n H H J n B B ε μ = = D E B H E d l = d dt B d s ∫∫ H d l = d dt D d s ∫∫ + I D d s ∫∫ = Q B d s ∫∫ = 0 ε μ = = D E B H
3 Faraday s law Faraday s law: Magnetic flux: Electromotive force voltage: induces currents in a wire loop. The currents produce the flux that opposes the inducing flux (Lenz s law) allows for transformers, generators, motors, etc.! Its existence is a foundation of Electromagnetics E d l C = d dt B d s S ∫∫ S d Φ = ∫∫ B s emf S d d V d dt dt Φ = = ∫∫ B s emf V emf V

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Transformers: Current à mutual flux Flux à voltage Energy conservation à Faraday s law (2) I 1 V 1 = I 2 V 2 I 1 I 2 = N 2 N 1 V 1 = N 1 d Φ dt , V 2 = N 2 d Φ dt V 1 V 2 = N 1 N 2
Electric generator: Rotating loop in a magnetic field à EMF Electric motor:

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