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 HJ ρ ∇⋅ = D 0 = B 12 2 1 12 2 1 12 2 1 12 2 1 ˆ () 0 ˆ ˆ ˆ 0 s s ×− = ⋅− = = = nE E nD D nH H J nB B ε μ = = DE BH 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 = =
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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 = ∫∫ Bs emf S dd Vd dt dt Φ = = 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
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Electric generator: Rotating loop in a magnetic field à EMF Electric motor: Opposite to the generator An AC current is sent to the coil in a constant magnetic field à coil spins Faraday s law (2)
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ece107_set7_nbg - ECE 107: Electromagnetism Set 7: Dynamic...

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