Induced emf and Magnetic Flux F

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# Induced emf and Magnetic Flux F - PowerPoint PPT Presentation

Induced emf and Magnetic Flux F. Faraday found that induced emf is produced by a changing magnetic field Constant magnetic field, B, induced NO emf Magnetic flux in weber, F B = BA cos q 1 Wb = 1 T-m 2 Faraday’s Law of Induction: E = -N( D F B / D t)

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Presentation Transcript
Induced emf and Magnetic Flux F
• Faraday found that induced emf is produced by a changing magnetic field
• Constant magnetic field, B, induced NO emf
• Magnetic flux in weber, FB = BA cos q
• 1 Wb = 1 T-m2
• Faraday’s Law of Induction: E = -N(D FB/ Dt)
• Lenz’s Law: An induced emf always gives rise to a current whose magnetic field opposes the original change in flux

Physics 21: Electromagnetic Induction and AC Circuits - Christopher Chui

emf Induced in a Moving Conductor
• Faraday’s law: E = -D FB/ Dt = B DA/ Dt = Blv
• A changing magnetic flux produces an electric field
• E = F/q = qvB/q = vB
• AC generator is based on Faraday’s law. It is also called a dynamo or an electric generator
• E = Blv = NBAw sin wt where w = 2pf
• A DC generator is like an ac generator except the slip rings are replaced by split-ring commutators
• Cars use ac generators or alternators
• Counter emf or back emf is a result of Lenz’ law
• Opposing the change in B, eddy currents are produced

Physics 21: Electromagnetic Induction and AC Circuits - Christopher Chui

Transformers and power transmission
• A transformer consists of two coils: primary and secondary
• Transformer equation I: Vs / Vp = Ns / Np
• Ns > Np produces a step-up transformer
• Ns < Np produces a step-down transformer
• Transformer equation II: Is / Ip = Np / Ns
• Transformers help power transmission
• Microphones use the principle of induction
• During recording, the audio or video signal voltage is sent to the recording head, acting like an electromagnet. Playback is opposite to recording

Physics 21: Electromagnetic Induction and AC Circuits - Christopher Chui

Mutual Inductance and LR Circuit
• E1 = -M(D I2/ Dt) and E2 = -M(D I1/ Dt) where M is mutual inductance
• The unit for M is henry, H. 1 H = 1 W-s
• For a single coil, E = -L(D I/ Dt) where L is self-inductance or simply inductance, or choke
• The energy stored in a magnetic field = U = ½ LI2
• The energy density in a magnetic field, u = ½ B2/mo
• In a LR circuit, I = (V/R) (1- e-t/t) where t = L/R is the time constant
• Imax = V/R and I = Imax e-t/t

Physics 21: Electromagnetic Induction and AC Circuits - Christopher Chui

AC Circuits and Impedance
• I = Io cos 2pft ; Irms = Io/sqrt 2 and Vrms = Vo/sqrt 2
• For a resistor, both current and voltage are in phase
• In an inductor, the current lags the voltage by 90o
• V = IXL and XL = 2pfL is the inductive reactance
• In a capacitor, the current leads the voltage by 90o
• V = IXC and XC = 1/2pfC is the capacitive reactance
• Only R (not C or L) dissipates energy
• LRC series ac circuit: V = Vo cos(2pft + f) voltage out of phase with current by f; cos f is the power factor
• Vrms = IrmsZ or Vo = IoZ and tan f = (XL-XC)/R
• Z = sqrt [R2 +(XL – XC)2] = sqrt [R2 + (2pfL - 1/2pfC)2]

Physics 21: Electromagnetic Induction and AC Circuits - Christopher Chui

Resonance and Oscillators
• Resonant freq of the circuit, fo = 1/(2p) [sqrt (1/LC)]
• An LC circuit oscillates and is used as an oscillator
• Maximum power is transmitted when the output impedance of one device equals the input impedance of the second—impedance matching
• Sometimes, a transformer is used to alter an impedance
• Zp/Zs = VpIs/VsIp = (Np/Ns)2

Physics 21: Electromagnetic Induction and AC Circuits - Christopher Chui