Induced emf and Magnetic Flux F

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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