When and where About Exam 3 Tuesday Nov 27th 5:30-7:00 pm (same location as Midterms 1 and 2) Format Closed book One 8x11 formula sheet allowed, must be self prepared, no photo copying/download-printing of solutions, lecture slides, etc. 20 multiple choice questions Bring a calculator (but no computer). Only basic calculation functionality can be used. Bring a B2 pencil for Scantron. Special requests: Should have been settled by now. All specially arranged tests are held in our 202 labs. (for approved requests only)
Chapters Covered Chapter 31: Electromagnetic Induction and Faraday s Law All sections covered. Chapter 32: Inductance. All sections covered. Chapter 33: AC Circuits. Section 33.1-33.7 Chapter 34: EM Waves All sections covered Displacement Current (34.1) only conceptual level. Solving differential equations (for Maxwell s eqs.) not required Chapter 16: Wave Motion. Not directly, but knowledge helps Ch. 34
Special Notes This review is meant as supplements to your own preparation. Exercises presented in this review do not form a problem pool for the test..
Exam Topics (1) Concepts: Understanding all key concepts in the covered chapters. Basic Quantities: Magnetic Field, Magnetic Field Lines, Magnetic Flux Electromotive Force (emf) Inductance (self & mutual) Time Constants (RC, L/R) Phase Angles, Phasors Resonance Frequency (1/sqrt(LC)) Impedance and reactuance Wave length (λ), amplitude (A), frequency(f,ω), period (T), phase (φ), wave speed (v) EM wave spectrum, energy, radiation pressure, Poynting Vector, speed of light.
Exam Topics(2) Magnetic Induction Faraday s Law emf ε=-dφ Β /dt Field emf: electric field produced due to change of Φ Β à no circuit/conductor is required. Motional emf: emf due to magnetic force. Lenz s Law. Important: identify direction of emf Self and Mutual Inductance. ε = -LdI/dt ε 2 = M di 1 /dt, ε 1 =M di 2 /dt
Exam Topics(3) Timing circuits: RC (τ=rc) RL (τ=l/r) LC (ω=1/sqrt(lc)) RCL series circuit (AC powered) Phasor relationship for R, L, C Voltage and current of RLC circuit. Impedance Resonance. Power Consideration Electromagnetic waves Speed of EM Wave E max, B max, f,ω,λ,φ, directional relationship of E, B, S Wave energy, Intensity Radiation pressure. Maxwell s equation at conceptual level. (no derivation)
Basic Techniques (1) Faraday s Law How to calculate magnetic flux from changing Φ B to emf motional emf for simple straight wire. directions, directions! B See exercises on following pages θ A Φ B =?
Reminder: All Those Right-Hand Rules
Standard Lecture Exercises: Determine Direction Of emf Indicate the direction of emf in the following cases: + + + + + + + + + + + + + + + + + +............ + + + + + + + + + + + + + + + + + +............ + + + + + + + + + + + + + + + + + +............ + + + + + + + + + + + + + + + + + + B............ + + + + + + + + + + + + + + + + + +............ + + + + + + + + + + + + + + + + + + B increases B decreases................................................ B.................................... B increases + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + B decreases B decreases path outside B
More Standard Lecture Exercises More configurations at the end of ch. 31.
Exercise 1: Jumping Ring In each of the following jumping ring configurations, what is the direction that the rings tends to move when the switch S is closing. Note that the battery is reversed in case d.2 as compared in case d.1. d.1 up & d.2 down, d.1 down & d.2 up, both up, both down d.1 d.2
Basic Techniques (2) Inductance (self and mutual): Know the definition Relate emf to L and di/dt LR, (RC) circuit Physical meaning of time constant time constant for LR (RC) circuit LC circuit concepts of intrinsic (resonant) frequency ω 0 for LC circuit ω ß à f what is Hz?
LR circuit Reminder: Time Constant turning on turning off I = V 0 R (1" e" t L / R ) I = I 0 e " t L / R RC circuit: check section 28.4
Exercise 2 An LR circuit has a time constant of 1s. Initially, there is no current in the circuit, at t=0, the circuit is being powered by a 3V battery in series. How long does it take for the current to ramp up to 80% of maximum? 1.6s (see board) If the voltage is doubled to 6V, is the answer to previous question (time to 80%) to be doubled? halved? same? neither?
AC Circuits: Basic Techniques (3) Impedances for R, L, C Simple combination of impedance for series/parallel Resonant condition. (again) ω ß à f. Simple RLC series circuit: I, ΔV and Z Simple phasor relationships Energy consumption for the whole RCL series circuit and at each component. When to apply factor ½? ( or when to use _rms and when to use _max)
Reminder: Summary of Phasor Relationship I R and ΔV R in phase I L 90 o behind ΔV L ΔV L 90 o ahead of I L I C 90 o ahead of ΔV C ΔV C 90 o behind I C I R = ΔV R /R I L = ΔV L /X L I C = ΔV C /X C
Reminder: RLC Series In AC Circuit The current at all point in a series circuit has the same amplitude and phase (set it be i=i max sinωt) Δv R = I max R sin(ωt + 0) Δv L = I max X L sin(ωt + π/2) Δv C = I max X C sin(ωt - π/2) i Voltage across RLC: Δv RLC = Δv R + Δv L + Δv R = I max Rsin(ωt) + I max X L sin(ωt + π/2) + I max X C sin(ωt - π/2) =ΔV max sin(ωt+φ) how to get them?
Reminder Current And Voltages in a Series RLC Circuit Δv R =(ΔV R ) max Sin(ωt) Δv L =(ΔV L ) max Sin(ωt + π/2) Δv C =(ΔV C ) max Sin(ωt - π/2) i= I max Sin(ωt) ΔV max Sin(ωt +φ) " V =! 2 2 max Imax R + ( X L X C )! X " = tan 1 ( L! R X C ) Δ V R _ Max = I max R, ΔV L _ Max = I max ( ω L), ΔVC _ Max = Imax /( ωc)
Quick Quiz: Series RLC Circuit: Maximum Voltage Across Component. i= I max Sin(ωt) ΔV max Sin(ωt +φ)!v R _ Max = I max R,!V L _ Max = I max (!L),!V C _ Max = I max / (!C) Quiz: can ΔV max across each components be larger than overall ΔV max? ΔV R_max can, but ΔV C_max or ΔV L_max can t; ΔV R_max can t, but ΔV C_max or ΔV L_max can; All potentially can; No, none of the individual ΔV max across a component can
Exercise 3: RCL Series AC Circuit A series RLC AC circuit has R=425 Ω, L=1.25 H, C= 3.50 µf, ΔV=(150V) sin377t. Find the maximum voltage across R, L, C. Solution ΔV R _ Max = I max R, ΔV L _ Max ( ω L), ΔV C _ Max R = 425, ωl = 377*1.25 = 471.3, 1/( ωc) = 757.8 = I max = I max /( ωc) I max = ΔV max / Z = ΔV max / + ( ωl 1/( ωc)) = 0.29 Answer: Δv Rmax = 124V, Δv Lmax = 138V, Δv Cmax = 221V R 2 2 Note: It is possible for ΔV C (and sometimes ΔV L ) to be greater than Δv max Further potential questions: What is the frequency?, what is the phase between ΔV and I, what is the average power consumed by R, (or L, C)?... What is the resonance (angular) frequency?
Exercise 4: Phasor diagram for Series RCL A Phasor diagram for a certain RCL series circuit is shown below. Label all phasors Δv Δv L Δv R ΔV Δv C
Electromagnetic Waves Basic Techniques (4) Knowing general concepts: e.g. can EM waves travel in vacuum? Are lights EM waves? Identify wave speed and direction for a traveling wave function. Asin(kx-ωt+φ) Understand directional relationship between E, B and S. Conversion between λ and f E(B) ß à u E (u B ) ß à flux (intensity)ß à Poynting ½? (rms vs. max) from source power to field intensity (for point/plane sources.) B E z y c x
Exercise 5: EM Wave The electric component of an EM wave has the form (in SI units): 3 3 E x ( z, t) = 5.0 10 sin(6.28 10 z + 1.884 10 6 t) v/m What is the speed of the wave, in which direction? 3x10 8 m/s, -z direction. (Why? See board) What are the wavelength and frequency of this wave? 1000m, 300kHz (why? see board) Write down the function form of the magnetic component of the wave 11 3 B y ( z, t) = 1.67 10 sin(6.28 10 z + 1.884 10 6 t) T Further potential questions (practice yourself): E max? B max?, average power? intensity? pressure?..
Exercise 6: EM Power And Intensity A radio station is broadcasting at an average power of 25 kw, uniformly in all direction. What is the average signal intensity at 5 km and 10km? A receiver is capable of being sensitive to an electric field of E rms =0.020V/m, how far can the receiver be away from the station and still have signal? (ε 0 =8.85x10-12 C 2 /Nm 2 ) Intensity = Power/Area = P/ (4πR 2 ) @ 5km, I 5km = 25000/(4*3.14*5000^2) =8x10-5 W/m 2 @10km, I 10km = I 5km /4 =2x10-5 W/m 2 I=ε 0 E rms 2 c = (0.02) 2 (8.85x10-12 c) = 1.06x10-6 W/m 2 à I = P/(4πR2 ) à R= 43.3 km