About Exam 3 When and where Monday Nov. 24 th 5:30-7:00 pm 2650, 3650 Humanities (same as exam 1 and 2) Format Closed book One 8x11 formula sheet allowed, must be self prepared, no photo copy of solutions, no photo copy of lecture slides. Four full problems. (~20 questions) Bring a calculator (but no computer). Only basic calculation functionality can be used. Special needs: McBurney students, please inform your proctor. No early test before Monday Nov 24 th possible. Alternative test available at 4:00pm and 7:00pm in lab rooms (for approved requests only)
Disclaimer This review is meant as supplements to your own preparation. Hints and exercises presented in this review are not going g to be of complete coverage of all material.
Chapters Covered Chapter 29: Electromagnetic Induction and Faraday s Law All sections covered. Chapter 30: Inductance and AC circuit. All sections covered except for 30.10 and 30.11. Chapter 15: Wave Motion Limited to lecture 20 and HW9 coverage. Chapter 31: Maxwell s equation and EM Waves All sections covered.
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)) Waves speed (v). Wave length (λ), amplitude (A), frequency(f,ω), period (T), phase (φ) EM wave spectrum, energy, radiation pressure, Poynting Vector.
Exam Topics(2) Magnetic Induction Faraday s Law emf ε=-dφ/dt Field emf: electric field produced due to change of Φ 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 light E max, B max, f,ω,λ,φ, Wave energy Radiation pressure. Maxwell s equation at conceptual level. (no derivation)
Basic Techniques (0) Write your solutions in clear steps! You ll have better chance to get your answers right You may yget partial credits
Basic Techniques (1) Faraday s Law How to calculate magnetic flux from changing Φ B to emf motional emf for simply straight wire. directions, directions! B See exercises next page θ A Φ B =?
Exercise 1: Determine Direction Of emf Indicate the direction of emf in the following cases: B + + + + + + + + + +++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +++++++++ + + + + + + + + + B increases B B increases + + + + + + + + + +++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +++++++++ + + + + + + + + + B decreases B decreases eases + + + + + + + +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + path outside B B decreases
More Exercise 1
Basic Techniques (2) Inductance (self and mutual): Knowing the definition Calculation for simple settings (solenoid, toroid..) LR, (RC) circuit meaning of time constant time constant for LR (RC) circuit LC circuit concepts of intrinsic (resonant) frequency ω 0 for LC circuit ω f what is Hz?
AC Circuits: Impedances for R, L, C Basic Techniques (3) Simple combination of impedance for series/parallel Resonant condition. (again) ω f. Simple RLC series circuit: I, ΔV and Z Simple phasor relationships Energy consumption for the whole RCL series circuit and at each component.
Exercise 2: 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 (board) Answer: Δv Rmax = 124V Δv Lmax = 138V Δv Cmax= 221V Note: It is possible for ΔV C (and sometimes ΔV L ) to be h greater than Δv max
Exercise 3: Phasor diagram for Series RCL A Phasor diagram for a certain RCL series circuit is shown below. Label all phasors ΔV Suppose all length are drawn in proportion with SI units (i.e. 1V and 1A will appear to have same length on graph), how big is R? (~1 Ω?, ~3Ω?, ~4Ω?, can not be determined?)
Basic Techniques (4) General waves Identify transverse and longitudinal waves Identify wave speed and direction for a traveling wave function Harmonic waves Identify and conversion among ω, f, T conversion using relationship λf=v Identify basic wave parameters A, λ, T, from y p,,, wave forms.
Exercise 4: Identify Wave Speed A wave function is in the form: y ( x, t ) = 5.0 e (1.8x+ 7.2t) What is the wave speed: Answer: - 4.0 m/s (to the left) 2 Why? y ( x, t ) = 5.0 e = 5.0e (1.8 x + 7.2 t ) 1.8 2 ( x+ 4.0t) 7.2 1.8 2 2 2 1.8 ( x+ ) t) 2 = 5.0 e = 5.0e 1.8 2 ( x ( 4.0) t) 2
Basic Techniques (5) Electromagnetic Waves Knowing general concepts: e.g. can EM waves travel in vacuum? Are lights EM waves? Understand directional relationship between E, B and S. Conversion between λ and f E(B) u E (u B ) flux (intensity) Poynting ½? (rms vs. max) from source power to field intensity (for point/plane sources.) B E z y c x
Exercise 5: EM Power And Intensity A radio station is broadcasting at an average power of 25 kw, uniformly in all direction. What is the signal intensity at 5 km and 10km? A receiver is capable of being sensitive to an electric field of 0.020V/m, how far can the receiver be away from the station and still have signal? (ε 0 =8.85x10-12 ) (see board)