Physics 102: Lecture 14 Electromagnetic Waves Physics 102: Lecture 14, Slide 1
Review: Phasors & Resonance At resonance Z is minimum (=R) I max is maximum (=V gen,max /R) V gen is in phase with I X L = X C V L (t) = -V C (t) At lower frequencies X C > X L V gen lags I At higher frequencies X C < X L V gen lead I I max X L φ I max R I max X C I max (X L -X C ) Physics 102: Lecture 14, Slide 2
Preflight 14.1 As the frequency of the circuit is either raised above or lowered below the resonant frequency, the impedance of the circuit: L C R Always increases Only increases for lowering the frequency Only increases for raising the frequency Resonance in AC Circuits Z f 0 frequency Physics 102: Lecture 14, Slide 3
Preflight 14.3 At the resonant frequency, which of the following is true? I leads V generator I lags V generator I is in phase with V generator V L V R φ = 0 V C Physics 102: Lecture 14, Slide 4
What is it good for? Current through circuit depends on frequency (maximum at resonance frequency f o ) Radio receiver Stereo equalizer NMR/MRI L C R Physics 102: Lecture 14, Slide 5
Resonance in Radios An AC circuit with R= 2 Ω, L = 0.30 μh and variable capacitance is connected to an antenna to receive radio signals at the resonance frequency. If you want to listen to music broadcasted at 96.1 MHz, what value of C should be used? L C R Physics 102: Lecture 14, Slide 6
ACT: Radios Your radio is tuned to FM 96.1 MHz and want to change it to FM 105.9 MHz, which of the following will work. 1. Increase Capacitance 2. Decrease Capacitance 3. Neither, you need to change R Physics 102: Lecture 14, Slide 7
James Clerk Maxwell (1831-1879) 4 laws unify electric & magnetic forces: 1. E-field generated by electric charge (Gauss Law Lecture 2) 2. No magnetic charges (Lecture 8) 3. E-field generated by changing magnetic flux (Faraday s Law Lecture 10) 4. B-field generated by moving electric charge & changing electric flux! (Ampere s Law Lecture 9) Physics 102: Lecture 14, Slide 8 Electromagnetic waves!
Radio antenna Generator creates oscillating current up and down metal rods I - y x + Physics 102: Lecture 14, Slide 9 This is an electric dipole! This is called an electric dipole antenna
Oscillating E field Electric dipole antenna creates an oscillating electric field In which direction does the E-field point at this time?... and now? NOT QUITE! E-fields do NOT appear everywhere in space instantaneously, they travel at a finite speed c Physics 102: Lecture 14, Slide 10
Electromagnetic radiation E-fields do NOT appear everywhere in space instantaneously, they travel at a finite speed c ct = λ y c EM wave! c x t=t t=0 (one full period) = 1/f Physics 102: Lecture 14, Slide 11 c = λf
ACT: EM Waves Which direction should I orient my antenna to receive a signal from a vertical transmission tower? 1) Vertical 2) Horizontal 3) 45 Degrees Direction wave travels demo Physics 102: Lecture 14, Slide 12
Electromagnetic radiation Current in antenna also creates oscillating B-field B-fields do NOT appear in space everywhere instantaneously they travel at a finite speed c I y x EM wave! E and B fields propagate together as EM waves Physics 102: Lecture 14, Slide 13 c = λf
Speed of EM wave in vacuum Recall fundamental constants of electricity and magnetism: 0 8.85 10 12 2 / 2 Permittivity of free space (electricity) 0 7 Permeability of free space (magnetism) Now multiply them: c = 0 0 8.85 10 12 2 2 4 10 7 / / Physics 102: Lecture 14, Slide 14 2 17 1.11 10 2 0 0 8 Note: 1T = 1 N/Cm/s (from F = qvbsin(θ)) 1A = 1 C/s (from I = ΔQ/Δt)
Electromagnetic Waves y x Transverse (vs. sound waves longitudinal) E perpendicular to B and always in phase E & B increase and decrease at same times Can travel in empty space (sound waves can t!) Speed of light in vacuum: v = c = 3 x 10 8 m/s (186,000 miles/second!) Frequency: f = v/λ = c/λ Period: T = 1/f Physics 102: Lecture 14, Slide 15
Preflight 14.6 14.12 Which of the following are transverse waves? sound light radio X-ray microwave water waves The Wave (i.e. at football games) Physics 102: Lecture 14, Slide 16
Electromagnetic Spectrum Light, Radio, TV, Microwaves, X-Rays are all electromagnetic waves! c = λf R O Y G B I V Physics 102: Lecture 14, Slide 17
EM Waves Practice Shown below is the E field of an EM wave broadcast at 96.1 MHz and traveling to the right. (1) What is the direction of the magnetic field? E Perpendicular to E, v: Into/out of the page (2) Label the two tic marks on the x axis (in meters). 3.1 6.2 x Physics 102: Lecture 14, Slide 18
Representing EM wave: Wavefronts This picture only represents EM wave along one line (x-axis) y Imagine a slice in y-z plane y z x z λ E-field & B-field same everywhere along plane Physics 102: Lecture 14, Slide 19 Wavefronts surfaces at crests of EM wave
Doppler Effect A police car emits light of wavelength λ e Now the car is moving to the left. Observed wavelength λ o different! Wavefronts λ e λ o < λ e λ o > λ e u Moving toward observer: f o = f e (1 + u/c) Moving away from observer: f o = f e (1 u/c) λ = f/c Physics 102: Lecture 14, Slide 20 Only relative velocity matters: u = v 1 + v 2 moving in opposite directions u = v 1 v 2 moving in same direction
ACT: Doppler Practice V = 32 m/s V = 50 m/s In the jeep, the frequency of the light from the troopers car will appear: (1) higher (more blue) (2) Lower (more red) What value should you use for u in the equation? (1) 32 (2) 50 (3) 50+32 (4) 50-32 Physics 102: Lecture 14, Slide 21