1. Physics 102: Lecture 14, Slide 1 Electromagnetic Waves Physics 102: Lecture 14

2. Physics 102: Lecture 14, Slide 2 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 -X C ) I max X L I max X C I max R V gen,max 

3. Physics 102: Lecture 14, Slide 3 Preflight 14.1 As the frequency of the circuit is either raised above or lowered below the resonant frequency, the impedance of the circuit: Always increases Only increases for lowering the frequency Only increases for raising the frequency f0f0 Z L R C

4. Physics 102: Lecture 14, Slide 4 Preflight 14.3 At the resonant frequency, which of the following is true? I is in phase with V generator I leads V generator I lags V generator VLVL VCVC VRVR V gen 

5. Physics 102: Lecture 14, Slide 5 What is it good for? Current through circuit depends on frequency (maximum at resonance frequency f o ) –Radio receiver –Stereo equalizer –NMR/MRI L R C

6. Physics 102: Lecture 14, Slide 6 Resonance in Radios An AC circuit with R= 2 , L = 0.30  H 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 R C

7. Physics 102: Lecture 14, Slide 7 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

8. Physics 102: Lecture 14, Slide 8 James Clerk Maxwell 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) 4 laws unify electric & magnetic forces: (1831-1879) Electromagnetic waves!

9. Physics 102: Lecture 14, Slide 9 Radio antenna Generator creates oscillating current up and down metal rods + - I x y This is called an electric dipole antenna This is an electric dipole!

10. Physics 102: Lecture 14, Slide 10 Oscillating E field Electric dipole antenna creates an oscillating electric field In which direction does the E-field point at this time? NOT QUITE! E-fields do NOT appear everywhere in space instantaneously, they travel at a finite speed c... and now?

11. Physics 102: Lecture 14, Slide 11 Electromagnetic radiation E-fields do NOT appear everywhere in space instantaneously, they travel at a finite speed c x y t=0t=T (one full period) = 1/f cT = c = f c c EM wave!

12. Physics 102: Lecture 14, Slide 12 ACT: EM Waves Which direction should I orient my antenna to receive a signal from a vertical transmission tower? 1) Vertical2) Horizontal 3) 45 Degrees Direction wave travels demo

13. Physics 102: Lecture 14, Slide 13 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 x y EM wave! c = f E and B fields propagate together as EM waves II

14. Physics 102: Lecture 14, Slide 14 Recall fundamental constants of electricity and magnetism: “Permeability of free space” (magnetism)“Permittivity of free space” (electricity) Speed of EM wave in vacuum Now multiply them: Note: 1T = 1 N/Cm/s (from F = qvBsin(θ)) 1A = 1 C/s (from I = ΔQ/Δt) c =

15. Physics 102: Lecture 14, Slide 15 Electromagnetic Waves x z y 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/  = c/  Period: T = 1/f

16. Physics 102: Lecture 14, Slide 16 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)

17. Physics 102: Lecture 14, Slide 17 Electromagnetic Spectrum Light, Radio, TV, Microwaves, X-Rays are all electromagnetic waves! c = f R O Y G B I V

18. Physics 102: Lecture 14, Slide 18 EM Waves Practice E x 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? (2) Label the two tic marks on the x axis (in meters). Perpendicular to E, v: Into/out of the page 3.16.2

19. Physics 102: Lecture 14, Slide 19 This picture only represents EM wave along one line (x-axis) x z y Representing EM wave: Wavefronts Imagine a slice in y-z plane y z E-field & B-field same everywhere along plane Wavefronts – surfaces at crests of EM wave

20. Physics 102: Lecture 14, Slide 20 Doppler Effect Now the car is moving to the left. Observed wavelength  o different! u A police car emits light of wavelength e e o  e o  e Moving toward observer: f o = f e (1 + u/c) Only relative velocity matters: u = v 1 + v 2 moving in opposite directions u = v 1 – v 2 moving in same direction  = f/c Moving away from observer: f o = f e (1 – u/c) Wavefronts

21. Physics 102: Lecture 14, Slide 21 ACT: Doppler Practice V = 32 m/sV = 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