Physics 2112 Lecture 23 Electricity & Magnetism Lecture 23, Slide 1

First…..two comments E&M waves like sounds waves (in many ways) So I’m going to say “Recall from Physics 2111….” a lot Slide 2 The animations in the pre-lectures are really nice for this topic. There are just some things that are tough to draw on the board.

Creating an Electromagnetic Wave Slide 3 E Dipole Antenna Signal Generator What does this Create? Electric Field changing in magnitude and direction with time and space E x = E o sin (kx –  t)

Key Point!!! Slide 4 Not just single sine wave! Same value of E z Plane wave!

Ampere’s Law / Faraday’s Law Slide 5 Ampere’s Law – Changing Electric Field causes Magnetic Field Faraday’s Law – Changing Magnetic Field causes Electric Field E x = E o sin (kx –  t) B y = B o sin (kx –  t) E o k cos (kx –  t) = B o  cos (kx –  t) E o /B o =  k = wave velocity E o = c B o = B/(  o  o ) 1/2 for wave only

Plane Waves from Last Time E and B are perpendicular and in phase Oscillate in time and space Direction of propagation given by E X B E 0 = cB 0 Argument of sin/cos gives direction of propagation Electricity & Magnetism Lecture 23, Slide 6 ExEx ByBy Not Really

Slide 7 The Electromagnetic Spectrum Clickers: f =24Ghz ~ 12.5cm f =24Ghz ~ 12.5cm Recall from 2111: v = f = c

Waves Carry Energy Electricity & Magnetism Lecture 23, Slide 8 Recall: Energy Density for E field = u E = ½  o E 2 Energy Density for B field = u B = ½ 1/  o B 2 Average Total Energy Density = = ½ (u E + u B ) = EB/c  o Recall from 2111: Intensity = Power/Area = Average Energy hitting a surface per unit time Intensity = c = EB/  o Define: Poynting Vector

Example 23.1: Sunshine Poynting Vector Slide 9 Sunlight puts an average of1000 Joules of energy every second into each square meter of the earth around the equator. What is the magnitude of the average Poynting vector for this light? a) |S avg | = 1000 Watts/m 2 b) |S avg | = 1000/ Watts/m 2 c) |S avg | = 1000 Watts/m 2 What is E max and B max for these E&M waves?

Just another way to keep track of all this: Its magnitude is equal to I Its direction is the direction of propagation of the wave Comment on Poynting Vector Electricity & Magnetism Lecture 23, Slide 10

Light has Momentum! Electricity & Magnetism Lecture 23, Slide 11 If it has energy and its moving, then it also has momentum: Analogy from mechanics: pressure For E  M waves: Radiation pressure

Example 23.2: Pressure from Sunshine Slide 12 Sunlight puts an average of 1000 Joules of energy every second into each square meter of the earth around the equator. What is the pressure this sunlight puts on the earth assuming it is all absorbed? What is the total force exerted on the earth by this sunlight? What is the pressure of this sunlight if it reflected back?

Doppler Shift The Big Idea As source approaches: Wavelength decreases Frequency Increases Electricity & Magnetism Lecture 23, Slide 13 Recall for sound from 2111: If source is moving wrt to air : If observer is moving wrt to air:

What’s Different from Sound or Water Waves ? Sound /Water Waves : You can calculate (no relativity needed) BUT Result is somewhat complicated: is source or observer moving wrt medium? Electromagnetic Waves : You need relativity (time dilation) to calculate BUT Result is simple: only depends on relative motion of source & observer   0 if source & observer are approaching   0 if source & observer are separating   v/c Doppler Shift for E-M Waves Electricity & Magnetism Lecture 23, Slide 14

v or f’ f v f Doppler Shift for E-M Waves Electricity & Magnetism Lecture 23, Slide 15 The Doppler Shift is the SAME for both cases! f ’/f only depends on the relative velocity

A Note on Approximations why? Doppler Shift for E-M Waves Electricity & Magnetism Lecture 23, Slide 16  if   1 Taylor Series: Expand around  Evaluate: NOTE:

A police k-band radar gun emits radio waves at a frequency of 24GHz which is reflected off an approaching car and received back at the gun. Which car will provide a higher reflected frequency? a) A car approaching at 67 mph b) A car approaching at 69mph c) Both will provide the same Electricity & Magnetism Lecture 23, Slide 17 Example 23.3: Police Radar What are the reflected frequencies for these two speeds?

Our Sun Star in a distant galaxy wavelength Wavelengths appear shifted higher lengths Red Shift Frequencies appear shifted lower (c = f) Star separating from us (Expanding Universe) Electricity & Magnetism Lecture 23, Slide 18 Light from distant stars

Red Shift (the whole story!) Electricity & Magnetism Lecture 23, Slide 19 Two additional effects can cause frequency shifts from distant stars. Gravity - Extreme case is a black hole. You can think of a black hole a “redshifting” light until  = infinity and f = 0 Expanding Universe - Can take so long to reach Earth that universe expanded during flight, stretching the wavelength Exact mixture depends – How long was wave in flight, how large was object emitting the wave and how fast was it moving wrt Earth.

We believe the energy in an e-m wave is carried by photons Question: What are Photons? Answer: Photons are Photons. Photons possess both wave and particle properties Particle: Energy and Momentum localized Wave: They have definite frequency & wavelength ( f  c) Question: How can something be both a particle and a wave? Answer: It can’t (when we observe it) What we see depends on how we choose to measure it! The mystery of quantum mechanics: More on this in PHYS 2115 (one cool class!) h  6.63e  34 J  s Planck’s constant Connections seen in equations: E  hf p  h/ Photons Electricity & Magnetism Lecture 23, Slide 20