physics 2112 lecture 23 electricity & magnetism lecture 23, slide 1

Physics 2112Lecture 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 spaceEx = Eo sin (kx – wt)

Key Point!!!

Slide 4

Not just single sine wave!

Same value of E

z

Plane wave!

Ampere’s Law / Faraday’s Law

Slide 5

dAdt

dEldB oo

dAdt

dBldE

Ampere’s Law – Changing Electric Field causes Magnetic Field

Faraday’s Law – Changing Magnetic Field causes Electric Field

Ex = Eo sin (kx – wt) By = Bo sin (kx – wt)

t

B

x

E

Eo k cos (kx – wt) = Bo w cos (kx – wt)

Eo/Bo = /w k = wave velocity

Eo = c Bo = B/(moeo)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

E0 = cB0

Argument of sin/cos gives direction of propagation


Ex

By

Not Really

The Electromagnetic Spectrum

Clickers: f =24Ghz l ~ 12.5cm

Recall from 2111:v = fl = c

Waves Carry Energy


Recall: Energy Density for E field = uE = ½ eo E2

Energy Density for B field = uB = ½ 1/mo B2

Average Total Energy Density = <u> = ½ (uE + uB) = EB/cmo

Recall from 2111:Intensity = Power/Area = Average Energy hitting a surface per unit time

Intensity = <u> c = EB/mo

Define:Poynting Vector

o

BES

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) |Savg| = 1000 Watts/m2

b) |Savg| = 1000/ Watts/m2

c) |Savg| = 1000 Watts/m2

22

What is Emax and Bmax for these E&M waves?

Just another way to keep track of all this:Its magnitude is equal to IIts direction is the direction of propagation of the wave

Comment on Poynting Vector


td

dp

m

p

td

dE

2

2

Light has Momentum!


If it has energy and its moving, then it also has momentum:

Analogy from mechanics:

td

dp

m

mv

pressureA

F

c

I

m

pE

2

2

vF

IAtd

dU

td

dEFor E - M waves:

cFIA

cv

Radiation pressure

c

IP

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 IdeaAs source approaches:Wavelength decreasesFrequency Increases


Recall for sound from 2111:

If source is moving wrt to air:)/1/( soundsso vvff

If observer is moving wrt to air: )/1( soundoso vvff

)/1(

)/1(

sounds

soundoso vv

vvff

If observer is moving wrt to air:

What’s Different from Sound or Water Waves ?

Sound /Water Waves : You can calculate (no relativity needed)

BUTResult is somewhat complicated: is source or observer moving wrt medium?

Electromagnetic Waves : You need relativity (time dilation) to calculate

BUTResult is simple: only depends on relative motion of source & observer

b > 0 if source & observer are approaching

b < 0 if source & observer are separating

b = v/c

Doppler Shift for E-M Waves


2

1

1

1'

ff

v

or f’f

v

ff’



The Doppler Shift is the SAME for both cases! f ’/f only depends on the relative velocity

2

1

1

1'

ff

A Note on Approximations

why?



2

1

1

1'

ff if b <<< 1 1' ff

Taylor Series: Expand around b = 0 2

1

1

1

F

2

!2

)0(

!1

)0(')0( FF

FF

Evaluate:1)0( F

1)0( F 1)(F

NOTE:2/1)1()( F

2

11)( F

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 mphb) A car approaching at 69mphc) Both will provide the same


Example 23.3: Police Radar

What are the reflected frequencies for these two speeds?

Our Sun Star in a distant galaxy

wav

elen

gth

Wavelengths appear shifted higher lengths

Red Shift

Frequencies appear shifted lower(c = lf)

Star separating from us(Expanding Universe)


Light from distant stars

Red Shift (the whole story!)


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 l = 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 propertiesParticle:

Energy and Momentum localized Wave:

They have definite frequency & wavelength ( fl = 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 = hfp = h/l

Photons


physics 2112 lecture 23 electricity & magnetism lecture 23, slide 1

Documents

sunshine slide

electromagnetic wave

lot slide

electromagnetic waves

sunshine poynting vector

average energy

wave onlyplane waves

e field