physics 211 topic 23 · 2020-05-04 · physics 211 topic 23 e&m waves - how they’re formed -...

Physics 211

Topic 23

E&M Waves- How they’re formed

- Poynting Vector (what the heck it means)- Doppler Effect for E&M waves

Electricity & Magnetism Lecture 23, Slide 1

What you thought…..

Poynting.

Didn't quite understand the waves of energy portion with the graphs

My understanding of the quantum mechanical theory of light is that the energy carried by light does depend on the angular frequency, right? That's what the photoelectric effect was all about?

The prelecture was making sense until after question 2. Once intensity (which looks just like current) was introduced along with power and poynting and 87 different averages, everything fell apart for me.

Because the prior lecture pulled the equations for the EM wave out of thin air, with little explanation, it was a bit hard to grasp the power portion of the pre-lecture.I'm starting to be ready for summer. Only about a month left.

Could you please explain the poynting vector and the importance of these average values mentioned in the prelecture (average pointing vector, average intensity, etc)? Also, what do we need to know about photons and waves as far as how we treat them in this class? Thank you.

Slide 2

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 3

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 4

E

Dipole

Antenna

Signal

Generator

What does this Create?

Electric Field changing in

magnitude and direction

with time and space

Ex = Eo sin (kx – wt)

Key Point!!!

Slide 5

Not just single sine wave!

Same value of E

z

Plane wave!

Electricity & Magnetism Lecture 22, Slide 6

Past Confusion

Nothing is moving here.

Arrows only represent strength of field.

Ampere’s Law / Faraday’s Law

Slide 7

=• 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/(oo)1/2

Question: When is this true?

For which situations does Eo = c*Bo?

A. Always

B. In all cases where the electric field is changing

C. In all cases where the magnetic field is changing

D. Only for a electro-magnetic wave

E. (B) and (C)

Slide 8

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

Electricity & Magnetism Lecture 23, Slide 9

Ex

By

Not Really

CheckPoint 1(A): Direction of Wave

Electricity & Magnetism Lecture 23, Slide 10

Which equation correctly describes the electromagnetic wave

shown above?

A. Ex = Eo sin (kz + ω t)

B. Ey = Eo sin (kz - ω t)

C. By = Bo sin (kz - ω t)

CheckPoint 1(A): Direction of Wave

Electricity & Magnetism Lecture 23, Slide 11

Which equation correctly describes the electromagnetic wave

shown above?

A. Ex = Eo sin (kz + ω t)

B. Ey = Eo sin (kz - ω t)

C. By = Bo sin (kz - ω t)

Welcome to

Physics 2112

Hit “E” on your clicker.

Electricity & Magnetism Lecture 23, Slide 13

Slide 14

The Electromagnetic Spectrum

Clickers:

f =24Ghz

l ~ 12.5cm

Recall from 2111:

v = fl = c

Waves Carry Energy

Electricity & Magnetism Lecture 23, Slide 15

Recall:

Energy Density for E field = uE = ½ o E2

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

Average Total Energy Density = <u> = ½ (uE + uB) = EmaxBmax/2co

Recall from 2111:

Intensity = Power/Area

= Average Energy hitting a surface per unit time

Intensity = <u> c = EmaxBmax/2o

Define:

Poynting Vector

o

BES

=

Example 23.1: Sunshine Poynting Vector

Slide 17

Sunlight puts an average of 1000 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/m22

2

Example 23.1: Sunshine Poynting Vector

Slide 18

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/m22

2

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

Electricity & Magnetism Lecture 23, Slide 20

CheckPoint 1(B): Energy of Wave

Which of the following actions will increase the energy carried by

this wave?

A. Increase E keeping ω constant

B. Increase ω keeping E constant

C. Both of the above actions will increase the energy of the

wave

D. Neither of the above actions will increase the energy of

the wave

Unit 23, Slide 21

Maybe some points of confusion?

Slide 23

Wasn’t there a frequency term

in the energy of sound wave in

2111? (Amplitude2*w2)

Good point!

But in sound, something

physical is moving so we have a

kinetic energy term

Maybe some points of confusion?

Slide 24

Why is it that I always hear that x-rays

are more dangerous than visible light

ray?

Isn’t that a frequency and energy deal?

Again, good point!

But now we’re in the area of quantum

mechanics and we’re thinking about light

in terms of photons. In high frequency

waves, there a higher energy photons,

but there are less of them.

Question: Wave Direction

An electromagnetic wave is described by: where is the unit vector in the +y direction.

A B C D

Which of the following graphs represents the z − dependence of Bx at t = 0?

x

y

z

j( )tkzEjE w−= cosˆ

0

Question: Wave Direction

Electricity & Magnetism Lecture 23, Slide 26

An electromagnetic wave is described by: where is the unit vector in the +y direction.

A B C D

Which of the following graphs represents the z − dependence of Bx at t = 0?

X X

x

y

z

E

B

x

y

z

Wave moves in +z direction

j( )tkzEjE w−= cosˆ

0

( )tkzEjE w−= cosˆ0

BE

Points in direction of propagation

( )tkzBiB w−−= cosˆ0

td

dp

m

p

td

dE

2

2=

Light has Momentum!

Electricity & Magnetism Lecture 23, Slide 27

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

Analogy from mechanics:

td

dp

m

mv=

pressureA

F

c

I=

m

pKE

2

2

=

vF=

IAtd

dE

td

KEd tot =→)(

For E − M waves:

cFIA =

cv →

Radiation pressure

c

IP =

Example 23.2: Pressure from Sunshine

Slide 28

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

Electricity & Magnetism Lecture 23, Slide 31

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

Electricity & Magnetism Lecture 23, Slide 32

2

1

1

1'

−

+=

b

bff

v

orf’

f

v

ff’

Doppler Shift for E-M Waves

Electricity & Magnetism Lecture 23, Slide 33

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

2

1

1

1'

−

+=

b

bff

A Note on Approximations

Doppler Shift for E-M Waves

Electricity & Magnetism Lecture 23, Slide 34

2

1

1

1'

−

+=

b

bff

if b <<< 1

( )b+ 1' ff

*f f b

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

Electricity & Magnetism Lecture 23, Slide 36

Example 23.3: Police Radar

What are the reflected frequencies for these two speeds?

CheckPoint 2(A): Clicker Waves

Unit 23, Slide 38

Your iclicker operates at a frequency of

approximately 900 MHz (900x106 Hz). What is

the approximate wavelength of the EM wave

produced by your iclicker?

A. 0.03 meters

B. 0.3 meters

C. 3.0 meters

D. 30 meters

Unit 23, Slide 39

CheckPoint 2(B): Clicker Waves

If you wanted to see the EM wave produced by

the iclicker with your eyes, which of the following

would work? (Note: Your eyes are sensitive to EM

waves with frequency around 1014 Hz)

A. Run away from the iclicker when it is voting.

B. Run toward the iclicker when it is voting.

C. Neither will work, moving relative to the

iclicker won't change the frequency

reaching your eyes.

Your iclicker operates at a frequency of approximately 900 MHz (900x106 Hz).

How fast would you have to run towards your to see the EM wave produced by the iclicker with your eyes, which of the following would work?

(Note: Your eyes are sensitive to EM waves with a frequency around 1014Hz)

Electricity & Magnetism Lecture 23, Slide 40

Example 23.4: Running towards your clicker

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)

Electricity & Magnetism Lecture 23, Slide 43

Light from

distant stars

Red Shift (the whole story!)

Electricity & Magnetism Lecture 23, Slide 44

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.

Spiral Arm galaxy

A spiral arm galaxy is rotating as shown above. Which portion of the galaxy will appear more “red shifted” (lower frequency)?

A. A

B. B

C. C

A

B

C

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 localizedWave:

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 constantConnections seen in equations:

E = hf

p = h/l

Photons

Electricity & Magnetism Lecture 23, Slide 46