Electromagnetic Waves

Chapter 23

Electromagnetic TheoryTheoretical understanding

Well developed by middle 1800’sCoulomb’s Law and Gauss’ Law explained electric

fields and forcesAmpère’s Law and Faraday’s Law explained magnetic

fields and forcesThe laws were verified in many experiments

Unanswered QuestionsWhat was the nature of electric and magnetic fields?What is the idea of action at a distance?How fast do the field lines associated with a charge

react to a movement in the charge?James Clerk Maxwell studied some of these

questions in the mid-1800’sHis work led to the discovery of electromagnetic

waves

Discovery of EM WavesA time-varying magnetic field gives rise to an electric

fieldA magnetic field can produce an electric field

Maxwell proposed a modification to Ampère’s LawA time-varying electric field produces a magnetic fieldThis gives a new way to create a magnetic fieldAlso gives equations of electromagnetism a symmetry

Section 23.1

Symmetry of E and BThe correct form of Ampère’s Law (due to Maxwell) says

that a changing electric flux produced a magnetic field. Since a changing electric flux can be caused by a changing

E, was an indication that a changing electric field produces a magnetic field

Faraday’s Law says that a changing magnetic flux produces an induced emf, and an emf is always associated with an electric fieldSince a changing magnetic flux can be caused by a

changing B, we can also say that a changing magnetic field produces an electric field

Section 23.1

Section 23.1

Symmetry of E and B, cont.

Electromagnetic WavesSelf-sustaining oscillations involving E and B are

possibleThe oscillations are an electromagnetic wave

Electromagnetic waves are also referred to as electromagnetic radiation

Both the electric and magnetic fields must be changing with time

Although Maxwell worked out the details of em waves in great mathematical detail, experimental proof of the existence of the waves wasn’t carried out until 1887

Section 23.1

Perpendicular FieldsAccording to Faraday’s

Law, a changing magnetic flux through a given area produces an electric fieldThe direction of the

electric field is perpendicular to the magnetic field that produced it

Similarly, the magnetic field induced by a changing electric field is perpendicular to the electric field that produced it

Section 23.1

Properties of EM WavesAn electromagnetic wave involves both an electric

field and a magnetic fieldThese fields are perpendicular to each otherThe propagation direction of the wave is

perpendicular to both the electric field and the magnetic field

Section 23.1

EM Waves are Transverse Waves

Imagine a snapshot of the electromagnetic waveThe electric field is along the x-axisThe wave travels in the z-direction

Determined by the right-hand rule #2The magnetic field is along the y-directionBecause both fields are perpendicular to each other, the wave is a

transverse wave

Section 23.2

Light is an EM WaveMaxwell found the speed of an em wave can be

expressed in terms of two universal constantsPermittivity of free space, εo Magnetic permeability of free space, μo

The speed of an em wave is denoted by c

Inserting the values, c = 3.00 x 108 m/sThe value of the speed of an electromagnetic wave is

the same as the speed of light

o o

cε μ

1

Section 23.2

Light as an EM Wave, cont.Maxwell answered the question of the nature of light

– it is an electromagnetic waveHe also showed that the equations of electricity and

magnetism provide the theory of light

EM Waves in a VacuumRemember that mechanical waves need a medium

to travel throughMany physicists searched for a medium for em

waves to travel throughEM waves can travel through many materials, but

they can also travel through a vacuumAll em waves travel with speed c through a vacuumThe frequency and wavelength are determined by

the way the wave is produced

Section 23.2

EM Waves in Material SubstancesWhen an em wave travels through a material

substance, its speed depends on the properties of the substance

The speed of the wave is always less than cThe speed of the wave depends on the wave’s

frequency

Section 23.2

EM Waves Carry EnergyAn em wave carries

energy in the electric and magnetic fields associated with the waves

Assume a wave interacts with a charged particle

The particle will experience an electric force

Section 23.3

EM Waves Carry Energy, cont.As the electric field oscillates, so will the forceThe electric force will do work on the chargeThe charge’s kinetic energy will increaseEnergy is transferred from the wave to the particleThe wave carries energyThe total energy per unit volume is the sum of its

electric and magnetic energiesutotal = umag + uelec

Section 23.3

EM Waves Carry Energy, finalAs the wave propagates, the energies per unit

volume oscillateThe electric and magnetic energies are equal and

this leads to the proportionality between the peak electric and magnetic fields

o o oo

o o

ε E Bμ

E c B

2 21 1

2 2

Section 23.3

Intensity of an EM WaveThe strength of an em wave is usually measured in

terms of its intensityUnits W/m2

Intensity is the amount of energy transported per unit time across a surface of unit area

Intensity also equals the energy density multiplied by the speed of the wave

I = utotal x c = ½ εo c Eo2

Since E = c B, the intensity is also proportional to the square of the magnitude field amplitude

Section 23.3

Quiz time!The miners recently rescued in

Chile wore sunglasses at night when they came out of the mine.

If their eyes could only handle 10W/m^2 what was the amplitude of the E field [V/m]?

A) 53B) 87C) 115D) 135E) 3.14

EM Waves Carry MomentumAn electromagnetic

wave has no mass, but it does carry momentum

Consider the collision shown

The momentum is carried by the wave before the collision and by the particle after the collision

Section 23.3

EM Waves Carry Momentum, cont.The absorption of the wave occurs through the

electric and magnetic forces on charges in the objectWhen the charge absorbs an electromagnetic wave,

there is a force on the charge in the direction of propagation of the original wave

The force on the charge is related to the charge’s change in momentum: FB = Δp / Δt

According to conservation of momentum, the final momentum on the charge must equal the initial momentum of the electromagnetic wave

The momentum of the wave is p = Etotal / cSection 23.3

Radiation PressureWhen an electromagnetic wave is absorbed by an

object, it exerts a force on the objectThe total force on the object is proportional to its

exposed areaRadiation pressure is the force of the

electromagnetic force divided by the areaThis can also be expressed in terms of the intensity

radiation

F IP

A c

Section 23.3

Electromagnetic SpectrumAll em waves travel through a vacuum at the speed

cc = 2.99792458 x 108 m/s ~ 3.00 x 108 m/sc is defined to have this value and the value of a meter

is derived from this speedElectromagnetic waves are classified according to

their frequency and wavelengthThe wave equation is true for em waves: c = ƒ λThe range of all possible electromagnetic waves is

called the electromagnetic spectrumSection 23.4

Quiz time!If the Death Star’s green

laser has a wavelength of 530nm

What is the frequency in Hz?

A) 2*10^16B) 1*10^15C) 7*10^13D) 5*10^14E) 3*10^8

Section 23.4

EM Spectrum, Diagram

EM Spectrum, NotesThere is no strict lower or upper limit for

electromagnetic wave frequenciesThe range of frequencies assigned to the different

types of waves is somewhat arbitraryRegions may overlapThe names of the different regions were chosen

based on how the radiation in each frequency interacts with matter and on how it is generated

Section 23.4

Radio WavesFrequencies from a few hertz up to about 109 hertzCorresponding wavelengths are from about 108

meters to a few centimetersUsually produced by an AC circuit attached to an

antennaA simple wire can function as an antenna

Antennas containing multiple conducting elements are usually more efficient and more common

Radio waves can be detected by an antenna similar to the one used for generation

Radio Waves, cont.Parallel wires can act as an

antennaThe AC current in the antenna is

produced by time-varying electric fields in the antenna

This then produces a time-varying magnetic field and the em wave

As the current oscillated with time, the charge is accelerated

In general, when an electric charge is accelerated, it produces electromagnetic radiation

Section 23.4

MicrowavesMicrowaves have

frequencies between about 109 Hz and 1012 Hz

Corresponding wavelengths are from a few cm to a few tenths of a mm

Microwave ovens generate radiation with a frequency near 2.5x109 Hz

The microwave energy is transferred to water molecules in the food, heating the food

Section 23.4

InfraredInfrared radiation has

frequencies from about 1012 Hz to 4 x 1014 Hz

Wavelengths from a few tenths of a mm to a few microns

We sense this radiation as heat

Blackbody radiation from objects near room temperature fall into this range

Also useful for monitoring the Earth’s atmosphere

Section 23.4

Visible LightFrequencies from about 4 x1014 Hz to 8 x1014 HzWavelengths from about 750 nm to 400 nmThe color of the light varies with the frequency

Low frequency; high wavelength – red High frequency; low wavelength – blue

The speed of light inside a medium depends on the frequency of the radiationThe effect is called dispersion

White light is separated into different colors

Section 23.4

Section 23.4

Dispersion Example

UltravioletUltraviolet (UV) light has frequencies from about 8 x

1014 Hz to 1017 HzCorresponding wavelengths are about 3 nm to 400

nmThe UV portion of the spectrum is commonly

subdivided into several regionsUV-A: 315 nm to 400 nmUV-B: 280 nm to 315 nmUV-C: 200 nm to 280 nm

Greatest potential for damaging tissue

Section 23.4

X-RaysFrequencies from about 1017 Hz to about 1020 HzDiscovered by Wilhelm Röntgen in 1895X-rays are weakly absorbed by skin and other soft

tissue and strongly absorbed by dense material such as bone, teeth, and metal

In the 1970’s CAT scans were developedAllows X-rays to be taken from many different angles

and combined through computer analysis

Section 23.4

Section 23.4

X-Ray Example

Gamma RaysGamma rays are the highest frequency

electromagnetic waves, with frequencies above 1020 Hz

Wavelengths are less than 10-12 mGamma rays are produced by processes inside

atomic nucleiThey are produced in nuclear power plants and in

the SunGamma rays reach us from outside the solar system

Section 23.4

Astronomy and EM Radiation

Different applications generally use different wavelengths of em radiation

Astronomy uses virtually all types of em radiationThe pictures show the Crab Nebula at various

wavelengthsColors indicate intensity at that wavelength

Section 23.4

Generation of EM WavesA radio wave can be

generated by using an AC voltage source connected to two wires

The two wires act as an antenna

As the voltage of the AC source oscillates, the electric potential of the two wires also oscillate

Electric charges are also flowing onto and off the wires as the voltage alternates

Section 23.5

Generation of EM Waves, cont.The electric field

continues to oscillate in size and direction

The wave propagates away from the antenna

The charges are accelerated

The charges undergo simple harmonic motion with a given frequency which is also the frequency of the AC voltage source and the frequency of the wave

Section 23.5

AntennasThe simple antenna

with two wires is called a dipole antenna

At any particular moment, the two wires are oppositely charged

The waves propagate perpendicular to the antenna’s axis

Section 23.5

Antennas, cont.Electromagnetic waves also propagate inside the

antenna wiresFor a very long antenna, these tend to cancelTherefore, most dipole antennas have a total length of λ/4

More complicated antennas also have the same cancellation effect, so the length of the antenna is usually comparable to the wavelength of the radiation

Antenna to Detect RadiationThe same antenna that

generates an em wave can also be used to detect the wave

The electric field associated with the wave exerts a force on the electrons in the antenna

This produces a current and an induced voltage across the antenna wires

This is the voltage source of the circuit in the receiver

Section 23.5

IntensityThere are cases where the charges are not confined to

one directionIn these cases, the radiation can propagate outward in all

directionsThe idea case of a very small source producing spherical

wave fronts is called a point source The intensity of a spherical wave decreases with

distance: I 1/r2 The intensity decreases as the constant amount of

energy spreads out over greater areasThis intensity relationship applies to many other

situations, including the strength of a radio signal from a distant station

Section 23.5

PolarizationThere are many directions of the electric field of an

em wave that are perpendicular to the direction of propagation

Knowing the actual direction of the electric field is important to determining how the wave interacts with matter

The previous wave (fig. 23.19) was linearly polarizedThe electric field was directed parallel to the z-axis

Most light is unpolarizedSection 23.6

PolarizersPolarized light can be

created using a polarizer The type of polarizer

shown consists of a thin, plastic film that allows an em wave to pass through it only if the electric field of the wave is parallel to a particular direction called the axis of the polarizer

Section 23.6

Polarizers, cont.The polarizer absorbs radiation with electric fields

that are not along the axisWhen the unpolarized light strikes a polarizer, the

light that come out is linearly polarizedAssume linearly polarized light strikes a polarizer

If the incident light is polarized parallel to the axis of the polarizer and the outgoing electric field is equal in amplitude to the incoming field

All the incident energy is transmitted through the polarizer

Section 23.6

Polarizers, finalIf the incident light is

polarized perpendicular to the axis of the polarizer, no light is transmitted

If the incident light is polarized at an angle θ relative to the axis of the polarizer, only a component of electric field is transmitted

Polarizers and Malus’ LawIf the electric field is parallel to the polarizer’s axis:

Eout = Ein

If the electric field is perpendicular to the polarizer’s axis, Eout = 0

If the electric field makes some angle θ relative to the polarizer’s axis, Eout = Ein cos θ

This relationship can be expressed in terms of intensity and is then called Malus’ Law:

Iout = Iin cos2 θ

Section 23.6

Malus’ Law and Unpolarized LightUnpolarized light can be thought of as a collection of

many separate light waves, each linearly polarized in different and random directions

Each separate wave is transmitted through the polarizer according to Malus’ Law

The average outgoing intensity is the average of all the incident waves:

Iout = (Iin cos2 θ)ave = ½ Iin Since the average value of the cos2 θ is ½

Section 23.6

Polarization Examples

In figure A, the unpolarized light passes through polarized oriented at 90°The intensity is reduced to ½ by the first polarizer and to 0

by the secondIn figure B, three polarizers are used and a non-zero

intensity results

Section 23.6

Polarizers, SummaryWhen analyzing light as it passes through several

polarizers in succession, always analyze the effect of one polarizer at a time

The light transmitted by a polarizer is always linearly polarizedThe polarization direction is determined solely by the

polarizer axisThe transmitted wave has no “memory” of its original

polarization

Section 23.6

Operation of a PolarizerMost applications use a

sandwich structure with certain types of long molecules placed between thin sheets of plastic

When the molecules are aligned parallel to each other, the sheets act as a polarizer with the axis perpendicular to the direction of the molecules

Section 23.6

Operation, cont.Electrons in the polarizer molecules respond to

electric fieldsWhen the electric field is parallel to the molecules

light is absorbedWhen the electric field is perpendicular to the

molecular direction the light is transmittedThe polarization axis is always perpendicular to the

molecular direction

Section 23.6

Polarization by Reflection

Light can be polarized by scatteringAir molecules act as antennasCharged particles respond to sunlight by oscillating in the direction of

the electric fieldThese particles produce new outgoing waves that are polarizedThe outgoing waves are called scattered wavesThe light is said to be polarized by reflection

Section 23.6

Optical ActivityWhen linearly polarized

light passes through certain materials, the polarization direction is rotated

This effect is called optical activity

These materials generally contain molecules with a screw-like or helical structure

Section 23.6

Applications of Polarized Light Many objects use LCD’s

Liquid Crystal Displays

Incident light is linearly polarized by a polarizing sheet

The light encounters an optically active material called a liquid crystal

The molecules in the liquid crystal rotate the light by 90° so that it can pass through an “output” polarizer

Voltages can be applied to rotate the light with respect to the output polarizer and the make the display appear dark Section 23.6

Spectral Lines

Astronomers use spectral lines to determine properties of starsEach dark line in the spectrum corresponds to a color

absorbed by the atoms in the objectThe location of each line corresponds to a particular

wavelength of lightSome spectra are observed to be shifted

Section 23.7

Red ShiftsObservations by Edwin Hubble showed that distant

galaxies were shifted to longer wavelengths relative to the wavelength of the same spectral line on EarthThis is called a red shift

Hubble proposed that those galaxies must be moving away from us

This would cause the frequency to appear lowerThis is similar to the Doppler Effect seen for sound

The size of the frequency shift can be used to determine the velocity of the galaxy emitting the light

Section 23.7

Expanding UniverseMost galaxies in the

observable universe were found to be moving away from us

The farther the galaxy is from the Earth, the faster it is receding

From any viewpoint, the galaxies would appear to be moving away from you

Section 23.7

Doppler Shift for LightThe Doppler Shift relationships for light are different

than for soundFor light:

vrel is the velocity of the source relative to the observer

A positive value of vrel corresponds to a source moving away from the observer

1ƒ ƒ

1

rel

obs source

rel

vc

vc

Section 23.7

FieldsThe existence of electromagnetic waves means that

electric and magnetic fields are realThere is no other way to explain how an em wave can

propagate through a vacuum, carrying energy and momentum

The analogy with gravitational fields suggests the existence of gravitational wavesWork is now being done to detect these waves

Section 23.8

Traveling Through a VacuumSince all mechanical waves travel through some material,

physicists of Maxwell’s time thought there was a material called the ether that supported em waves

The ether permeated all space, including vacuumsThe ether would allow objects to travel through it without

experiencing any frictional force due to the etherMany experiments were designed to study the ether and

its propertiesIn 1900, the existence of the ether was disprovedTherefore, em waves can carry energy even through a

vacuum

Section 23.8

EM Waves and Quantum TheoryNewton proposed that light was made up of particlesOther physicists thought light was a wave

Maxwell’s work seemed to show conclusively that light is a wave

It is now known that light has both wavelike and particle-like properties

The “particles” of light are called photonsSubsequent chapters will discuss experiment

evidence of both natures

Section 23.8