Nicholas J. Giordano

Marilyn Akins, PhD • Broome Community College

www.cengage.com/physics/giordano

Chapter 23

Electromagnetic Waves

Electromagnetic Theory

• Theoretical understanding of electricity and magnetism • Seemed complete by around 1850 • Coulomb’s Law and Gauss’ Law explained electric

fields and forces • Ampère’s Law and Faraday’s Law explained

magnetic fields and forces • The laws were verified in many experiments

Introduction

Unanswered Questions

• What 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’s • His work led to the discovery of electromagnetic

waves

Introduction

Discovery of EM Waves

• A time-varying magnetic field gives rise to an electric field • A magnetic field can produce an electric field

• Maxwell proposed a modification to Ampère’s Law • A time-varying electric field produces a magnetic field • This gives a new way to create a magnetic field • Also gives equations of electromagnetism a symmetry

Section 23.1

Symmetry of E and B

• The 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, there 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 field • Since 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 Waves

• Self-sustaining oscillations involving E and B are possible

• The 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 Fields

• According to Faraday’s Law, a changing magnetic flux through a given area produces an electric field

• The 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 Waves

• An electromagnetic wave involves both an electric field and a magnetic field

• These fields are perpendicular to each other • The 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 wave • The electric field is along the x-axis • The wave travels in the z-direction

• Determined by the right-hand rule #2

• The magnetic field is along the y-direction • Because both fields are perpendicular to the direction of

propagation, the wave is a transverse wave Section 23.2

Light is an EM Wave

• Maxwell found the speed of an em wave can be expressed in terms of two universal constants • Permittivity 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/s • The 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 wave

• He also showed that the equations of electricity and magnetism provide the theory of light

Section 23.2

EM Waves in a Vacuum

• Remember that mechanical waves need a medium to travel through

• Many physicists searched for a medium for em waves to travel through

• EM waves can travel through many materials, but they can also travel through a vacuum

• All em waves travel with speed c through a vacuum • The frequency and wavelength are determined by

the way the wave is produced

Section 23.2

EM Waves in Material Substances

• When 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 c • The speed of the wave depends on the wave’s

frequency

Section 23.2

EM Waves Carry Energy

• An em wave carries energy in the electric and magnetic fields associated with the wave

• 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 force • The electric force will do work on the charge • The charge’s kinetic energy will increase • Energy is transferred from the wave to the particle • The wave carries energy • The total energy per unit volume is the sum of its

electric and magnetic energies • utotal = uelec + umag

Section 23.3

elec o mago

u E and u Bεµ

= =2 21 12 2

EM Waves Carry Energy, final

• As the wave propagates, the energies per unit volume oscillate

• The electric and magnetic energies are equal and this leads to the proportionality between the peak electric and magnetic fields

o o oo

o o

E B

E c B

εµ

=

=

2 21 12 2

Section 23.3

Intensity of an EM Wave

• The strength of an em wave is usually measured in terms of its intensity • SI unit is 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 × c = ½ εo c Eo2

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

Section 23.3

Solar Cells

• The intensity of sunlight on a typical sunny day is about 1000 W/m²

• A solar cell converts the energy from sunlight into electrical energy

• Current photovoltaic cells capture only about 15% of the energy that strikes them

• Also must account for nights and cloudy days • Making better and more practical solar cells is an

important engineering challenge

Section 23.3

EM Waves Carry Momentum

• An 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 object

• When 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 / c

Section 23.3

Radiation Pressure

• When an electromagnetic wave is absorbed by an object, it exerts a force on the object

• The total force on the object is proportional to its exposed area

• Radiation pressure is the force of the electromagnetic force divided by the area

• This can also be expressed in terms of the intensity

radiationF IPA c

= =

Section 23.3

Electromagnetic Spectrum

• All em waves travel through a vacuum at the speed c • c = 2.99792458 x 108 m/s ~ 3.00 x 108 m/s • c is defined to have this value and the value of a meter

is derived from this speed • Electromagnetic waves are classified according to

their frequency and wavelength • The wave equation is true for em waves: c = ƒ λ • The range of all possible electromagnetic waves is

called the electromagnetic spectrum

Section 23.4

Section 23.4

EM Spectrum, Diagram

EM Spectrum, Notes

• There is no strict lower or upper limit for electromagnetic wave frequencies

• The range of frequencies assigned to the different types of waves is somewhat arbitrary

• Regions may overlap • The 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 Waves

• Frequencies from a few hertz up to about 109 hertz • Corresponding wavelengths are from about 108

meters to a few centimeters • Usually produced by an AC circuit attached to an

antenna • A simple wire can function as an antenna

• Antennas containing multiple conducting elements or shaped as “dishes” 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 antenna

• The 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 oscillates with time, the charge is accelerated

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

Section 23.4

Microwaves

• Microwaves 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 2.5 x 109 Hz

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

Section 23.4

Infrared

• Infrared 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 falls into this range

• Also useful for monitoring the Earth’s atmosphere

Section 23.4

Visible Light

• Frequencies from about 4 x1014 Hz to 8 x1014 Hz • Wavelengths from about 750 nm to 400 nm • The 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 radiation • The effect is called dispersion

• White light is separated into different colors

Section 23.4

Section 23.4

Dispersion Example

Ultraviolet

• Ultraviolet (UV) light has frequencies from about 8 x 1014 Hz to 1017 Hz

• Corresponding wavelengths are about 3 nm to 400 nm

• UV radiation stimulates the production of vitamin D in the body

• Excessive exposures to UV light can cause sunburn, skin cancer and cataracts

Section 23.4

X-Rays

• Frequencies from about 1017 Hz to about 1020 Hz • Discovered by Wilhelm Röntgen in 1895 • X-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 CT (CAT) scans were developed

Section 23.4

Section 23.4

X-Ray Example

CT Scan

• With a single X-ray image, there will always be parts of the person’s body that are obscured

• Images can be taken from different angles

• A CT scan takes many X-ray images at many different angles

• Computer analysis is used to combine the images into a three-dimensional representation of the object

Section 23.4

Gamma Rays

• Gamma rays are the highest frequency electromagnetic waves, with frequencies above 1020 Hz

• Wavelengths are less than 10-12 m • Gamma rays are produced by processes inside

atomic nuclei • They are produced in nuclear power plants and in

the Sun • Gamma rays also 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 radiation • The pictures show the Crab Nebula at various

wavelengths • Colors indicate intensity at each wavelength

Section 23.4

Generation of EM Waves

• A 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

Antennas

• The 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 wires • For a very long antenna, these tend to cancel • Therefore, 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 Radiation

• The 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

Intensity

• There are cases where the charges are not confined to one direction

• In these cases, the radiation can propagate outward in all directions

• The ideal 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 areas

• This intensity relationship applies to many other situations, including the strength of a radio signal from a distant station Section 23.5

Polarization

• There 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 (from the dipole antenna) was linearly polarized • The electric field was directed parallel to the z-axis

• Most light is unpolarized

Section 23.6

Polarizers

• Polarized 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 axis

• When the unpolarized light strikes a polarizer, the light that come out is linearly polarized

• Assume 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, final

• If 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’ Law

• If 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 Light

• Unpolarized 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 polarizers oriented at 90°

• The intensity is reduced to ½ by the first polarizer and to 0 by the second

• In figure B, three polarizers are used and a non-zero intensity results

Section 23.6

Polarizers, Summary

• When 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 polarized • The polarization direction is determined solely by the

polarizer axis • The transmitted wave has no “memory” of its original

polarization

Section 23.6

Operation of a Polarizer

• Most 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 fields

• When the electric field is parallel to the molecules light is absorbed

• When the electric field is perpendicular to the molecular direction the light is transmitted

• The polarization axis is always perpendicular to the molecular direction

Section 23.6

Polarization by Reflection

• Light can be polarized by scattering • Air molecules act as antennas • Charged particles respond to sunlight by oscillating in the

direction of the electric field • These particles produce new outgoing waves that are polarized • The outgoing waves are called scattered waves • The light is said to be polarized by reflection Section 23.6

Optical Activity

• When 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

Section 23.6

LCDs, cont.

• 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 thus make the display appear dark

• By applying different voltages to different areas of the liquid crystal, a pattern of light and dark regions can be formed • Corresponding to letters and numbers you see in the

display

Section 23.6

Spectral Lines

• Astronomers use spectral lines to determine properties of stars

• Each dark line in the spectrum corresponds to a color absorbed by the atoms in the object

• The location of each line corresponds to a particular wavelength of light

• Some spectra are observed to be shifted Section 23.7

Red Shifts

• Observations by Edwin Hubble showed that distant galaxies were shifted to longer wavelengths relative to the wavelength of the same spectral line on Earth • This is called a red shift

• Hubble proposed that those galaxies must be moving away from us

• This would cause the frequency to appear lower • This 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 Universe

• Most 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 Light

• The Doppler Shift relationships for light are different than for sound

• For 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

Section 23.7

Fields

• The existence of electromagnetic waves means that electric and magnetic fields are real • There 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 waves • Work is now being done to detect these waves

Section 23.8

Traveling Through a Vacuum

• Since 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 vacuums • The ether would allow objects to travel through it

without experiencing any frictional force due to the ether

• Many experiments were designed to study the ether and its properties

• In 1900, the existence of the ether was disproved • Therefore, em waves can carry energy even through

a vacuum Section 23.8

EM Waves and Quantum Theory

• Newton proposed that light was made up of particles • Other 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 photons

Section 23.8