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Chapter 23 Electromagnetic Waves – Lecture 14 23.1 The Discovery of Electromagnetic Waves 23.2 Properties of Electromagnetic Waves 23.3 Electromagnetic Waves Carry Energy and Momentum 23.4 Types of Electromagnetic Radiation: The Electromagnetic Spectrum 23.5 Generation and Propagation of Electromagnetic Wave 23.6 Polarization 23.7 Doppler Effect 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 B L o Ienclosed closed path 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 Symmetry of E and B, cont. Section 23.1 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 (Maxwell equations), 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 (em) 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 (from the Maxwell equations) • Permittivity of free space, εo • Magnetic permeability of free space, μo • The speed of an em wave is denoted by c c 1 o o (from the Maxwell equations) • Inserting the values of εo and μo, we obtain c = 3.00 x 108 m/s ! • The value of the speed of an electromagnetic wave is the same as the speed of light • 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 1 uelec umag 2 o E 2 , Eq. 18.48 and 1 2 B , Eq. 21.35 2 o Section 23.3 EM Waves Carry Energy, final • As the wave propagates, the energies per unit volume oscillate • It turns out that the electric and magnetic energies are equal, and this leads to the proportionality between the peak electric and magnetic fields uelect umag uelec umag 1 1 2 2 o Eo Bo 2 2 o Eo c Bo c 1 o E 2 , Eq. 18.48 and 2 1 2 B , Eq. 21.35 2 o 1 o o 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 1 1 1 1 2 2 2 2 Bo I utotal c o cEo cBo o Eo 1 2 2 o 2 2 o c Eo c Bo o o 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 electromagnetic force divided by the area F Pradiation A • This can also be expressed in terms of the intensity Pradiation Pradiation F I A c F F L Work I utotal A A L Volume c I utotal 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 Light is an Electromagnetic Wave f c Figure 23-8 p797 Radio Waves • Frequencies from a few hertz up to about 109 hertz • Corresponding wavelengths are from about 108 meters to a few centimeters • 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 • 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 Dispersion Example Section 23.4 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 X-Ray Example Section 23.4 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 Xray 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