Electromagnetic Waves Chapter 23 Electromagnetic Waves

Electromagnetic Theory Theoretical understanding Well developed by middle 1800’s 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

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

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, 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, 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 each other, 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 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

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 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 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 = umag + uelec Section 23.3

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 Section 23.3

Intensity of an EM Wave The strength of an em wave is usually measured in terms of its intensity Units 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) 53 B) 87 C) 115 D) 135 E) 3.14

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 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

Quiz time! If the Death Star’s green laser has a wavelength of 530nm What is the frequency in Hz? A) 2*10^16 B) 1*10^15 C) 7*10^13 D) 5*10^14 E) 3*10^8

EM Spectrum, Diagram Section 23.4

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 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 oscillated 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 2.5x109 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 fall 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

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 The UV portion of the spectrum is commonly subdivided into several regions UV-A: 315 nm to 400 nm UV-B: 280 nm to 315 nm UV-C: 200 nm to 280 nm Greatest potential for damaging tissue 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 CAT scans were developed Allows X-rays to be taken from many different angles and combined through computer analysis Section 23.4

X-Ray Example 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 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 that 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 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 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 (fig. 23.19) 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 polarized 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 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 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 Subsequent chapters will discuss experiment evidence of both natures Section 23.8