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 cos2θ 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 cos2θ)ave = ½ Iin • Since the average value of the cos2θ 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

Electromagnetic Waves