Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 1 Chapter 22: Electromagnetic Waves Production of EM waves Maxwell’s Equations Antennae The EM Spectrum Speed of EM Waves Energy Transport Polarization Doppler Effect

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 2 §22.1 Production of EM Waves A stationary charge produces an electric field. A charge moving at constant speed produces electric and magnetic fields.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 3 A charge that is accelerated will produce variable electric and magnetic fields. These are electromagnetic waves. If the charge oscillates with a frequency f, then the resulting EM wave will have a frequency f. If the charge ceases to oscillate, then the EM wave is a pulse (a finite- sized wave).

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 4 §22.2 Maxwell’s Equations Gauss’s Law Gauss’s Law for magnetism Faraday’s Law Ampère-Maxwell Law

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 5 Gauss’s Law: Electric fields (not induced) must begin on + charges and end on – charges. Gauss’s Law for magnetism: There are no magnetic monopoles (a magnet must have at least one north and one south pole).

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 6 Faraday’s Law: A changing magnetic field creates an electric field. Ampère-Maxwell Law A current or a changing electric field creates a magnetic field.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 7 When Maxwell’s equations are combined, the solutions are electric and magnetic fields that vary with position and time. These are EM waves. An electric field only wave cannot exist, nor can a magnetic field only wave.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 8 §22.3 Antennae An electric field parallel to an antenna (electric dipole) will “shake” electrons and produce an AC current.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 9 An EM wave also has a magnetic component. A magnetic dipole antenna can be oriented so that the B-field passes into and out of the plane of a loop, inducing a current in the loop. The B-field of an EM wave is perpendicular to its E-field and also the direction of travel.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 10 Example (text problem 22.5): A dipole radio antenna has its rod-shaped antenna oriented vertically. At a point due south of the transmitter, what is the orientation of the emitted wave’s B-field? Looking down from above the Electric Dipole antenna N W S E South of the transmitter, the E-field is directed into/out of the page. The B-field is perpendicular to this direction and also to the direction of travel (South). The B-field must be east-west.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 11 §22.4 The EM Spectrum EM waves of any frequency can exist.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 12 The EM Spectrum: Energy increases with increasing frequency.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 13 §22.5 Speed of Light Maxwell was able to derive the speed of EM waves in vacuum. EM waves do not need a medium to travel through.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 14 In 1675 Ole Römer presented a calculation of the speed of light. He used the time between eclipses of Jupiter’s Gallilean Satellites to show that the speed of light was finite and that its value was 2.25  10 8 m/s. Fizeau’s experiment of 1849 measured the value to be about 3  10 8 m/s. (done before Maxwell’s work)

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 15 When light travels though a material medium, its speed is reduced. where v is the speed of light in the medium and n is the refractive index of the medium. When a wave passes from one medium to another the frequency stays the same, but the wavelength is changed.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 16 A dispersive medium is one in which the index of refraction depends on the wavelength of light.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 17 §22.6 Properties of EM Waves All EM waves in vacuum travel at the “speed of light” c. Both the electric and magnetic fields have the same oscillation frequency f. The electric and magnetic fields oscillate in phase.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 18 The fields are related by the relationship EM waves are transverse. The fields oscillate in a direction that is perpendicular to the wave’s direction of travel. The fields are also perpendicular to each other.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 19 The direction of propagation is given by The wave carries one-half of its energy in its electric field and one-half in its magnetic field.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 20 The amplitude wave number angular frequency The wave speed is phase constant

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 21 Example (text problem 22.27): The electric field of an EM wave is given by: (a) In what direction is this wave traveling? The wave does not depend on the coordinates x or z; it must travel parallel to the y-axis. The wave travels in the +y direction.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 22 (b) Write expressions for the magnetic field of this wave. must be in the +y-direction (E is in the z-direction). Therefore, B must be along the x-axis. Example continued:

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 23 § 22.7 Energy Transport by EM Waves The intensity of a wave is This is a measure of how much energy strikes a surface of area A every second for normal incidence. Surface The rays make a 90  angle with the surface.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 24 where u av is the average energy density (energy per unit volume) contained in the wave. Also, For EM waves:

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 25 Example (text problem 22.35): The intensity of the sunlight that reaches Earth’s upper atmosphere is 1400 W/m 2. (a) What is the total average power output of the Sun, assuming it to be an isotropic source?

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 26 (b) What is the intensity of sunlight incident on Mercury, which is 5.8  m from the Sun? Example continued:

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 27 What if the EM waves strike at non-normal incidence?  Replace A with Acos .

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 28 § 22.8 Polarization A wave on a string is linearly polarized. The vibrations occur in the same plane. The orientation of this plane determines the polarization state of a wave. For an EM wave, the direction of polarization is given by the direction of the E-field.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 29 The EM waves emitted by an antenna are polarized; the E- field is always in the same direction. A source of EM waves is unpolarized if the E-fields are in random directions.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 30 A polarizer will transmit linear polarized waves in the same direction independent of the incoming wave. It is only the component of the wave’s amplitude parallel to the transmission axis that is transmitted.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 31 If unpolarized light is incident on 1 polarizer, the intensity of the light passing through is I= ½ I 0. If the incident wave is already polarized, then the transmitted intensity is I=I 0 cos 2  where  is the angle between the incident wave’s direction of polarization and the transmission axis of the polarizer. (Law of Malus)

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 32 Example (text problem 22.40): Unpolarized light passes through two polarizers in turn with axes at 45  to each other. What is the fraction of the incident light intensity that is transmitted? After passing through the first polarizer, the intensity is ½ of its initial value. The wave is now linearly polarized. 45  Transmission axis of 2 nd polarizer. Direction of linear polarization

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 33 § 22.9 The Doppler Effect For EM waves, the Doppler shift formula is where f s is the frequency emitted by the source, f o is the frequency received by the observer, v is the relative velocity of the source and the observer, and c is the speed of light.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 34 When v/c<<1, the previous expression can be approximated as: If the source and observer are approaching each other, then v is positive, and v is negative if they are receding.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 35 Example (text problem 22.48): Light of wavelength nm is emitted by a star. The wavelength of this light as measured on Earth is nm. How fast is the star moving with respect to the Earth? Is it moving toward Earth or away from it? The wavelength shift is small (  << ) so v<<c. Star is receding.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 36 Summary Maxwell’s Equations EM Spectrum Properties of EM Waves Energy Transport by EM Waves Polarization Doppler Effect