Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 35. Electromagnetic Fields and Waves To understand a laser beam, we need to know how electric and magnetic fields change with time. Examples of time-dependent electromagnetic phenomena include high-speed circuits, transmission lines, radar, and optical communications. Chapter Goal: To study the properties of electromagnetic fields and waves.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. E or B? It Depends on Your Perspective Whether a field is seen as “electric” or “magnetic” depends on the motion of the reference frame relative to the sources of the field.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Transformations The Galilean field transformation equations are where V is the velocity of frame S' relative to frame S and where the fields are measured at the same point in space by experimenters at rest in each reference frame. NOTE: These equations are only valid if V << c.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Example transformation Consider a charge at rest at the origin in S where B=0 and E is given by Coulomb’s Law. In S’, the charge is moving and there is both an electric field E’=E and a magnetic field B’. Biot Savart LawCopyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Maxwell’s Equations and Electromagnetic Waves Maxwell’s equations provide a unified description of the electromagnetic field and predict that • Electromagnetic waves can exist at any frequency, not just at the frequencies of visible light. This prediction was the harbinger of radio waves. • All electromagnetic waves travel in a vacuum with the same speed, a speed that we now call the speed of light.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Light speed Maxwell’s equations predict EM waves move at a unique (light) speed relative to ANY frame of reference. That is impossible if the Galilean velocity addition rule v’ = v+vrel holds. This paradox is resolved by Einstein’s Special Theory of Relativity.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Discovery of artificial EM waves by Hertz Magnified view of the spark gap and dipole transmitting ("feed") antenna at the focal point of the reflector. The high voltage spark jumped the gap between the spherical electrodes. The electrical impulse produced by the spark generated damped oscillations in the dipole antenna.!Magnified view of the spark gap and dipole receiving antenna at the focal point of a receiving reflector similar to the transmitting one. The width of the small spark gap on the right is controlled by the screw below it. The vertical dipole antenna at the left was about 40 centimeters long.!EM wave Transmitter spark gap Receiver spark gapCopyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Schematic of operation of antenna An oscillating electric dipole is surrounded by an oscillating electric (and magnetic) field. Field disturbances propagate away at light speed perpendicular to the dipole. Operating in reverse, an EM wave excites charges oscillation in a dipole.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Marconi’s transatlantic signal experiment Left to right: Kemp, Marconi, and Paget pose in front of a kite that was used to keep aloft the receiving aerial wire used in the transatlantic radio experiment.!Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Marconi’s transatlantic signal generator Capacitor banks Induction coils Spark gapCopyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Radio Like two identical tuning forks coupled resonantly through a sound wave, two tuned LC or other resonant circuits can be coupled through an EM wave. A high frequency EM can carry audio frequency analog information by warbling the frequency (FM) or amplitude (AM). An optimal antenna has a size of order a wavelength. More compact loop antennas work through induction.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Harmonic Waves A harmonic plane wave is generated by a single frequency source current distribution and is characterized by frequency f and wavelength c/f. E, B, v form a right handed coordinate system. A “linearly polarized” wave has the orientation of E fixed.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Generation of electromagnetic waves EM waves are emitted in general by accelerated charges which shed free force fields. Synchrotron light source Dipole antennaCopyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EM wave spectrum EM waves are observed over a wide range of frequencies. Megahertz natural and artificial sources produce radio waves. Ultra high frequency motions inside nuclei source gamma ray radiation.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Properties of Electromagnetic Waves 1. The fields E and B and are perpendicular to the direction of propagation vem.Thus an electromagnetic wave is a transverse wave. 2. E and B are perpendicular to each other in a manner such that E × B is in the direction of vem. 3. The wave travels in vacuum at speed vem = c 4. E = cB at any point on the wave. Any electromagnetic wave must satisfy four basic conditions:Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Energy of Electromagnetic Waves Energy density in E-field Energy density in B-field uE=εoE2r,t( )/2 uB= B2r,t( )/2µoTotal uTot=εoE2/2 + B2/2µo=εoE2/2 + E2/2c2µo=εoE2r,t( )= B2r,t( )/µo uTot=εoE2=εoEo2cos2kz −ωt( )moves w/ EM wave at speed c EM waves carry energy density u and momentum density u/c.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The energy flow of an electromagnetic wave is described by the Poynting vector defined as The magnitude of the Poynting vector is Poynting vector The intensity of an electromagnetic wave whose electric field amplitude is E0 isCopyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 35.4 The electric field of a laser beam Laser light is monochromatic and sourced by
View Full Document
Unlocking...