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Chapter 34 Electromagnetic Waves Electromagnetic Waves •Mechanical waves require the presence of a medium. •Electromagnetic waves can propagate through empty space. •Maxwell’s equations form the theoretical basis of all electromagnetic waves that propagate through space at the speed of light. •Hertz confirmed Maxwell’s prediction when he generated and detected electromagnetic waves in 1887. •Electromagnetic waves are generated by oscillating electric charges. – The waves radiated from the oscillating charges can be detected at great distances. •Electromagnetic waves carry energy and momentum. •Electromagnetic waves cover many frequencies. James Clerk Maxwell •1831 – 1879 •Scottish theoretical physicist •Developed the electromagnetic theory of light •His successful interpretation of the electromagnetic field resulted in the field equations that bear his name. •Also developed and explained – Kinetic theory of gases – Nature of Saturn’s rings – Color vision Maxwell’s Equations Correcting Ampere’s Law Two surfaces S1 and S2 near the plate of a capacitor are bounded by the same path P. Ampere’s Law states that But it is zero on S2 since there is no conduction current through it. This is a contradiction. Maxwell fixed it by introducing the displacement current: Fig. 34-1, p. 984 Maxwell hypothesized that a changing electric field creates an induced magnetic field. Displacement Current d E d( EA) d(q / ε0 ) 1 dq dt dt dt ε0 dt dq dE ε0 dt dt The displacement current is equal to the conduction current!!! B ds μ o I μoεoId Maxwell’s Equations In his unified theory of electromagnetism, Maxwell showed that electromagnetic waves are a natural consequence of the fundamental laws expressed in these four equations: q E dA εo d B E ds dt B dA 0 d E B ds μo I μoεo dt Maxwell’s Equations in Vector Form Maxwell’s Equations in Free Space No charges or conduction currents: E dA 0 B dA 0 dB E ds dt dE B ds μoεo dt E 0 B E t Divergence: Curl: E B x t B 0 E B μ0ε0 t dB E ds dt dE B ds μoεo dt Fig. 34-6, p. 989 A sinusoidal electromagnetic wave moves in the positive x direction with a speed c. Fig. 34-8, p. 990 EM Wave Equations From Maxwell’s equations applied to empty space, the following partial derivatives can be found: 2 E 2E 2B 2B μoεo 2 and μoεo 2 2 2 x t x t These are wave equations with v c Substituting the values for μo and εo gives c = 2.99792 x 108 m/s 1 μoεo E & B Waves •The simplest solution to the partial differential equations is a sinusoidal wave: E = Emax cos (kx – ωt) B = Bmax cos (kx – ωt) •The angular wave number is k = 2π/λ – λ is the wavelength •The angular frequency is ω = 2πƒ – ƒ is the wave frequency ω 2π ƒ λƒ c k 2π λ E & B Waves E(x,t) = Emax cos (kx – ωt) B(x,t) = Bmax cos (kx – ωt) Emax ω c Bmax k Properties of Electromagnetic Waves The energy flow of an electromagnetic wave is described by the Poynting vector defined as The magnitude of the Poynting vector is The intensity of an electromagnetic wave whose electric field amplitude is E0 is Intensity I Savg 2 2 E max Bmax E max c Bmax 2 μo 2 μo c 2 μo •The wave intensity, I, is the time average of S (the Poynting vector) over one or more cycles. – This defines intensity in the same way as earlier. – The optics industry calls power per unit area the irradiance. • Radiant intensity is defined as the power in watts per solid angle. •When the average is taken, the time average of cos2(kx - ωt) = ½ is involved. Section 34.4 Energy Density •The energy density, u, is the energy per unit c 1 μoεo volume. •For the electric field, uE= ½ εoE2 •For the magnetic field, uB = ½ μoB2 •Since B = E/c and 1 B2 uB uE 2 εo E 2 2μo The instantaneous energy density associated with the magnetic field of an em wave equals the instantaneous energy density associated with the electric field. In a given volume, the energy is shared equally by the two fields. Energy Density •The total instantaneous energy density is the sum of the energy densities associated with each field. u =uE + uB = εoE2 = B2 / μo •When this is averaged over one or more cycles, the total average becomes – uavg = εo(E2)avg = ½ εoE2max = B2max / 2μo •In terms of I, I = Savg = cuavg – The intensity of an em wave equals the average energy density multiplied by the speed of light. Radiation Pressure It’s interesting to consider the force of an electromagnetic wave exerted on an object per unit area, which is called the radiation pressure prad. The radiation pressure on an object that absorbs all the light is I Savg where I is the intensity of the light wave. For a perfectly reflecting surface, p = 2I/c=2S/c Accelerating Charges All forms of the various types of radiation are produced by the same phenomenon – accelerating charges. The EM Spectrum •Note the overlap between types of waves •Visible light is a small portion of the spectrum. •Types are distinguished by frequency or wavelength Section 34.7 Oscillating Charges Radio & Microwave Frequency of EM wave is the same as the frequency of oscillation. Heinrich Rudolf Hertz •1857 – 1894 •German physicist •First to generate and detect electromagnetic waves in a laboratory setting •The most important discoveries were in 1887. •He also showed other wave aspects of light. Section 34.2 Hertz’s Experiment •From a circuit viewpoint, this is equivalent to an LC circuit. •Sparks were induced across the gap of the receiving electrodes when the frequency of the receiver was adjusted to match that of the transmitter. •In a series of other experiments, Hertz also showed that the radiation generated by this equipment exhibited wave properties. – Interference, diffraction, reflection, refraction and polarization •He also measured the speed of the radiation. – It was close to the known value of the speed of light. Production of EM Waves by an Antenna •This is a half-wave antenna. •Two conducting rods are connected to a source of alternating voltage. •The length of each rod is one-quarter of the wavelength of the radiation to be emitted. Far Fields: Radiation Fields Fields detach from the dipole and propagate freely. EM Spectrum cf Increasing Energy IR, Visible and UV Light is emitted when an electron in an atom jumps between energy levels either by excitation or collisions. Light Emission Atomic Emission of Light Each chemical element produces its own unique set of spectral lines when it burns Hydrogen Spectra Visible Light •Different wavelengths correspond to different colors. •The range is from red (λ ~ 7 x 10-7 m) to violet (λ ~4 x 10-7 m). Section 34.7 Thermal Excitation: Incandescence f ~T Color shifts to shorter wavelengths (higher frequency) as an object is heated. increasing temperature Limits of Thermal Excitation Material breaks down before Xrays are produced. increasing temperature X-Ray Production By High Voltage Discharge Accelerating Charges Synchrotron Radiation X-Ray and Radio How can we SEE Black Holes? We see the X Rays produced by matter falling into them. X Ray Imaging when X-ray light shines on us, it goes through our skin, but allows shadows of our bones to be projected onto and captured by film. When X-ray light shines on us, it goes through our skin, but allows shadows of our bones to be projected onto and captured by film. Gamma Ray Production by Nuclear Decay when X-ray light shines on us, it goes through our skin, but allows shadows of our bones to be projected onto and captured by film. 239 P U He 235 46 Gamma Ray Production Matter-antimatter annihilation Gamma Ray Burst Ionizing Radiation: UV, Xray & Gamma Energy to ionize atom or molecule: 10-1000eV Ionizing Radiation: UV, Xray & Gamma Light can Kill Biological Effects of Gamma Radiation Atomic Thermal Blast IR, VISIBLE, UV Cosmic EM Radiation The Atmosphere Visible Sun: The Photosphere Atomic Excitations: 400-700 nm at a few thousand Kelvin. Radio Image of the Sun Synchrotron Radiation: 10.7 cm – 2800MHz Infrared Sun More than half the Sun’s power is radiated in IR. UV Sun X-Ray Sun Bremsstrahlung Radiation (braking, in German) Gamma Ray Sun Bremsstrahlung Radiation (braking, in German)