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Lecture3

# Lecture3 - Chapter 2 Electromagnetic Radiation E&M...

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1 1 Chapter 2: Electromagnetic Radiation E&M Principle (Maxwell’s Equations): A changing electric field induces a magnetic field, and a changing magnetic field induces an electric field. H X EM waves travel at a constant speed in a vacuum: c = 3.0 x 10 8 m/s EM Waves often described as “ rays that are perpendicular to “ wave fronts ”. What is Electromagnetic Radiation? Classically , radiation is considered to be a transverse traveling wave of oscillating electric and magnetic fields, perpendicular to each other and to the propagation direction. 2 Wavelength ( λ ) Amplitude Time Characteristics of an EM Wave Wavelength ( λ ) The distance from peak to peak in a wave Always given in units of distance One "unit" of electromagnetic energy is a photon . EM radiation can be thought of as a particle, but it possesses many properties that are more like those of a wave. This is the so-called "wave-particle duality" of light in quantum mechanics. Frequency ( ν ) The number of waves that pass a given point each second Typically given as s -1 or Hertz (Hz) One Wave

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2 3 The wavelength and frequency of light are related Long Wavelength Low Frequency Low Energy Short Wavelength High Frequency High Energy The energy of a photon is related to its wavelength: E = h ν = hc/ λ (h = 6.626 x 10 -34 J s) Light flux = power/area = W m -2 Power = Energy / time 1 W = 1 J s -1 Whether we treat EM radiation as a wave or particle depends on the observation. Scattering & reflection, which involve “interference”: waves Absorption & emission, which involve atomic or molecular transitions: quantized particles 4 H X Consider only the electric vector (implied H). Can be plotted in space or time: x t A(t) A(x) A is the amplitude of the electric vector. Amplitude and direction of electric vector (force per unit charge) represents the movement of a positive test charge placed in an oscillating charged field: + - + - + + + + - + + + - + - + - - - + - - - - + - - - - - - - + - - - + - + - + + + - + + + + - + + + - + - + t0 t1 t2 t3 t4 t5 t6 + + + + + + + Time EM “wave” traces out the electric vector amplitude
3 5 The same qualitative explanation holds for oscillations in position: + - + - + + + + - + + + - + - + - - - + - - - - + - - - - - - - + - - - + - + - + + + - + + + + - + + + - + - + x0 x1 x2 x3 x4 x5 x6 + + + + + + + Position Combine the oscillations in space and time to visualize an EM wave. Characteristics of an EM wave: A λ direction of propagation A = amplitude (A 2 = “Intensity”) A o = maximum amplitude λ = wavelength (m) = wavenumber (m -1 ) = 1/ λ ν = frequency (cycles s -1 , Hz) = # crests that pass a given point each second c = velocity (3.0 x 10 8 m s -1 ) = ν λ ω = circular frequency (radians s -1 ) = 2 π ν (there are 2 π radians per cycle) k = 2 π / λ (sometimes referred to as wavenumber, but confusing) τ = period (s) = 2 π / ω (# seconds per cycle; analogous to λ but for time plot) A (x,t) = A o cos (± k x – ω t) or A (x,t) = A o sin (± k x – ω t) ν ~ 6 EM Wave: A (x,t) = A o cos(±kx– ω t) or A(x,t) = A o sin(±kx– ω t) k=2 π / λ , ω = 2 π ν = 2 π / τ Does this make sense? Consider time t=0, so that A = A o sin(kx) and look at x axis. Should see: x 0 2 λ 4 λ 4 3 λ λ t = 0 x = 0 Often more convenient to write wave as an exponential function.

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