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The topics of electromagnetic waves, maxwell's equations, and related concepts such as gauss's law, faraday's law, and ampere maxwell law. The document also discusses the properties of electromagnetic waves, including their wave equations, polarizations, and the relationship between wavelength and frequency.
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Electromagnetic Waves (EM Waves) Review: Waves and Wave Equation Maxwell’s equation Propagation of E and B Energy Carried by EM Wave, Poynting Vector Momentum Carried by EM Wave Spectrum of EM wave.
ε 0
E • d = − d Φ B dt
0
0
0 d Φ E dt
Gauss’s Law/ Coulomb’s Law Faraday’s Law Gauss’s Law of Magnetism, no magnetic charge Ampere Maxwell Law Also, Lotentz force Law These are the foundations of the electromagnetism
x y z E B c Two polarizations possible
Because of the wave equation the wavelength of and frequency of a EM wave in vacuum are related by: Example: Determine the wavelength of an EM wave of frequency 50 MHz in free space € λ f = c = 3 ⋅ 10 8 m / s λ = c f = 3 ⋅ 10 8 m / s 50 MHz = 3 ⋅ 10 8 m / s 5 ⋅ 10 7 s − 1 = 6 m
Recall: energy densities u E = ½ ε 0
2 , u B
2 /μ 0 For a EM wave, at any time/location, u E = ½ ε 0
2 = ½ B 2 /μ 0 =u B (using E/B=c) In an electromagnetic wave, the energies carried by electric field and magnetic field are always the same. Total energy stored (per unit of volume): u=u E +u B = ε 0
2 = B 2 /μ 0 Power transmitted per unit of area is equal to uc in the direction of wave Averaging over time: u av = ½ ε 0
max 2 = ½ B max 2 /μ 0 , u av c = I (intensity) x y z E B
The rate of flow of energy in an em wave is described by a vector, S , called the Poynting vector The Poynting vector is defined as Its direction is the direction of propagation This is time dependent Its magnitude varies in time Its magnitude reaches a maximum at the same instant as E and B
0
Power per unit of area € I = S av
The average intensity of the EM radiation from the Sun on Earth is S ~ 10 3 W/m 2 What is the average radiation pressure for 100% absorption: What is the force exerted by EM radiation by the Sun on a surface of 1 m 2 € P = S c = 10 3 W m 2 3 ⋅ 10 8 m s = 3.3⋅ 10 − 6 N m 2 F = PA = 3.3⋅ 10 − 6 N m 2 ⋅ 1 m 2 = 3.3⋅ 10 − 6 N
Antennas are essentially arrangement of conductors for transmitting and receiving radio waves. Parameters: gain, impedance, frequency, orientation, polarization, etc. half-wave antenna loop λ/ λ/ maximum strength mocristrip
