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Lecture 2 Electromagnetic Waves in Homogenous Media

Lecture 2 Electromagnetic Waves in Homogenous Media. 6.013. ELECTROMAGNETICS AND APPLICATIONS. Luca Daniel. Today’s Outline. Course Overview and Motivations Maxwell Equations (review from 8.02) in integral form in differential form EM waves in homogenous lossless media EM Wave Equation

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Lecture 2 Electromagnetic Waves in Homogenous Media

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  1. Lecture 2Electromagnetic Wavesin Homogenous Media 6.013 ELECTROMAGNETICS AND APPLICATIONS Luca Daniel

  2. Today’s Outline • Course Overview and Motivations • Maxwell Equations (review from 8.02) • in integral form • in differential form • EM waves in homogenous lossless media • EM Wave Equation • Solution of the EM Wave equation • Uniform Plane Waves (UPW) • Complex Notation (phasors) • Wave polarizations • EM Waves in homogeneous lossy media Today

  3. Maxwell’s Equations in linear isotropic homogeneous lossless media Constitutive Relations Gauss‘s Law Faraday’s Law: 0 Ampere’s Law: 0 Second derivative in space  second derivative in time, therefore solution is any function with identical dependencies on space and time (up to a constant) or

  4. What are Electromagnetic Waves A “wave” is a fixed disturbance propagating through a medium A,B B wave motion 0 z A A,B energy density null 0 z Medium A B A energy B energy String stretch velocity potential kinetic Acoustic pressure velocity potential kinetic Ocean height velocity potential kinetic Electromagnetic E H electric magnetic

  5. Solutions of the Wave Equation Possible solutions are many Try Uniform Plane Wave (UPW), e.g. assume: 1) 0 0 2) 3) E+(t – z/ν) propagation In air/vacuum waves moves at velocity t = t t = 0 z z=vt 0

  6. 0 0 0 0 Sinusoidal Uniform Plane Wave (UPW) in +z direction General solution: Ey(z,t) = E+(t - z/v) [V/m] One special solution: where To find the magnetic field: Faraday’s Law: In air/vacuum Note:

  7. Uniform Plane Wave: EM fields EM Wave in z direction: Wavelength x z y

  8. Complex Notation (Phasors) Complex notation for a single frequency (f = /2) “Phasor”: contains all amplitude, vector, spatial and phase information UPW case Time domain E Example: Phasor E

  9. Uniform Plane Wave (UPW) in Complex Notation x direction of propagation z y wavelength

  10. Uniform Plane Wave (UPW) Linear vs. Circular vs. Elliptical Polarization Linear Polarization Circular Polarization Image source: http://en.wikipedia.org x Linear Polarization z y

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