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Lecture 2 Electromagnetic Waves in Homogenous MediaPowerPoint Presentation

Lecture 2 Electromagnetic Waves in Homogenous Media

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Lecture 2 Electromagnetic Waves in Homogenous Media

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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
- Solution of the EM Wave equation
- Uniform Plane Waves (UPW)
- Complex Notation (phasors)
- Wave polarizations

- EM Waves in homogeneous lossy media

Today

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

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

MediumA BA energyB energy

Stringstretchvelocitypotentialkinetic

Acousticpressurevelocitypotentialkinetic

Oceanheightvelocitypotentialkinetic

ElectromagneticEHelectricmagnetic

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=vt

0

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:

EM Wave in z direction:

Wavelength

x

z

y

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

x

direction of propagation

z

y

wavelength

Linear Polarization

Circular Polarization

Image source: http://en.wikipedia.org

x

Linear Polarization

z

y