Electromagnetic waves

1
Presentationby
Tonmoy Ibne Arif(35177946)
Master'sinElectricalCommunicationEngineering
Electromagnetic waves

2
1.Fundamentals
2.Wave number
3.Wavelength
4.Frequency
5.Properties of Electromagnetic waves
6.Plane waves
7.Helmholtz equation from Maxwell‘s Equation
8.Wave vector
9.The polarization of electromagnetic waves
10.Polychromatic wave
11. Dispersion
Outline

3
Fundamentals behind electromagnetics wave
i. Every moving electric charge in space and time is surrounded by an electric field
and magnetic field.
ii. Any change in this magnetic field creates a changing electric field.
ii. Change in the electric field creates a change in the magnetic field or vice versa.
iv. Changing magnetic creates changing electric field.
Real life example:
Figure 1:A simple transformer[1]
Internet:
1.http://www.hk-phy.org/energy/power/transmit_phy05_e.html(01.01.2019)

4
Fundamentals behind electromagnetics wave:
1.Electromagnetics waves do not need matter to transfer energy.
2.EM waves are made by vibrating electric charges and have the ability to travel
through space by transmitting energy between vibrating electric and magnetic fields.
Figure 2: Sinusoidal time varying electromagnetic field [2]
Internet:
2.From: https://byjus.com/physics/characteristics-of-em-waves/ (01.01.2019)

5
Wave number:
The number of complete wave cycles of electromagnetic wave exists in one meter of
linear space. So, in short, wavenumber is the number of electromagnetic waves per uni
distance. Unit of wave number is reciprocal meters(m-1).
Wavelength:
The horizontal distance between any two successive equivalent points on the
propagating wave is represented by wavelength(λ). Wavelength represents a repeating
pattern of traveling energy.
Frequency:
The number of complete cycles per second for an oscillating wave in a certain
propagation direction. The frequency measured in cycles per seconds or hertz(Hz).
f=1/T. Here, T is the period which represents the time required for the wave to travel a
distance of one wavelength. If we know the wavelength and frequency of a wave, we can
calculate speed of that wave, Speed of wave v=λ/T= λf.

6
Properties of electromagnetic waves:
1. All matters diffuse Electromagnetic waves as all objects contain charged
particles inside it. This charged particle move inside of that inside that substance.
2. As the temperature of a material increases, the wavelengths become shorter.
3. As the wavelength decreases, frequency increases.
4. All electromagnetic waves carry radiant energy.
Electromagnetic spectrum depicts the frequencies.
Figure 3:The electromagnetic spectrum [3]
Article:
3. Priv.-Doz. Dr.-Ing. habil. René Marklein et al “ Introduction to Waves”,p(4)

7
Properties of electromagnetic waves:
5. An electromagnetic field composes of mutually perpendicular and oscillating electric
and magnetic fields. These electric and magnetic fields vary sinusoidally with time
perpendicular to the propagation direction. In addition, the fields vary with the same
frequency and in phase with each other.
6. A transverse wave electric and magnetic fields are perpendicular to the direction
in which the wave travels. The cross product of the electric and magnetic field
always gives the wave propagation direction.
7. Electromagnetic waves can travel through a vacuum or any material object.
8. All electromagnetic waves travel through a vacuum at the same speed. This speed
represented by the speed of light in vacuum, c = 299792458 m/s.
9. The magnitude of the fields at every instant and at every point are related by,
E/B=c(amplitude ratio).
E B

8
Sinusoidal Uniform (homogenous)Plane waves:
A plane wave is the solution of homogenous Maxwell’s equations Plane
waves have infinite energy .
The homogenous wave equation of electro(E) and Magnetic field(H) of a
Plane wave in
Where c represents the phase velocity ,which can be written as follows,
…………………………….……….(i) [3]
……….(ii) [3]

9
Applying Fourier transform with regards to the time coordinate t on the equation
(ii),
……………………………………………..(iii) [3]
Wave number :
It is a unit of frequency in atomic, molecular and nuclear spectroscopy equal
to the true frequency divided by the speed of light and number of waves in a
unit distance.[3]
Now with the wavenumber ,
…………………..…….…………………………………(iv) [3]

10
After applying the seperation of variables yields the plane wave,
….……………………………………(v) [3]
….……………………………………(vi) [3]
Here,
According to the Cartessian coodinate system, can be wrriten as follows,
….……………………(vii) [3]

11
Wave number vector:
The wave vector of a plane wave is a vector which points the wave propagation
direction. Wave vector always perpendicular to the wavefronts. The wavenumber is
the magnitude of the wave vector. Here wave number represents the real part.
Now from the equation (viii) the wavenumber vector is defined as follows,
Figure 4:Definiation of polar angles [4]
Article:
4. Priv.-Doz. Dr.-Ing. habil. René Marklein et al “Electromagnetic Theory for Microwaves and Antennas”,

12
Helmholz equation:
The Plane Wave is a Solution of the Homogenous Helmholtz equation. So if the
wavenumber vector K satisfies the separation condition,
Where,
As
….……………………(viii)
….………………………(ix)
Equation (ix) is called the dispersion relation. From dispersion relation we can define
the frequency dependency of the wavenumber vector K as a function of

13
Maxwell‘s equations:
Now from the equation(ix) ,as a product of
….……………………(x)
So,Now from the plane wave equation (v),
….……………………(xi)
Where,
Is satified if and only if
Soucre free case,
If This means k and E must be perpendicular to each other.
From the above equation we can see the solution of Maxwell‘s equation

14
Maxwell’s Equations
This is first Maxwell equation also known as Gauss Law
………………………………………………………..(a) [4]
……………………………………………………………..(b) [4]
………………………………………………………………..…..(c) [4]
………………………………………………………….…..(d) [4]
This is Maxwell second equation
Maxwell‘s third equation which is also known as Faraday‘s law
Maxwell fourth equation or Ampere‘s law

Maxwell‘s equations:
Gauss‘ law:“ The total of the electric flux of a closed surface is equal to the charge
enclosed divided by the permittivity.“[5]
Equation (a)-> dictates that how electric field behaves around electric charges.
Where electric flux density D is equal to the volume electric charge density.
Equation (b)->which declares, magnetic charge does not exist.
Faraday‘s law(19ᵗʰ century)-depictes the symetrical condition of universe.If a
changing current gives rises to a magnetic field then also vice versa can
happen[6].Additionally the final equation of Maxwell tell us more about this
symmetry.
Ampere‘s law(1820)-> Maxwell describe Ampere‘s law usingequation(d) that a
flowing current (J) gives rise to amgnetic field that circles the current. [7]
Internet:
5. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html(15.01.2019)
6. https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-flux-faradays-law/a/what-is-faradays-law(15.01.2019)
7. https://em.geosci.xyz/content/maxwell1_fundamentals/formative_laws/ampere_maxwell.html(15.01.2019)

15
Helmholtz equation from Maxwell‘s Equation
Applying constitutive relations on the above equation
As we know from that Ampere‘s law relates the curl of the magnetic to the
electric field, From equation(b) or Faraday's law we can write as follows .We are
solving those two curl equations taking into account E,D,B,H and J are
interdependent. We are also assuming that we are in a uniform material where
permittivity epsilon ε0 and permeability mu are μ0 constant.
Now ,lets take of both sides of Faraday‘s law.
………………………………………….……..(e) [8]
………………………………………………………..(f) [8]
Now from the equation (c) & (d) ,we can swap into the modified Faraday‘s Law
………………………………………………….(g) [8]
From(g) we can see that two Maxwell‘s curl equation condensed into one
equation with nothing but E. This also one of the forms of the Helmholtz wave
equation.
Internet:
8.From :http://bklein.ece.gatech.edu/laser-photonics/maxwells-equations-and-the-helmholtz-wave-equation/ (15.01.2019)

16
Vector identity :
Where A is any vector field.
………………………………………………….(h)
Now the Gauss‘s Law becomes as follows
Where e doesn‘t depend on position. Now dividing both sides e finally give us.
………………………………………………….(i)
………………………………………………….(j) [8]
So, now from equation (h) we can replace generic field A with electric field E
………………………………………………….(k) [8]
) [8]
[8]
Internet:

17
is zero as long as we are in a region with no charge and
permittivity e is constant .
………………………………………………….(l) [8]
Rearanging the above equation we get,
This is the Helmholtz wave equation.
[8]
Internet:

18
The polarization of electromagnetic waves:
The electric component of an electromagnetic wave can oscillate in any direction of
the wave propagation.
A randomly or unpolarized electromagnetic wave polarization vary in time whereas a
linear polarized electromagnetic wave electric field oscillates in one direction.
Figure 5: Electromagnetic wave[2] Figure 6:Polarization [9]
Internet:
2.From: https://byjus.com/physics/characteristics-of-em-waves/ (01.01.2019)
9.From: http://www.writeopinions.com/polarization-waves (13.01.2019)

19
Polychromatic wave:
The term polychromatic means having several colors. It is used to describe
light that exhibits more than one color. Wave that contains radiation of more
than one wavelength is a polychromatic wave.
Dispersion:
The process of separating polychromatic light into its components
wavelengths. Dispersion is a special case where the light bends such that
polychromatic light(white light) separates into its component wavelengths.
The lower the wavelength which means higher frequency the more light
bends.
Real life scenarios:
i. Blue light has a short wavelength that‘s why appears on the bottom of the
rainbow.
ii. Red light has a long wavelength, bends least and appears at the top of the
rainbow.

20
Visible light spectrum represents about 2.5 percent of the entire
electromagnetic spectrum. The color is not a property of visible light. The
photon's energy lies between 1.6 to 3.2 electron-volts. The visible region of the
electromagnetic spectrum lies within a narrow frequency band from 386 to 769
terahertz.
Internet:
10. From :https://www.olympus-lifescience.com/en/microscope-resource/primer/lightandcolor/electromagintro/(15.01.2019)
Polychromatic wave:
Figure 7: Waveforms of Electromagnetic Radiation States[10] Figure 8: Ultraviolet-visible absorbtion spectrum[10]

21
Dispersion:
The separation of visible light into its component colors is called dispersion.
The angle of deviation varies with wavelength. Colors of the light spectrum
with shorter wavelengths deviate more from their original path than the
colors with longer wavelengths.
Outline
where,
n =refractive index
c=speed of light
ω=frequency
k=wavenumber
λ=wavelength
ν =temporal frequency
Figure 9:Disperssion of light using prism [11]
Internet:
11.From :https://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms(15.01.2019)

Electromagnetic waves

More Related Content

What's hot (20)

Similar to Electromagnetic waves (20)

Recently uploaded (20)

Electromagnetic waves