Laws of Electromagnetism
Beginning of Electromagnetics
Henry Cavendish
• Coulomb’s Law
• Ohm’s Law
• Relation to Maxwell
Beginning of Electromagnetics
The Cavendish Apparatus
Beginning of Electromagnetics
Cavendish in his Laboratory
Pioneers of the Field
Benjamin Franklin
•Concept of electricity
•Lightning is electrical
•Use of electrical ground
Pioneers of the Field
Andre Marie Ampere
• Ampere’s Law
Pioneers of the Field
Johann Carl Friedrich Gauss
• Gauss’s Law
Pioneers of the Field
Michael Faraday
• Faraday’s Law
Pioneers of the Field
George Gabriel Stokes
• Stokes’s Theorem
Pioneers of the Field
James Clerk Maxwell
• Maxwell’s Equations
Pioneers of the Field
Sir J C Bose
• Short wavelength radio waves
• Existence of EM radiation from sun
• Sir J. C. Bose invented the Mercury
Coherer (together with the telephone
receiver) used by Marconi to receive the
radio signal in his first transatlantic
radio communication over a distance of
2000 miles in December 1901.
• Marconi was celebrated worldwide for
this achievement, but the fact that the
receiver was invented by Bose was
totally concealed
Pioneers of the Field
Sir J C Bose’s Apparatus
Pioneers of the Field
Sir J C Bose
Bose’s spiral-spring receiver
used for 5-mm radiation
One of Bose's transmitter
antennas
Pioneers of the Field
J.C. Bose at the Royal Institution, London, 1897
Pioneers of the Field
Sir J C Bose
A close up of the spark gaps
normally mounted inside the
transmitting antenna
Pioneers of the Field
Sir J C Bose
A complete set up showing
the transmitting antenna at
the left, with the receiving
antenna at right
Applications in Wireless Communication
Guglielmo Marconi
• Invention of Radio
• Concept of Ionosphere
• Wireless Telegraph
Applications in Wireless Communication
Marconi’s 2 meter antennae
Applications in Wireless Communication
Heinrich Hertz
First Wireless link in 1901
• First to broadcast and receive
radio waves
• Produced EM waves and measured
their wavelength & velocity
Applications in Wireless Communication
Hertz’s Experiment
Copy Right: Pozar D.M., “ Microwave Engineering”, John Wiley & Sons.
Applications in Wireless Communication
Hertz Resonator
Applications in Wireless Communication
Hertz’s First
Spark Gap
Oscillators
Applications in Wireless Communication
Relationship between current density and radiation
Maxwell’s Equations Frequency Domain
Laws in Media With Dielectric Constant as Tensor
Maxwell’s Two Curl Equations get modified as
Appleton-Hartee Equation
Where
Fractional Domain Electrodynamics
Fractional Dimension
Sierpinski triangle
Fractional Domain Electrodynamics
Koch curve
Dimension
Construction
Fractional Domain Electrodynamics
Fractional Calculus
Fractional derivative & example
Hausdorff-Besicovitch Dimension
Fractional Domain Electrodynamics
Measurement of Hausdroff-Besicovitch Dimension
•Theoretically
where N(h) is the number of disks of size
h needed to cover the object
Thus Koch coastline has a Hausdorff-Besicovitch dimension is
•Experimentally
By surrounding the Koch coastline with boxes
Fractional Domain Electrodynamics
Measurement of Hausdroff-Besicovitch Dimension
Surrounding the Koch Coastline with Boxes & graph
Fractional Domain Electrodynamics
Measurement of Hausdroff-Besicovitch Dimension
Experimental data
Dimension(experimental)
=1.18
Dimension(Theoretical)
=1.26
Deviation=6%
CONCLUSION
• In this project we have tried to represent the
Maxwell’s equations of EM in fractional
dimension which is one of the emerging field in
electromagnetics
• And studied the effect of EM field in
ionospheric propagation
• Application of electromagnetics in wirelwss
communication
REFERENCES:
[1] Sadiku M. N.O.Elements of Electromagnetics,Oxford,2002
[2] Colin R.E. “Microwave Engineering”,Mc Graw Hill,2000
[3] H.O.Peitgen,H.Jurgens & D. Saupe,”Chaos and Fractals”:New
Frontiers of Science. New York, Springer Verlag, Inc., 1992
[4] B. B. Mandelbrot, “The Fractal Geometry of Nature, San
Fransisco, CA:Freeman,1983
[5] www.factus.com
[6] www.fractenna.com
[7] www.mathworld.com
Thank You