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Laws of Electromagnetism

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Beginning of Electromagnetics Henry Cavendish Coulomb’s Law Ohm’s Law Relation to Maxwell

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Beginning of Electromagnetics The Cavendish Apparatus

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Beginning of Electromagnetics Cavendish in his Laboratory

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Pioneers of the Field Benjamin Franklin Concept of electricity Lightning is electrical Use of electrical ground

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Andre Marie Ampere Ampere’s Law Pioneers of the Field

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Johann Carl Friedrich Gauss Gauss’s Law

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Pioneers of the Field Michael Faraday Faraday’s Law

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Pioneers of the Field George Gabriel Stokes Stokes’s Theorem

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Pioneers of the Field James Clerk Maxwell Maxwell’s Equations

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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

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Pioneers of the Field Sir J C Bose’s Apparatus

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Pioneers of the Field Sir J C Bose Bose’s spiral-spring receiver used for 5-mm radiation One of Bose's transmitter antennas

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Pioneers of the Field J.C. Bose at the Royal Institution, London, 1897

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Pioneers of the Field Sir J C Bose A close up of the spark gaps normally mounted inside the transmitting antenna

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Sir J C Bose A complete set up showing the transmitting antenna at the left, with the receiving antenna at right Pioneers of the Field

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Applications in Wireless Communication Guglielmo Marconi Invention of Radio Concept of Ionosphere Wireless Telegraph

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Applications in Wireless Communication Marconi’s 2 meter antennae

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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

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Hertz’s Experiment Copy Right: Pozar D.M., “ Microwave Engineering”, John Wiley & Sons. Applications in Wireless Communication

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Hertz Resonator Applications in Wireless Communication

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Hertz’s First Spark Gap Oscillators Applications in Wireless Communication

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Relationship between current density and radiation

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Maxwell’s Equations Frequency Domain

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Laws in Media With Dielectric Constant as Tensor Maxwell’s Two Curl Equations get modified as Appleton-Hartee Equation Where

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Fractional Domain Electrodynamics Fractional Dimension Sierpinski triangle

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Koch curve Fractional Domain Electrodynamics Construction Dimension

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Fractional Domain Electrodynamics Fractional Calculus Hausdorff-Besicovitch Dimension Fractional derivative & example

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Fractional Domain Electrodynamics Measurement of Hausdroff-Besicovitch Dimension 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 Theoretically Experimentally By surrounding the Koch coastline with boxes

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Fractional Domain Electrodynamics Measurement of Hausdroff-Besicovitch Dimension Surrounding the Koch Coastline with Boxes & graph

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Fractional Domain Electrodynamics Measurement of Hausdroff-Besicovitch Dimension Experimental data Dimension(experimental) =1.18 Dimension(Theoretical) =1.26 Deviation=6%

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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

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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

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Thank You

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