Method of images in electromagnetic theory

THE METHOD OF IMAGES A useful technique for solving (i.e. finding) E(r) and / or V(r) for a certain class / special classes of electrostatic (and magnetostatic) problems that have some (or high) degree of mirror-reflection symmetry. ← Exploit awesome power of symmetry intrinsic to the problem, if present We try to use the method of images by placing a single image charge q' a distance b from the sphere center along the line joining the center to the point charge q. We need to find values of q' and b that satisfy the zero potential boundary condition at r = R. The potential at any point P outside the sphere i Electromagnetic Field Theory (EMT) Lecture # 22 1) Methods of Images 2) Magneto-statics 1) Biot-Savarat'sLaw 2) Ampere'sLaw. Method of Images The method of images, is commonly used to determine V, E, D,. Today in Physics 217: the method of images Solving the Laplace and Poisson equations by sleight of hand Introduction to the method of images Caveats Example: a point charge and a grounded conducting sphere Multiple images y x b b bb a a q q-q-q a a. 9 October 2002 Physics 217, Fall 2002

2.25 Method of Images Electrostatic CHAPTER 2 Table of Contents. 2.2 Electromagnetic Theory [EC] GATE ACADEMY. Electromagnetic field theory is often the least popular course in the electrical engineering curriculum. Heavy reli­ 2.6 THE METHOD OF IMAGES WITH LINE CHARGES AND CYLINDERS 93 2.6.1 Two Parallel Line Charges 93 2.6.2 The Method of Images 96 (a) GeneralProperties 9 2.4.3 Method of Images 35 2.4.4 Many many more problems 37 2.4.5 A History of Electrostatics 39 3. Magnetostatics 41 3.1 Amp ere's Law 42 3.1.1 A Long Straight Wire 42 3.1.2 Surface Currents and Discontinuities 43 3.2 The Vector Potential 46 3.2.1 Magnetic Monopoles 47 { 603: Electromagnetic Theory I CONTENTS • Maxwell's Equations: Introduction; units; boundary conditions. • Electrostatics: Uniqueness theorem; Green's theorem; gauge potentials; energy • Boundary value problems in electrostatics: Method of images; separation of variables in Cartesian, spherical polar and cylindrical polar coordinates The method of image charges (also known as the method of images and method of mirror charges) is a basic problem-solving tool in electrostatics

In this video we explained the Method of Images and its technique to solve problems .We also explained how to solve Multiple Image Problems .Lecture By - S.. The notion of cohomology allows a deep understanding of many points, notably in the study of the differential operators grad, curl, div with their kernels and their images, in an open domain Q; and then in the trace spaces on the boundary T of Q for electromagnetic fields of finite energy Method of images I: point charge in front of a grounded metallic plane -I; Week 3- Introduction to Electromagnetism. Method of imagesII: point charge in front of a grounded metallic plane and grounded metal sphere; Laplaces equations in some other physical phenomena; Energy of a charge distribution-I; Energy of a charge distribution-II An exampl Electromagnetic Field Theory as one file: (PDF 1 of 3 - 3.9MB) (PDF 2 of 3 - 3.2MB) (PDF 3 of 3 - 3.3MB) Electromagnetic Field Theory Textbook Components. 2.6 The method of images with line charges and cylinders, pp. 93-103. 2.7 The method of images with point charges and spheres, pp. 103-110. Problems, pp. 110-134 This text provides a mathematically precise but intuitive introduction to classical electromagnetic theory and wave propagation, with a brief introduction to special relativity. While written in a distinctive, modern style, Friedrichs manages to convey the physical intuition and 19th century basis of the equations, with an emphasis on.

2.7: The Method of Images with Point Charges and Spheres ..

iv Electromagnetic Field Theory 15 More on Interesting Physical Phenomena 141 15.1 More on Interesting Physical Phenomena, Homomorphism, Plane Waves, Trans University of Kentucky, PHY 611, Electromagnetic Theory I, Fall 2012. Date. Topic. Reading Assignment. Problem Set. Wed Aug 22. Mathematics Review [ pdf] review vector calculus. PS #1: [ pdf Lectures on Electromagnetic Field Theory Weng Cho CHEW1 Fall 2019, Purdue University 1Updated: December 4, 201 The final chapter gives, for the first time in book form, a unified presentation of EIT, the exact image theory, introduced by this author and colleagues. EIT is a general method for solving problems involving layered media by replacing them through image sources located in complex space Electromagnetic Field Theory Fundamentals - July 2004. examine several methods (Gauss's law, Poisson's and Laplace's equations, method of images) of solving electrostatic field problems; and develop the concept of capacitance and obtain an equation for the energy stored in a capacitor

Method of image charges - Wikipedi

  1. ECE1228H Electromagnetic Theory Professor M. Mojahedi Fundamentals: Maxwell's equations, constitutive relations and boundary conditions, wave polarization. Field representations: potentials, Green's functions and integral equations. Theorems and concepts: duality, uniqueness, images, equivalence, reciprocity and Babinet's principles
  2. MATHEMATICAL METHOD OF PHYSICS 0.introduction of all exam by men prakash sahu 1.matrices notes by men prakash sahu 2.vector notes by men prakash sahu 3.differential equations notes by men prakash sahu 3.dimensional analysis notes by men prakash sahu 5.special function notes by men prakash sahu 6.Fourier series and Fourier transform notes by men prakash sahu 7.laplace transform notes by men.
  3. Transcribed image text: 1 As shown in Figure, there are several short antennas (can be viewed as current element) placed in different directions, draw their images against the ground. 140 2 Which the knowledge points of electromagnetic field theory is related to the KCL and KVL in the course of circuit theory? Please write the differential forms of KCL and KVL by the method of field
  4. Handout 11 [PDF]: Faraday's Law and electromagnetic Induction, non-uniqueness of voltages in magnetoquasistatics, current-charge continuity equation in electromagnetism, power-energy continuity equation in electromagnetism, Poynting's vector, electromagnetic energy and power flow and connection with electrical circuit theory
Eddy current Theory

Lecture -2.4 Part-2/2 Method of Images ..

Mathematical Methods in Electromagnetism Series on

  1. A relatively simple method for calculating the properties of a paraxial beam of electromagnetic radiation propagating in vacuum is presented. The central idea of the paper is that the vector potential field is assumed to be plane-polarized. The nonvanishing component of the vector potential obeys a scalar wave equation. A formal solution employing an expansion in powers of $\frac{{w}_{0}}{l.
  2. As he stated in his 1864 work Dynamical Theory of the Electromagnetic Field, we have strong reason to conclude that light itself— including radiant heat, and other radiations if any —is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws
  3. Electromagnetism is fundamental to the whole of electrical and electronic engineering. It provides the basis for understanding the uses of electricity and for the design of the whole spectrum of devices from the largest turbo-alternators to the smallest microcircuits. This subject is a vital part of the education of electronic engineers

The history of electromagnetic theory begins with ancient measures to understand atmospheric electricity, in particular lightning. People then had little understanding of electricity, and were unable to explain the phenomena. Scientific understanding into the nature of electricity grew throughout the eighteenth and nineteenth centuries through the work of researchers such as Coulomb, Ampère. Actually this is a conceptual ques . That is from.my mind . I need to get clarified over thi Physics 351: Electricity and Magnetism. I have also a paper afloat, with an elec­tro­mag­netic the­ory of light, which, till I am con­vinced of the con­trary, I hold to be great guns. Wel­come to Physics 351! In this class we will study charges, cur­rents, elec­tric and mag­netic fields, and their in­ter­ac­tions

Sensors | Free Full-Text | Non-Destructive Techniques

NPTEL :: Physics - NOC:Introduction to Electromagnetic Theor

PHYS 3165. Electromagnetic Theory I. 3 Credits. Electrostatics and magnetostatics, electric and magnetic fields in matter, scalar and vector potentials, electromagnetic induction. Maxwell's equations. Methods of vector and tensor calculus are developed as needed, as are the method of images, Fourier series, and some computational methods Electromagnetic nondestructive tests are important and widely used within the field of nondestructive evaluation (NDE). The recent advances in sensing technology, hardware and software development dedicated to imaging and image processing, and material sciences have greatly expanded the application fields, sophisticated the systems design and made the potential of electromagnetic NDE imaging. Measurement of Temperature using Infrared Methods. When using a Thermal Imager it is helpful to have a basic knowledge of infrared theory. An object when heated radiates electromagnetic energy. The amount of energy is related to the object's temperature Electromagnetic waves . Propagation of electromagnetic waves in free space [1D] Finite Difference Time Development method (EM waves in non-magnetic media) Propagation of electromagnetic waves and the finite difference time development method; Gaussian EM pulse propagating in non-lossy medi

Turning a non-magnetic metal into a magnet using laserEmDrive could work: hypothetical propulsion method is

A method is described for the exact calculation of the field distributions and the phase constants of single and coupled dielectric image lines of rectangular cross section. Field distributions and phase constants calculated by this method are presented as well as experimental results from lines fabricated of paraffin wax. The physical properties of the electromagnetic fields and the mode. Journal description. This journal covers all aspects of electromagnetic wave theory and its various applications. The journal publishes original papers and review articles on new theories.

Electromagnetic theory was applied to relate a building's physical characteristics to the features present in a SAR image. This understanding was used to quantify the precision of building information contained in SAR data, and to identify the inputs needed for accurate simulation Electromagnetic Simulation Using the FDTD Method with Python, Third Edition is written with the goal of enabling readers to learn the FDTD method in a manageable amount of time. Some basic applications of signal processing theory are explained to enhance the effectiveness of FDTD simulation Electromagnetic Fields and Waves, by Corson and Lorrain, W. H. Freeman and Co. (1970); Foundations of Electromagnetic Theory, by Reitz and Milford, Addison-Weseley (1967); The presentation here is at the graduate physics level. The student is expected to have a fairly good grasp of many of the basic concepts in EM theory

Textbook contents Electromagnetic Field Theory: A

  1. a Plasmon hybridization theory and b coupled-mode theory, specifically the Born-Kuhn model, describing the electromagnetic chiral response of the coupled nanorod system shown in a
  2. Image segmentation is one of the most important tasks in medical image analysis and is often the first and the most critical step in many clinical applications. In brain MRI analysis, image segmentation is commonly used for measuring and visualizing the brain's anatomical structures, for analyzing brain changes, for delineating pathological regions, and for surgical planning and image.
  3. The electromagnetic field affects the change in the behaviour of charged objects surrounding a particular place. It extends indefinitely throughout space and known as electromagnetic interactions. It is a combination of electric field and a magnetic field and often considered as the sources of the electromagnetic field
  4. 2: THE ELECTRIC FIELD. The ancient Greeks observed that when the fossil resin amber was rubbed, small light-weight objects were attracted. Yet, upon contact with the amber, they were then repelled. No further significant advances in the understanding of this mysterious phenomenon were made until the eighteenth century when more quantitative.

Mathematical Methods of Electromagnetic Theor

Inverse Acoustic and Electromagnetic Scattering Theory, 273-302. (2018) Fast identification of small perfectly conducting cracks without diagonal elements of multi-static response matrix. Journal of Electromagnetic Waves and Applications 32 :18, 2490-2502 The whole subject of three-dimensional (3-D) electromagnetic (EM) modelling and inversion has experienced a tremendous progress in the last decade. Accordingly there is an increased need for reviewing the recent, and not so recent, achievements in the field. In the first part of this review paper I consider the finite-difference, finite-element and integral equation approaches that are. The method of printing full-color materials using the transparent cyan, magenta, yellow, and black inks. Color separation is the process of dividing the colors of a multicolored original into the subtractive, or printing, primaries (CMY) and black (K) Electromagnetic Theory for Complete Idiots (Electrical Engineering for Complete Idiots) - Kindle edition by SMITH, DAVID. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Electromagnetic Theory for Complete Idiots (Electrical Engineering for Complete Idiots) This paper describes the drop charging and drop deflection processes in an electrostatic ink jet printer. Included in the discussion of drop charging are induction interaction effects and charge synchronization requirements, as well as design considerations for the charge electrode

Electromagnetism - an overview ScienceDirect Topic

Also try to MATLAB software for the analysis of electromagnetic theory and simulation. so that readers from a complex mathematical expression to express the physical images they see. the abstract theory of electromagnetic fields show the vivid and intuitive side Modern Management Methods. Architecture, Historical Value, and the Electromagnetic Image Architecture, Historical Value, and the Electromagnetic Image. Caitlin Blanchfield and Farzin Lotfi-Jam Caitlin Blanchfield is a PhD candidate in architectural history and theory at Columbia University and an editor of the Avery Review James Clerk Maxwell, (born June 13, 1831, Edinburgh, Scotland—died November 5, 1879, Cambridge, Cambridgeshire, England), Scottish physicist best known for his formulation of electromagnetic theory. He is regarded by most modern physicists as the scientist of the 19th century who had the greatest influence on 20th-century physics, and he is ranked with Sir Isaac Newton and Albert Einstein.

Electromagnetic Metrology, fields and waves, radio communication systems and signal processing, electromagnetic environment and interference, wave propagation and remote sensing, ionospheric radio and propagation, waves in plasmas, electromagnetics in biology and medicine Electromagnetic theory, Computational electromagnetics, hybrid methods. ified image method was used to calculate the lightning-radiated electromagnetic field in which the mirror image of a real source was multiplied by a correction factor [12]. The correction factor is related to the angular frequency, the permittivities of the air and soil, and the conductivity of soil. A quasiimage method wa Finite difference methods. Tensors. Introductory group theory: SU(2), O(3). II. Classical Mechanics Dynamical systems, Phase space dynamics, stability analysis. Poisson brackets and canonical transformations. Symmetry, invariance and Noether's theorem. Hamilton-Jacobi theory. III. Electromagnetic Theory. Dispersion relations in plasma Since the 'method of images' of electromagnetic theory is often quoted as the basis for this concept, it is useful to identify the fallacies underlying the correlation. Section 8.1 does just that. Designers should resist the temptation to treat the structure as a convenient return path for signals and power Leontovich, M. A. & Fock, V. A. 1965 Solution of the problem of propagation of electromagnetic waves along the earth's surface by the method of parabolic equations. In Electromagnetic Diffraction and Propagation Problems (ed. V. A. Fock), chap. 11. Pergamon Press

It follows a detailed discussion of electrostatics, flux problems, magnetostatics, quasi stationary fields, and electromagnetic waves. The author presents how to apply numerical methods like finite differences, finite elements, boundary elements, image charge methods, and Monte-Carlo methods to field theory problems Electromagnetic Field Theory (Including Antennas and Wave Propagation) by K.A. Gangadhar and P.M. Ramanathan and a great selection of related books, art and collectibles available now at AbeBooks.com Introduction. lucernhammer is a state of the art electromagnetic signature prediction code suite, used for the prediction of scattered far-zone electric fields and radar cross section (RCS) of realistic radar targets. It is used by U.S. Government agencies and its contractors in areas such as ballistic missile defense (BMD), automatic target recognition (ATR), inverse SAR (ISAR) image. 3.1. Transient Electromagnetic Method. The transient electromagnetic method (TEM) belongs to the time-domain electromagnetic induction method. Before 1990s, it was mainly used to search for metal deposits, coalfields, petroleum, gas, and other fields Electromagnetic Interference, EMI is the interference caused by one electrical or electronic device to another by the electromagnetic fields set up by its operation. There are many forms of electromagnetic interference, EMI that can affect circuits and prevent them from working in the way that was intended

Method of Images in Electrostatics - Wolfram

  1. ation of physical quantities, the role of abstractions, and the methods of physical investigation. Kinematics is treated not as a mathematical theory, but from a physical point of view
  2. Principles and methods of modern electromagnetic wave theory: anisotropic media, dyadic green functions, Huygen's principle, contour integration methods, asymptotic integration. Applications in radiation and scattering. Ec En 661 Advanced Optical Engineering Theory and analysis of optical systems, including beam propagation, image formation.
  3. Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as sound, images, and scientific measurements. Signal processing techniques can be used to improve transmission, storage efficiency and subjective quality and to also emphasize or detect components of interest in a measured signal
  4. Machine Intell. 15 1131-1147 [7] Colton D, Haddar H and Monk P 2002 The Linear Sampling Method for Solving the Electromagnetic Inverse Scattering Problem SIAM J. Sci. Comput. 24 719-731 [8] Colton D, Haddar H and Piana M 2003 The linear sampling method in inverse electromagnetic scattering theory Inverse Problems 19 S105-S137 [9] Colton D and.
  5. Basic Electromagnetic Theory-James Babington 2016-06-09 Basic Electromagnetic Theory is designed as a concise introduction to electromagnetic field theory emphasizing the physical foundations of the subject. It is aimed at both undergraduates and interested laypersons. It has been based on the author's experienc
  6. Electromagnetic Imaging refers to the use of electromagnetic fields (from static to microwave and higher frequencies) for providing and image of an object. The problem of obtaining an image of the interior of an object from a set of noisy measurements is usually ill-posed, that is either does not admit a solution, or the solution is not unique.

News - Cornell Universit

Physicist Heinrich Hertz (Germany) uses a new method to derive equations for Maxwell's Electrodynamic Theory, clarifying the theory and better defining the relationship between electric and magnetic fields. 1884: German engineer Paul Nipkow patents his concept for a complete electromechanical television system Integration of Remotely Sensed Images and Electromagnetic Models into a Bayesian Approach for Soil Moisture Content Retrieval: Methodology and in theory, improve the SM estimate. The general consensus of the The developed method has been applied to two main test sites, one located in Argentina and. the electromagnetic spectrum. THz imaging has great potential in applications such as security screening, non-destructive testing, and biological detection [1-4], where the high requirement of image quality is indispensable. Obviously, the edge detection is important for image recognition at the visible, infrared and other bands. The image can b electromagnetic concepts, solving for soil properties with high resolutions spatially and temporally THEORY In a resistive medium such as soil, electrical potential measurements to monitor spatial variations can The case of method of images is a physical equivalent of the determination of the appropriate F(x,x ') to satisfy the boundary. ning the entire electromagnetic spectrum, from dc to light, from the electrically and magnetically based (elctromechanics) technologies to the electronics tech-nologies to the photonics technologies. As such, in the context of engineering education, it is fundamental to the study of electrical and computer engineering, a

University of Kentucky, PHY 611, Electromagnetic Theory I

  1. eral exploration. The technique is proficient in direct detection of conductive sulfide deposits, in which large conductivity contrasts exist between the orebodies and country/host rocks or thin overburden cover
  2. imum, the following: ter
  3. Method We wrapped a wire around an iron nail and connected it to a D.C power supply. Keeping the voltage constant, we recorded how many paper clips the electromagnet could pick up in a chain. Results. Conclusion Increasing the number of turns in the coil of wire did increase the strength of the electromagnet. For example at 20 turns, it could.
  4. g out of the world cyclocross championships in Belgium last weekend has confirmed the first documented.
  5. Outcome measures: An oscilloscope, current probes, and photo negatives were used to acquire >50,000 images. A type of discharged electromagnetic field (EMF), with a frequency of approximately 0.3-200 MHz, was recorded. Results: The microdischarge pulses were positive, with a pulse width from 2-100 ns and with a total charge of approximately 0.
  6. Special theory of relativity. The other major conceptual advance in electromagnetic theory was the special theory of relativity.In Maxwell's time, a mechanistic view of the universe held sway. Sound was interpreted as an undulatory motion of the air, while light and other electromagnetic waves were regarded as undulatory motions of an intangible medium called ether
  7. Remote sensing techniques allow taking images of the earth surface in various wavelength region of the electromagnetic spectrum (EMS). One of the major characteristics of a remotely sensed image is the wavelength region it represents in the EMS. Some of the images represent reflected solar radiatio
CLU-IN | Technologies > Characterization and Monitoring

We can get a good understanding of electromagnetic waves (EM) by considering how they are produced. Whenever a current varies, associated electric and magnetic fields vary, moving out from the source like waves. Perhaps the easiest situation to visualize is a varying current in a long straight wire, produced by an AC generator at its center, as. For a time -harmonic electromagnetic wave, the power density Per unit area associate with the wave is defined in complex Representation by vector S, S= E x H* (W/m2) Time average pontying vector <s> is defined as average of the Time domain Poynting vector S over a period T=2π/ω. < >= ∫ × π ω π 2 0 ( ) ( , , , ) ( , , ,) 2 1 S d t E x. On a method of making a direct comparison of electrostatic with electro­magnetic force; with a note on the electromagnetic theory of light James Clerk Maxwell Google Schola We present a general theory of effective media to set up the relationship between the particle responses and the macroscopic system behaviors for artificial metamaterials composed of periodic resonant structures. By treating the unit cell of the periodic structure as a particle, we define the average permittivity and permeability for different unit structures and derive a general form of. ECE 222C. Applied Electromagnetic Theory—Computational Methods for Electromagnetics (4) Computational techniques for numerical analysis of electromagnetic fields, including the finite difference time domain (FDTD) method, finite difference frequency domain (FDFD) method, method of moments (MOM), and finite element method (FEM)

&quot;Antigravity&quot; Method 15b of 15 Photonic Mechanical and

Methods for Electromagnetic Field Analysis (IEEE Press

All diffraction methods are based on generation of X-rays in an X-ray tube. These X-rays are directed at the sample, and the diffracted rays are collected. A key component of all diffraction is the angle between the incident and diffracted rays. Powder and single crystal diffraction vary in instrumentation beyond this MRI, considered as a highly precise diagnostic method, revealed simultaneous muscle growth, fat reduction and reduced abdominal separation at 2 months and at 6 months post treatments, unrelated with dieting. Further research should investigate the exact physiological processes which stand behind the

Design/methodology/approach. The developed model is based on the combination of the sub-domain's method and the image's theory. First, the magnetic field expressions because of the PMs are obtained by solving the three-dimensional Maxwell equations by the method of separation of variables, using a magnetic scalar potential formulation and a magnetic field strength formulation A light wave is an electromagnetic wave that travels through the vacuum of outer space. Light waves are produced by vibrating electric charges. The nature of such electromagnetic waves is beyond the scope of The Physics Classroom Tutorial.For our purposes, it is sufficient to merely say that an electromagnetic wave is a transverse wave that has both an electric and a magnetic component The image shows the magnitude of the electromagnetic wave, where red and blue are high and low values, respectively. Beam splitters can split a beam of light, such as one with a 700-nm wavelength, into two. To create a beam splitter, one method is depositing a layer of metal between two prisms made of glass

Electrostatics (Chapter 3) - Electromagnetic Field Theory

A final method of heat transfer involves radiation. Radiation is the transfer of heat by means of electromagnetic waves. To radiate means to send out or spread from a central location. Whether it is light, sound, waves, rays, flower petals, wheel spokes or pain, if something radiates then it protrudes or spreads outward from an origin. The. James Clerk Maxwell has utilized the ideas of Faraday as the basis of his quantitative electromagnetic theory. In the year 1834, Heinrich Lenz has invented the law to explain the flux throughout the circuit. The induced e.m.f direction can be received from the Lenz's law & the current results from the electromagnetic induction Simply because this algorithm is the most straightforward way of simulating the physical phenomena that cause objects to be visible. For that reason, we believe ray-tracing is the best choice, among other techniques, when writing a program that creates simple images. To start, we will lay the foundation with the ray-tracing algorithm Theory of Synthetic Aperture Radar. Electromagnetic Theory Unlike optical and infrared imaging sensors which are inherently passive, meaning they rely on reflected or radiated energy, radar is an active sensor--providing its own illumination in the form of microwaves Also in 1839, only three weeks after Daguerre's announcement of his method, Henry Fox Talbot announced in England his negative-positive system.Talbot found that he could slow the effect of light upon silver nitrate with a salty solution, and through a friend, had heard about Daguerre's use of sodium thiosulphate, which halted the process

Electromagnetics Course Catalogue Electrical & Computer

Electromagnetic radiation such as visible light is commonly treated as a wave phenomenon, characterized by a wavelength or frequency. Wavelength is defined on the left below, as the distance between adjacent peaks (or troughs), and may be designated in meters, centimeters or nanometers (10-9 meters) The Electromagnetic Theory and Transmission Lines Notes Pdf - EMTL Pdf Notes book starts with the topics covering Coulomb's Law, Ampere's circuital law & applications, transformer emf &inconsistency of Ampere's law, Wave equations for conducting & perfect dielectric media, for perfect conductors and perfect dielectrics, etc

Quantum Theory: Max Planck

Ask an expert anytime. Take a photo of your question and get an answer in as little as 30 mins*. With over 21 million homework solutions, you can also search our library to find similar homework problems & solutions. Try Chegg Study. *Our experts' time to answer varies by subject & question apparatus and method for generating a time variant non-electromagnetic force field due to the dynamic interaction of relatively moving bodies and for transforming such force fields into energy for doing useful work The study of waves can be traced back to antiquity where philosophers, such as Pythagoras (c. 560-480 BC), studied the relation of pitch and length of string in musical instruments. However, it was not until the work of Giovani Benedetti (1530-90), Isaac Beeckman (1588-1637) and Galileo (1564-1642) that the relationship between pitch and frequency was discovered When Michael Faraday made his discovery of electromagnetic induction in 1831, he hypothesized that a changing magnetic field is necessary to induce a current in a nearby circuit. To test his hypothesis he made a coil by wrapping a paper cylinder with wire. He connected the coil to a galvanometer, and then moved a magnet back and forth inside.