DOCSLIB.ORG

Revision of Electromagnetic Theory Lecture 1 Maxwell’S Equations Static Fields Electromagnetic Potentials Electromagnetism and Special Relativity

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Revision of Electromagnetic Theory Lecture 1 Maxwell’S Equations Static Fields Electromagnetic Potentials Electromagnetism and Special Relativity Revision of Electromagnetic Theory Lecture 1 Maxwell’s Equations Static Fields Electromagnetic Potentials Electromagnetism and Special Relativity Andy Wolski University of Liverpool, and the Cockcroft Institute Electromagnetism in Accelerators Electromagnetism has two principle applications in accelerators: magnetic fields can be used to steer and focus beams; • electric fields can be used to control the energy of particles. • However, understanding many diverse phenomena in accelerators, and the design and operation of many different types of components, depends on a secure knowledge of electromagnetism. Electromagnetism 1 Lecture 1: Fields and Potentials Electromagnetism in Accelerators In these lectures, we will revise the fundamental principles of electromagnetism, giving specific examples in the context of accelerators. In particular, in this first lecture, we will: revise Maxwell’s equations and the associated vector • calculus; discuss the physical interpretation of Maxwell’s equations, • with some examples relevant to accelerators; see how the dynamics of particles in an accelerator are • governed by the Lorentz force; discuss the electromagnetic potentials, and their use in • solving electrodynamical problems; briefly consider energy in electromagnetic fields; • show how the equations of electromagnetism may be • written to show explicitly their consistency with special relativity. The next lecture will be concerned with electromagnetic waves. Electromagnetism 2 Lecture 1: Fields and Potentials Further Reading Recommended text: • I.S.Grant and W.R. Phillips, “Electromagnetism” Wiley, 2nd Edition, 1990 Free to download: • B. Thide, “Electromagnetic Field Theory” http://www.plasma.uu.se/CED/Book/index.html Comprehensive reference for the very ambitious: • J.D.Jackson, “Classical Electrodynamics” Wiley, 3rd Edition, 1998 Electromagnetism 3 Lecture 1: Fields and Potentials Electromagnetism in Accelerators Understanding the properties of electromagnetic fields is essential for understanding the design, operation and performance of a wide variety of accelerator components. Electromagnetism 4 Lecture 1: Fields and Potentials Maxwell’s Equations Maxwell’s equations determine the electric and magnetic fields in the presence of sources (charge and current densities), and in materials of given properties. D~ = ρ, (1) ∇ · B~ = 0 , (2) ∇ · ∂B~ E~ = , (3) James Clerk Maxwell, ∇ × − ∂t ∂D~ 1831–1879 H~ = J~ + . (4) ∇ × ∂t ρ is the electric charge density, and J~ the electric current density. The electric field E~ and magnetic field (flux density) B~ determine the force on a charged particle (moving with velocity ~v ), according to the Lorentz force equation: F~ = q E~ + ~v B~ . (5) × Electromagnetism 5 Lecture 1: Fields and Potentials Permittivity and Permeability The electric displacement D~ and magnetic intensity H~ are related the the electric and magnetic fields by: D~ = εrε0E,~ (6) B~ = µrµ0H.~ (7) The quantities ε0 and µ0 are fundamental physical constants; respectively, the permittivity and permeability of free space: ε 8.854 10 12 Fm 1, (8) 0 ≈ × − − µ = 4 π 10 7 Hm 1. (9) 0 × − − Note that: 1 8 1 µ0 c = 2.998 10 ms − , Z 0 = 376 .73 Ω . (10) √µ0ε0 ≈ × s ε0 ≈ Electromagnetism 6 Lecture 1: Fields and Potentials Permittivity and Permeability The relative permittivity εr and relative permeability µr are dimensionless quantities that characterise the response of a material to electric and magnetic fields. Often, the relative permittivity and permeability of a given material are approximated by constants; in reality, they are themselves functions of the fields that are present, and functions also of the frequency of oscillations of the external fields. Electromagnetism 7 Lecture 1: Fields and Potentials Vector Operators Maxwell’s equations are written in differential form using the operators div (divergence): ∂F x ∂F y ∂F z F~ + + , (11) ∇ · ≡ ∂x ∂y ∂z and curl: xˆ yˆ zˆ ∂F z ∂F y ∂F x ∂F z ∂F y ∂F x ∂ ∂ ∂ F~ , , . ∂x ∂y ∂z ∇ × ≡ ∂y − ∂z ∂z − ∂x ∂x − ∂y ! ≡ Fx Fy Fz (12) We will also encounter the grad (gradient) operator: ∂φ ∂φ ∂φ φ , , , (13) ∇ ≡ ∂x ∂y ∂z ! and the Laplacian: ∂2φ ∂2φ ∂2φ 2φ + + . (14) ∇ ≡ ∂x 2 ∂y 2 ∂z 2 Electromagnetism 8 Lecture 1: Fields and Potentials Integral Theorems We wrote down Maxwell’s equations as a set of differential equations; however, the physical interpretation becomes clearer if the equations are converted to integral form. This may be achieved using two useful integral theorems. First, we consider Gauss’ theorem: F~ dV F~ dS,~ (15) ZV ∇ · ≡ I∂V · where ∂V is a closed surface enclosing volume V . Electromagnetism 9 Lecture 1: Fields and Potentials Gauss’ Theorem Let us apply Gauss’ theorem to Maxwell’s equation: D~ = ρ, (16) ∇ · to give: D~ dS~ = ρ dV. (17) I∂V · ZV This is the integral form of Maxwell’s equation (1). From this form, we can find a physical interpretation of Maxwell’s equation (1). The integral form of the equation tells us that the electric displacement integrated over any closed surface equals the electric charge contained within that surface. Electromagnetism 10 Lecture 1: Fields and Potentials Gauss’ Theorem and Coulomb’s Law In particular, if we consider a sphere of radius r bounding a spherically symmetric charge q at its centre, then performing the integrals gives: 4πr 2 D~ = q, (18) ~ ~ which, using D = εrε0E becomes Coulomb’s law: q ~ = ˆ (19) E 2 r. 4πε rε0r Electromagnetism 11 Lecture 1: Fields and Potentials Gauss’ Theorem Similarly, we can find an integral form of Maxwell’s equation (2): B~ dS~ = 0 . I∂V · In this case, we see that the total magnetic flux crossing any closed surface is zero. In other words, lines of magnetic flux only occur in closed loops. Put yet another way, there are no magnetic monopoles. Electromagnetism 12 Lecture 1: Fields and Potentials Stokes’ Theorem Next, we consider Stokes’ theorem: F~ dS~ F~ d~`, (20) ZS ∇ × · ≡ I∂S · where ∂S is a closed loop bounding a surface S. This tells us that the integral of the curl of a vector field over a surface is equal to the integral of that vector field around a loop bounding that surface. Electromagnetism 13 Lecture 1: Fields and Potentials Stokes’ Theorem If we apply Stokes’ theorem to Maxwell’s equation (3): ∂B~ E~ = , ∇ × − ∂t we obtain Faraday’s law of electromagnetic induction: ∂ E~ d~` = B~ dS.~ (21) I∂S · −∂t ZS · This is the integral form of Maxwell’s equation (3). It is often written as: ∂Φ = , (22) E − ∂t where is the electromotive force around a loop, and Φ the E total magnetic flux passing through that loop. Electromagnetism 14 Lecture 1: Fields and Potentials Stokes’ Theorem Finally, we can apply Stokes’ theorem to Maxwell’s equation (4): ∂D~ H~ = J~ + , ∇ × ∂t to find the integral form: ∂ H~ d~` = I + D~ dS,~ (23) I∂S · ∂t ZS · where I is the total electric current flowing through the closed loop ∂S . Electromagnetism 15 Lecture 1: Fields and Potentials Stokes’ Theorem and Amp`ere’s Law Note that there are two terms on the right hand side of (23). The first term, I, is simply a flow of electric current; in this context, it is sometimes called the conduction current . In the case of a uniform current flow along a long straight wire, the conduction current term leads to Amp`ere’s law: I H~ = θ.ˆ (24) 2πr Electromagnetism 16 Lecture 1: Fields and Potentials Displacement Current The second term on the right hand side of the integral form of Maxwell’s equation (23) is sometimes called the displacement current , ID: ∂ ~ ~ ID = D dS. (25) ∂t ZS · The need for this term can be understood by considering the current flow into a parallel-plate capacitor. We must find the same magnetic field around the wire using Stokes’ theorem, whether we integrate over a surface cutting through the wire, or over a “deformed” surface passing between the plates... Electromagnetism 17 Lecture 1: Fields and Potentials Displacement Current Using Maxwell’s equation (1): D~ = ρ, (26) ∇ · and applying Gauss’ theorem over a volume enclosing the surface of one plate of the capacitor, we find: D~ dV = D~ dS~ = q, (27) ZV ∇ · ZS · where q is the charge on one plate. The conduction current is: dq ∂ ~ ~ I = = D dS = ID. (28) dt ∂t ZS · In this case, we see that the displacement current between the plates is equal to the conduction current carrying charge onto the plates. Hence, we arrive at the same magnetic field, no matter which surface we choose. Electromagnetism 18 Lecture 1: Fields and Potentials Displacement Current and Conservation of Charge The displacement current term in Maxwell’s equation (4) has an important physical consequence. If we take the divergence of this equation, we obtain: ∂ H~ = J~ + D.~ (29) ∇ · ∇ × ∇ · ∂t ∇ · Now, if we use the vector identity: F~ 0, (30) ∇ · ∇ × ≡ and Maxwell’s equation (1), we find: ∂ρ J~ + = 0 . (31) ∇ · ∂t This is the continuity equation , which expresses local conservation of electric charge. Electromagnetism 19 Lecture 1: Fields and Potentials Displacement Current and Conservation of Charge The physical interpretation of the continuity equation becomes clearer if we use Gauss’ theorem, to put it into integral form: ∂ J~ dS~ = ρ dV. (32) Z∂V · −∂t ZV We see that the rate of decrease of electric charge in a region V is equal to the total current flowing out of the region through its boundary, ∂V . Since current is the rate of flow of electric charge, the continuity equation expresses the local conservation of electric charge. Electromagnetism 20 Lecture 1: Fields and Potentials Example 1: The Betatron Donald Kirst with the world’s first induction accelerator, at the University of Illinois, 1940. A betatron uses a time-dependent magnetic field passing through a toroidal vacuum chamber to accelerate a beam. By Maxwell’s equation (3): ∂B~ E~ = , ∇ × − ∂t the varying magnetic field induces an electromotive force around the vacuum chamber, which accelerates the particle.
Load more

Recommended publications
  • Electromagnetism As Quantum Physics
    Electromagnetism as Quantum Physics Charles T. Sebens California Institute of Technology May 29, 2019 arXiv v.3 The published version of this paper appears in Foundations of Physics, 49(4) (2019), 365-389. https://doi.org/10.1007/s10701-019-00253-3 Abstract One can interpret the Dirac equation either as giving the dynamics for a classical field or a quantum wave function. Here I examine whether Maxwell's equations, which are standardly interpreted as giving the dynamics for the classical electromagnetic field, can alternatively be interpreted as giving the dynamics for the photon's quantum wave function. I explain why this quantum interpretation would only be viable if the electromagnetic field were sufficiently weak, then motivate a particular approach to introducing a wave function for the photon (following Good, 1957). This wave function ultimately turns out to be unsatisfactory because the probabilities derived from it do not always transform properly under Lorentz transformations. The fact that such a quantum interpretation of Maxwell's equations is unsatisfactory suggests that the electromagnetic field is more fundamental than the photon. Contents 1 Introduction2 arXiv:1902.01930v3 [quant-ph] 29 May 2019 2 The Weber Vector5 3 The Electromagnetic Field of a Single Photon7 4 The Photon Wave Function 11 5 Lorentz Transformations 14 6 Conclusion 22 1 1 Introduction Electromagnetism was a theory ahead of its time. It held within it the seeds of special relativity. Einstein discovered the special theory of relativity by studying the laws of electromagnetism, laws which were already relativistic.1 There are hints that electromagnetism may also have held within it the seeds of quantum mechanics, though quantum mechanics was not discovered by cultivating those seeds.
    [Show full text]
  • Electromagnetic Field Theory
    Lecture 4 Electromagnetic Field Theory “Our thoughts and feelings have Dr. G. V. Nagesh Kumar Professor and Head, Department of EEE, electromagnetic reality. JNTUA College of Engineering Pulivendula Manifest wisely.” Topics 1. Biot Savart’s Law 2. Ampere’s Law 3. Curl 2 Releation between Electric Field and Magnetic Field On 21 April 1820, Ørsted published his discovery that a compass needle was deflected from magnetic north by a nearby electric current, confirming a direct relationship between electricity and magnetism. 3 Magnetic Field 4 Magnetic Field 5 Direction of Magnetic Field 6 Direction of Magnetic Field 7 Properties of Magnetic Field 8 Magnetic Field Intensity • The quantitative measure of strongness or weakness of the magnetic field is given by magnetic field intensity or magnetic field strength. • It is denoted as H. It is a vector quantity • The magnetic field intensity at any point in the magnetic field is defined as the force experienced by a unit north pole of one Weber strength, when placed at that point. • The magnetic field intensity is measured in • Newtons/Weber (N/Wb) or • Amperes per metre (A/m) or • Ampere-turns / metre (AT/m). 9 Magnetic Field Density 10 Releation between B and H 11 Permeability 12 Biot Savart’s Law 13 Biot Savart’s Law 14 Biot Savart’s Law : Distributed Sources 15 Problem 16 Problem 17 H due to Infinitely Long Conductor 18 H due to Finite Long Conductor 19 H due to Finite Long Conductor 20 H at Centre of Circular Cylinder 21 H at Centre of Circular Cylinder 22 H on the axis of a Circular Loop
    [Show full text]
  • Electro Magnetic Fields Lecture Notes B.Tech
    ELECTRO MAGNETIC FIELDS LECTURE NOTES B.TECH (II YEAR – I SEM) (2019-20) Prepared by: M.KUMARA SWAMY., Asst.Prof Department of Electrical & Electronics Engineering MALLA REDDY COLLEGE OF ENGINEERING & TECHNOLOGY (Autonomous Institution – UGC, Govt. of India) Recognized under 2(f) and 12 (B) of UGC ACT 1956 (Affiliated to JNTUH, Hyderabad, Approved by AICTE - Accredited by NBA & NAAC – ‘A’ Grade - ISO 9001:2015 Certified) Maisammaguda, Dhulapally (Post Via. Kompally), Secunderabad – 500100, Telangana State, India ELECTRO MAGNETIC FIELDS Objectives: • To introduce the concepts of electric field, magnetic field. • Applications of electric and magnetic fields in the development of the theory for power transmission lines and electrical machines. UNIT – I Electrostatics: Electrostatic Fields – Coulomb’s Law – Electric Field Intensity (EFI) – EFI due to a line and a surface charge – Work done in moving a point charge in an electrostatic field – Electric Potential – Properties of potential function – Potential gradient – Gauss’s law – Application of Gauss’s Law – Maxwell’s first law, div ( D )=ρv – Laplace’s and Poison’s equations . Electric dipole – Dipole moment – potential and EFI due to an electric dipole. UNIT – II Dielectrics & Capacitance: Behavior of conductors in an electric field – Conductors and Insulators – Electric field inside a dielectric material – polarization – Dielectric – Conductor and Dielectric – Dielectric boundary conditions – Capacitance – Capacitance of parallel plates – spherical co‐axial capacitors. Current density – conduction and Convection current densities – Ohm’s law in point form – Equation of continuity UNIT – III Magneto Statics: Static magnetic fields – Biot‐Savart’s law – Magnetic field intensity (MFI) – MFI due to a straight current carrying filament – MFI due to circular, square and solenoid current Carrying wire – Relation between magnetic flux and magnetic flux density – Maxwell’s second Equation, div(B)=0, Ampere’s Law & Applications: Ampere’s circuital law and its applications viz.
    [Show full text]
  • Displacement Current and Ampère's Circuital Law Ivan S
    ELECTRICAL ENGINEERING Displacement current and Ampère's circuital law Ivan S. Bozev, Radoslav B. Borisov The existing literature about displacement current, although it is clearly defined, there are not enough publications clarifying its nature. Usually it is assumed that the electrical current is three types: conduction current, convection current and displacement current. In the first two cases we have directed movement of electrical charges, while in the third case we have time varying electric field. Most often for the displacement current is talking in capacitors. Taking account that charge carriers (electrons and charged particles occupy the negligible space in the surrounding them space, they can be regarded only as exciters of the displacement current that current fills all space and is superposition of the currents of the individual moving charges. For this purpose in the article analyzes the current configuration of lines in space around a moving charge. An analysis of the relationship between the excited magnetic field around the charge and the displacement current is made. It is shown excited magnetic flux density and excited the displacement current are linked by Ampere’s circuital law. ъ а аа я аъ а ъя (Ива . Бв, аав Б. Бв.) В я, я , я , яя . , я : , я я. я я, я я . я . К , я ( я я , я, я я я. З я я я. я я. , я я я я . 1. Introduction configurations of the electric field of moving charge are shown on Fig. 1 and Fig. 2. First figure represents The size of electronic components constantly delayed potentials of the electric field according to shrinks and the discrete nature of the matter is Liénard–Wiechert and this picture is not symmetrical becomming more obvious.
    [Show full text]
  • Notes 4 Maxwell's Equations
    ECE 3317 Applied Electromagnetic Waves Prof. David R. Jackson Fall 2020 Notes 4 Maxwell’s Equations Adapted from notes by Prof. Stuart A. Long 1 Overview Here we present an overview of Maxwell’s equations. A much more thorough discussion of Maxwell’s equations may be found in the class notes for ECE 3318: http://courses.egr.uh.edu/ECE/ECE3318 Notes 10: Electric Gauss’s law Notes 18: Faraday’s law Notes 28: Ampere’s law Notes 28: Magnetic Gauss law . D. Fleisch, A Student’s Guide to Maxwell’s Equations, Cambridge University Press, 2008. 2 Electromagnetic Fields Four vector quantities E electric field strength [Volt/meter] D electric flux density [Coulomb/meter2] H magnetic field strength [Amp/meter] B magnetic flux density [Weber/meter2] or [Tesla] Each are functions of space and time e.g. E(x,y,z,t) J electric current density [Amp/meter2] 3 ρv electric charge density [Coulomb/meter ] 3 MKS units length – meter [m] mass – kilogram [kg] time – second [sec] Some common prefixes and the power of ten each represent are listed below femto - f - 10-15 centi - c - 10-2 mega - M - 106 pico - p - 10-12 deci - d - 10-1 giga - G - 109 nano - n - 10-9 deka - da - 101 tera - T - 1012 micro - μ - 10-6 hecto - h - 102 peta - P - 1015 milli - m - 10-3 kilo - k - 103 4 Maxwell’s Equations (Time-varying, differential form) ∂B ∇×E =− ∂t ∂D ∇×HJ = + ∂t ∇⋅B =0 ∇⋅D =ρv 5 Maxwell James Clerk Maxwell (1831–1879) James Clerk Maxwell was a Scottish mathematician and theoretical physicist.
    [Show full text]
  • Chapter 1 ELECTROMAGNETICS of METALS
    Chapter 1 ELECTROMAGNETICS OF METALS While the optical properties of metals are discussed in most textbooks on condensed matter physics, for convenience this chapter summarizes the most important facts and phenomena that form the basis for a study of surface plas- mon polaritons. Starting with a cursory review of Maxwell’s equations, we describe the electromagnetic response both of idealized and real metals over a wide frequency range, and introduce the fundamental excitation of the conduc- tion electron sea in bulk metals: volume plasmons. The chapter closes with a discussion of the electromagnetic energy density in dispersive media. 1.1 Maxwell’s Equations and Electromagnetic Wave Propagation The interaction of metals with electromagnetic fields can be firmly under- stood in a classical framework based on Maxwell’s equations. Even metallic nanostructures down to sizes on the order of a few nanometres can be described without a need to resort to quantum mechanics, since the high density of free carriers results in minute spacings of the electron energy levels compared to thermal excitations of energy kBT at room temperature. The optics of met- als described in this book thus falls within the realms of the classical theory. However, this does not prevent a rich and often unexpected variety of optical phenomena from occurring, due to the strong dependence of the optical prop- erties on frequency. As is well known from everyday experience, for frequencies up to the vis- ible part of the spectrum metals are highly reflective and do not allow elec- tromagnetic waves to propagate through them. Metals are thus traditionally employed as cladding layers for the construction of waveguides and resonators for electromagnetic radiation at microwave and far-infrared frequencies.
    [Show full text]
  • Metamaterials for Space Applications Final Report
    Metamaterials for Space Applications Design of invisibility cloaks for reduced observability of objects Final Report Authors: F. Bilotti, S. Tricarico, L. Vegni Affiliation: University Roma Tre ESA Researcher(s): Jose M. Llorens and Luzi Bergamin Date: 20.7.2008 Contacts: Filiberto Bilotti Tel: +39.06.57337096 Fax: +39.06.57337026 e-mail: [email protected] Leopold Summerer Tel: +31(0)715655174 Fax: +31(0)715658018 e-mail: [email protected] Ariadna ID: 07/7001b Study Duration: 4 months Available on the ACT website http://www.esa.int/act Contract Number: 21263/07/NL/CB Contents Abstract ...................................................................................................................3 Objectives of the study .........................................................................................4 1 Design of Invisibility Cloaks at Microwaves ..............................................7 1.1 Cloak with ENZ materials at microwaves...................................................... 7 1.2 Cloak with MNZ materials at microwaves ................................................... 12 1.3 Full wave simulations of an ideal MNZ-ENZ cloak at microwaves.......... 15 1.4 Design of an MNZ-ENZ cloak at microwaves with magnetic inclusions 21 2 Design of a cloak with ENZ metamaterials at THz and/or optical frequencies............................................................................................................ 26 3 Reduction of the radiation pressure by optical cloaking ...................... 34 4 Conclusions..................................................................................................
    [Show full text]
  • Electromagnetic Theory (3-1-0) Module-I (10 Hours)
    Veer Surendra Sai University of Technology, Orissa, Burla, India Department of Electrical Engineering, Syllabus of Bachelor of Technology in Electrical Engineering, 2010 (6TH SEMESTER) ELECTROMAGNETIC THEORY (3-1-0) MODULE-I (10 HOURS) Representation of vectors in Cartesian, Cylindrical and Spherical coordinate system, Vector products, Coordinate transformation. The Law of force between elementary electric Charges, Electric Field Intensity and Potential due to various charge configuration, Electric Flux density, Gauss law and its application, Application of Gauss Law to differential Volume element, Divergence Theorem. Potential Gradient, Dipole, and Energy Density in Electrostatic Field. MODULE-II (10 HOURS) Current and Conductors, Continuity of Current, Conductor Properties and Boundary Conditions. The Method of Images, Nature of dielectric Materials, Boundary Conditions for Perfect Dielectric Materials Capacitance, Poisson’s & Laplace equation, Uniqueness Theorem, Analytical Solution in one dimension.- Use of MATLAB Steady Magnetic Field: Biot Savart Law, Ampere’s Circuital Law, Stoke’s Theorem, Scalar and Vector Magnetic Potential, MODULE-III (10 HOURS) Force on a moving Charge, Force on a differential Current Element, Force & Torque Magnetisation & Permeability, Magnetic Boundary Conditions, Inductance & Mutual Inductance. Time Varying Fields: Faraday’s Law, Displacement Current, Maxwell’s Equation. MODULE-IV (10 HOURS) Wave propagation in Free Space, Dielectric, and Good Conductor. Poynting’s Theorem and wave power, Wave polarization, Reflection and Transmission of Uniform Plane Waves at Normal & Oblique incidence, Standing Wave Ratio, Basic Wave Guide Operation and Basic Antenna Principles. BOOKS [1]. W. H. Hayt (Jr ), J. A. Buck, “Engineering Electromagnetics”, TMH [2]. K. E. Lonngren, S.V. Savor, “Fundamentals of Electromagnetics with Matlab”, PHI [3]. E.C.Jordan, K.G.
    [Show full text]
  • Electromagnetic Field Control and Optimization Using Metamaterials Jeffrey S
    Air Force Institute of Technology AFIT Scholar Theses and Dissertations Student Graduate Works 12-9-2009 Electromagnetic Field Control and Optimization Using Metamaterials Jeffrey S. McGuirk Follow this and additional works at: https://scholar.afit.edu/etd Part of the Electrical and Computer Engineering Commons Recommended Citation McGuirk, Jeffrey S., "Electromagnetic Field Control and Optimization Using Metamaterials" (2009). Theses and Dissertations. 1966. https://scholar.afit.edu/etd/1966 This Dissertation is brought to you for free and open access by the Student Graduate Works at AFIT Scholar. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of AFIT Scholar. For more information, please contact [email protected]. Electromagnetic Field Control and Optimization Using Metamaterials DISSERTATION Je®rey S. McGuirk, Major, USAF AFIT/DEE/ENG/09-13 DEPARTMENT OF THE AIR FORCE AIR UNIVERSITY AIR FORCE INSTITUTE OF TECHNOLOGY Wright-Patterson Air Force Base, Ohio APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. The views expressed in this dissertation are those of the author and do not reflect the o±cial policy or position of the United States Air Force, Department of Defense, or the United States Government. AFIT/DEE/ENG/09-13 Electromagnetic Field Control and Optimization Using Metamaterials DISSERTATION Presented to the Faculty Graduate School of Engineering and Management Air Force Institute of Technology Air University Air Education and Training Command in Partial Ful¯llment of the Requirements for the Degree of Doctor of Philosophy Je®rey S. McGuirk, B.S.E.E., M.S.E.E. Major, USAF December 2009 APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED.
    [Show full text]
  • "Wave Optics" Lecture 21 (PDF)
    Lecture 21 Reminder/Introduction to Wave Optics Program: 1. Maxwell’s Equations. 2. Magnetic induction and electric displacement. 3. Origins of the electric permittivity and magnetic permeability. 4. Wave equations and optical constants. 5. The origins and frequency dependency of the dielectric constant. Questions you should be able to answer by the end of today’s lecture: 1. What are the equations determining propagation of the waves in the media? 2. What are the relationships between the electric field and electric displacement and magnetic field and magnetic induction? 3. What is the nature of the polarization? How can we gain intuition about the dielectric constant for a material? 4. How do Maxwell’s equations lead to the wave nature of light? 5. What is refractive index and how it relates to the dielectric constant? How does it relate to the speed of light inside the material? 6. What is the difference between the phase and group velocity? 1 Response of materials to electromagnetic waves – propagation of light in solids. We classified materials with respect to their conductivity and related the observed differences to the existence of band gaps in the electron energy eigenvalues. The optical properties are determined to a large extent by the electrons and their ability to interact with the electromagnetic field, thus the conductivity classification of materials, which was a result of the band structure and band filling, is also useful for classifying the optical response. The most widely used metric for quantifying the optical behavior of materials is the index of refraction, which captures the extent to which the electromagnetic wave interacts with the material.
    [Show full text]
  • Dielectric Characterization and Reference Materials
    UNITED STATES DEPARTMENT OF COMMERCE NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY NisrNATL INST. OF STAND i TECH R.I.C. A111D3 m7M3M j_ NIST Technical PUBLICATIONS NIST Note 1338 NATIONAL INSTITUTE OF STANDARDS & TECHNOLOGY Research Information Center Gaithersburg, MD 20899 'i tpi f lip Dielectric Characterization and Reference Materials Richard G. Geyer Electromagnetic Fields Division Center for Electronics and Electrical Engineering National Engineering Laboratory National Institute of Standards and Technology Boulder, Colorado 80303-3328 .^et*TO.eo^ ^4, Q .^ \ K<r U.S. DEPARTMENT OF COMMERCE, Robert A. Mosbacher, Secretary NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, John W. Lyons, Director Issued April 1990 National Institute of Standards and Technology Technical Note 1338 Natl. Inst. Stand. Technol., Tech. Note 1338, 124 pages (Apr. 1990) CODEN:NTNOEF U.S. GOVERNMENT PRINTING OFFICE WASHINGTON: 1990 For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325 CONTENTS Page ABSTRACT 1 1. INTRODUCTION 2 2. NATIONAL NEED FOR ENHANCED DIELECTRIC METROLOGY AND REFERENCE MATERIALS 3 3. DESIRABLE PROPERTIES OF REFERENCE MATERIALS .... 7 4. ELECTROMAGNETIC CHARACTERISTICS OF MATERIALS 11 4.1 Physical Concepts Governing Electromagnetic Behavior 11 4.1.1 Anisotropy 12 4.1.2 Class A Dielectrics 13 4.1.3 Polar Versus Nonpolar Materials 14 4.1.4 Complex Material Constituent Properties 16 4.1.5 Distinction Between Ohmic Conductivity and Dielectric Loss Factor or Between Faradaic Diffusion Transport and In-phase Polarization Phenomena 17 4.1.6 Quality Factor of Dielectrics 18 4.2 Polarization Mechanisms Intrinsic to Materials 19 4.3 Dispersion and Relaxation Processes in Materials 22 24 4.3.1 Debye Relaxation .
    [Show full text]
  • MPM542 15 Winarno.Pdf
    Materials Physics and Mechanics 42 (2019) 617-624 Received: May 9, 2019 THE EFFECT OF CONDUCTIVITY AND PERMITTIVITY ON PROPAGATION AND ATTENUATION OF WAVES USING FDTD N.Winarno1*, R.A. Firdaus2, R.M.A. Afifah3 1Department of Science Education, Universitas Pendidikan Indonesia, Jl. Dr. Setiabudi No. 229, Bandung 40154, Indonesia 2Department of Physics, Institut Teknologi Sepuluh Nopember, Jl. Raya ITS, Surabaya 60111, Indonesia 3SMA Taruna Bakti, Jl. L.LRE. Marthadinata No. 52 Bandung, Indonesia *e-mail: [email protected] Abstract. The purpose of this study was to investigate the effect of conductivity and permittivity on wave propagation and attenuation on the plate using FDTD (The Finite Difference Time Domain). The FDTD method is used to describe electromagnetic waves. The method used in this study was the basic principle of the numerical approach of differential equations by taking into account boundary conditions, stability, and absorbing boundary conditions. The results of the simulation showed that if the permittivity of the material increased, the propagation would increase as well; however, the attenuation would decrease exponentially. If material conductivity increased, propagation and attenuation would increase. Attenuation and propagation produced the same value when the permittivity value was 2. This simulation could be used to select materials and identify physical phenomena related to electromagnetic waves. Keywords: conductivity, permittivity, propagation, attenuation, FDTD 1. Introduction Electromagnetic waves are waves that are difficult to visualize like real conditions in our lives; thus, we need the right method to overcome this problem. The Finite Difference Time Domain (FDTD) method was first introduced by Kane Yee in 1966 to analyze electromagnetic fields [1].
    [Show full text]