Chapter 30 – Inductance
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Determination of the Magnetic Permeability, Electrical Conductivity
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2018.2885406, IEEE Transactions on Industrial Informatics TII-18-2870 1 Determination of the magnetic permeability, electrical conductivity, and thickness of ferrite metallic plates using a multi-frequency electromagnetic sensing system Mingyang Lu, Yuedong Xie, Wenqian Zhu, Anthony Peyton, and Wuliang Yin, Senior Member, IEEE Abstract—In this paper, an inverse method was developed by the sensor are not only dependent on the magnetic which can, in principle, reconstruct arbitrary permeability, permeability of the strip but is also an unwanted function of the conductivity, thickness, and lift-off with a multi-frequency electrical conductivity and thickness of the strip and the electromagnetic sensor from inductance spectroscopic distance between the strip steel and the sensor (lift-off). The measurements. confounding cross-sensitivities to these parameters need to be Both the finite element method and the Dodd & Deeds rejected by the processing algorithms applied to inductance formulation are used to solve the forward problem during the spectra. inversion process. For the inverse solution, a modified Newton– Raphson method was used to adjust each set of parameters In recent years, the eddy current technique (ECT) [2-5] and (permeability, conductivity, thickness, and lift-off) to fit the alternating current potential drop (ACPD) technique [6-8] inductances (measured or simulated) in a least-squared sense were the two primary electromagnetic non-destructive testing because of its known convergence properties. The approximate techniques (NDT) [9-21] on metals’ permeability Jacobian matrix (sensitivity matrix) for each set of the parameter measurements. -
Units in Electromagnetism (PDF)
Units in electromagnetism Almost all textbooks on electricity and magnetism (including Griffiths’s book) use the same set of units | the so-called rationalized or Giorgi units. These have the advantage of common use. On the other hand there are all sorts of \0"s and \µ0"s to memorize. Could anyone think of a system that doesn't have all this junk to memorize? Yes, Carl Friedrich Gauss could. This problem describes the Gaussian system of units. [In working this problem, keep in mind the distinction between \dimensions" (like length, time, and charge) and \units" (like meters, seconds, and coulombs).] a. In the Gaussian system, the measure of charge is q q~ = p : 4π0 Write down Coulomb's law in the Gaussian system. Show that in this system, the dimensions ofq ~ are [length]3=2[mass]1=2[time]−1: There is no need, in this system, for a unit of charge like the coulomb, which is independent of the units of mass, length, and time. b. The electric field in the Gaussian system is given by F~ E~~ = : q~ How is this measure of electric field (E~~) related to the standard (Giorgi) field (E~ )? What are the dimensions of E~~? c. The magnetic field in the Gaussian system is given by r4π B~~ = B~ : µ0 What are the dimensions of B~~ and how do they compare to the dimensions of E~~? d. In the Giorgi system, the Lorentz force law is F~ = q(E~ + ~v × B~ ): p What is the Lorentz force law expressed in the Gaussian system? Recall that c = 1= 0µ0. -
On the First Electromagnetic Measurement of the Velocity of Light by Wilhelm Weber and Rudolf Kohlrausch
Andre Koch Torres Assis On the First Electromagnetic Measurement of the Velocity of Light by Wilhelm Weber and Rudolf Kohlrausch Abstract The electrostatic, electrodynamic and electromagnetic systems of units utilized during last century by Ampère, Gauss, Weber, Maxwell and all the others are analyzed. It is shown how the constant c was introduced in physics by Weber's force of 1846. It is shown that it has the unit of velocity and is the ratio of the electromagnetic and electrostatic units of charge. Weber and Kohlrausch's experiment of 1855 to determine c is quoted, emphasizing that they were the first to measure this quantity and obtained the same value as that of light velocity in vacuum. It is shown how Kirchhoff in 1857 and Weber (1857-64) independently of one another obtained the fact that an electromagnetic signal propagates at light velocity along a thin wire of negligible resistivity. They obtained the telegraphy equation utilizing Weber’s action at a distance force. This was accomplished before the development of Maxwell’s electromagnetic theory of light and before Heaviside’s work. 1. Introduction In this work the introduction of the constant c in electromagnetism by Wilhelm Weber in 1846 is analyzed. It is the ratio of electromagnetic and electrostatic units of charge, one of the most fundamental constants of nature. The meaning of this constant is discussed, the first measurement performed by Weber and Kohlrausch in 1855, and the derivation of the telegraphy equation by Kirchhoff and Weber in 1857. Initially the basic systems of units utilized during last century for describing electromagnetic quantities is presented, along with a short review of Weber’s electrodynamics. -
Electric Units and Standards
DEPARTMENT OF COMMERCE OF THE Bureau of Standards S. W. STRATTON, Director No. 60 ELECTRIC UNITS AND STANDARDS list Edition 1 Issued September 25. 1916 WASHINGTON GOVERNMENT PRINTING OFFICE DEPARTMENT OF COMMERCE Circular OF THE Bureau of Standards S. W. STRATTON, Director No. 60 ELECTRIC UNITS AND STANDARDS [1st Edition] Issued September 25, 1916 WASHINGTON GOVERNMENT PRINTING OFFICE 1916 ADDITIONAL COPIES OF THIS PUBLICATION MAY BE PROCURED FROM THE SUPERINTENDENT OF DOCUMENTS GOVERNMENT PRINTING OFFICE WASHINGTON, D. C. AT 15 CENTS PER COPY A complete list of the Bureau’s publications may be obtained free of charge on application to the Bureau of Standards, Washington, D. C. ELECTRIC UNITS AND STANDARDS CONTENTS Page I. The systems of units 4 1. Units and standards in general 4 2. The electrostatic and electromagnetic systems 8 () The numerically different systems of units 12 () Gaussian systems, and ratios of the units 13 “ ’ (c) Practical ’ electromagnetic units 15 3. The international electric units 16 II. Evolution of present system of concrete standards 18 1. Early electric standards 18 2. Basis of present laws 22 3. Progress since 1893 24 III. Units and standards of the principal electric quantities 29 1. Resistance 29 () International ohm 29 Definition 29 Mercury standards 30 Secondary standards 31 () Resistance standards in practice 31 (c) Absolute ohm 32 2. Current 33 (a) International ampere 33 Definition 34 The silver voltameter 35 ( b ) Resistance standards used in current measurement 36 (c) Absolute ampere 37 3. Electromotive force 38 (a) International volt 38 Definition 39 Weston normal cell 39 (b) Portable Weston cells 41 (c) Absolute and semiabsolute volt 42 4. -
SKIFFS: Superconducting Kinetic Inductance Field-Frequency Sensors for Sensitive Magnetometry in Moderate Background Magnetic Fields
SKIFFS: Superconducting Kinetic Inductance Field-Frequency Sensors for sensitive magnetometry in moderate background magnetic fields Cite as: Appl. Phys. Lett. 113, 172601 (2018); https://doi.org/10.1063/1.5049615 Submitted: 24 July 2018 . Accepted: 10 October 2018 . Published Online: 25 October 2018 A. T. Asfaw , E. I. Kleinbaum, T. M. Hazard , A. Gyenis, A. A. Houck, and S. A. Lyon ARTICLES YOU MAY BE INTERESTED IN Multi-frequency spin manipulation using rapidly tunable superconducting coplanar waveguide microresonators Applied Physics Letters 111, 032601 (2017); https://doi.org/10.1063/1.4993930 Publisher's Note: “Anomalous Nernst effect in Ir22Mn78/Co20Fe60B20/MgO layers with perpendicular magnetic anisotropy” [Appl. Phys. Lett. 111, 222401 (2017)] Applied Physics Letters 113, 179901 (2018); https://doi.org/10.1063/1.5018606 Tunneling anomalous Hall effect in a ferroelectric tunnel junction Applied Physics Letters 113, 172405 (2018); https://doi.org/10.1063/1.5051629 Appl. Phys. Lett. 113, 172601 (2018); https://doi.org/10.1063/1.5049615 113, 172601 © 2018 Author(s). APPLIED PHYSICS LETTERS 113, 172601 (2018) SKIFFS: Superconducting Kinetic Inductance Field-Frequency Sensors for sensitive magnetometry in moderate background magnetic fields A. T. Asfaw,a) E. I. Kleinbaum, T. M. Hazard, A. Gyenis, A. A. Houck, and S. A. Lyon Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA (Received 24 July 2018; accepted 10 October 2018; published online 25 October 2018) We describe sensitive magnetometry using lumped-element resonators fabricated from a supercon- ducting thin film of NbTiN. Taking advantage of the large kinetic inductance of the superconduc- tor, we demonstrate a continuous resonance frequency shift of 27 MHz for a change in the magnetic field of 1.8 lT within a perpendicular background field of 60 mT. -
Chapter 32 Inductance and Magnetic Materials
Chapter 32 Inductance and Magnetic Materials The appearance of an induced emf in one circuit due to changes in the magnetic field produced by a nearby circuit is called mutual induction. The response of the circuit is characterized by their mutual inductance. Can we find an induced emf due to its own magnetic field changes? Yes! The appearance of an induced emf in a circuit associated with changes in its own magnet field is called self-induction. The corresponding property is called self-inductance. A circuit element, such as a coil, that is designed specifically to have self-inductance is called an inductor. 1 32.1 Inductance Close: As the flux through the coil changes, there is an induced emf that opposites this change. The self induced emf try to prevent the rise in the current. As a result, the current does not reach its final value instantly, but instead rises gradually as in right figure. Open: When the switch is opened, the flux rapidly decreases. This time the self- induced emf tries to maintain the flux. When the current in the windings of an electromagnet is shut off, the self-induced emf can be large enough to produce a spark across the switch contacts. 2 32.1 Inductance (II) Since the self-induction and mutual induction occur simultaneously, both contribute to the flux and to the induced emf in each coil. The flux through coil 1 is the sum of two terms: N1Φ1 = N1(Φ11 + Φ12 ) The net emf induced in coil 1 due to changes in I1 and I2 is d V = −N (Φ + Φ ) emf 1 dt 11 12 3 Self-Inductance It is convenient to express the induced emf in terms of a current rather than the magnetic flux through it. -
Guide for the Use of the International System of Units (SI)
Guide for the Use of the International System of Units (SI) m kg s cd SI mol K A NIST Special Publication 811 2008 Edition Ambler Thompson and Barry N. Taylor NIST Special Publication 811 2008 Edition Guide for the Use of the International System of Units (SI) Ambler Thompson Technology Services and Barry N. Taylor Physics Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899 (Supersedes NIST Special Publication 811, 1995 Edition, April 1995) March 2008 U.S. Department of Commerce Carlos M. Gutierrez, Secretary National Institute of Standards and Technology James M. Turner, Acting Director National Institute of Standards and Technology Special Publication 811, 2008 Edition (Supersedes NIST Special Publication 811, April 1995 Edition) Natl. Inst. Stand. Technol. Spec. Publ. 811, 2008 Ed., 85 pages (March 2008; 2nd printing November 2008) CODEN: NSPUE3 Note on 2nd printing: This 2nd printing dated November 2008 of NIST SP811 corrects a number of minor typographical errors present in the 1st printing dated March 2008. Guide for the Use of the International System of Units (SI) Preface The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measurement. Long the dominant measurement system used in science, the SI is becoming the dominant measurement system used in international commerce. The Omnibus Trade and Competitiveness Act of August 1988 [Public Law (PL) 100-418] changed the name of the National Bureau of Standards (NBS) to the National Institute of Standards and Technology (NIST) and gave to NIST the added task of helping U.S. -
Relationships of the SI Derived Units with Special Names and Symbols and the SI Base Units
Relationships of the SI derived units with special names and symbols and the SI base units Derived units SI BASE UNITS without special SI DERIVED UNITS WITH SPECIAL NAMES AND SYMBOLS names Solid lines indicate multiplication, broken lines indicate division kilogram kg newton (kg·m/s2) pascal (N/m2) gray (J/kg) sievert (J/kg) 3 N Pa Gy Sv MASS m FORCE PRESSURE, ABSORBED DOSE VOLUME STRESS DOSE EQUIVALENT meter m 2 m joule (N·m) watt (J/s) becquerel (1/s) hertz (1/s) LENGTH J W Bq Hz AREA ENERGY, WORK, POWER, ACTIVITY FREQUENCY second QUANTITY OF HEAT HEAT FLOW RATE (OF A RADIONUCLIDE) s m/s TIME VELOCITY katal (mol/s) weber (V·s) henry (Wb/A) tesla (Wb/m2) kat Wb H T 2 mole m/s CATALYTIC MAGNETIC INDUCTANCE MAGNETIC mol ACTIVITY FLUX FLUX DENSITY ACCELERATION AMOUNT OF SUBSTANCE coulomb (A·s) volt (W/A) C V ampere A ELECTRIC POTENTIAL, CHARGE ELECTROMOTIVE ELECTRIC CURRENT FORCE degree (K) farad (C/V) ohm (V/A) siemens (1/W) kelvin Celsius °C F W S K CELSIUS CAPACITANCE RESISTANCE CONDUCTANCE THERMODYNAMIC TEMPERATURE TEMPERATURE t/°C = T /K – 273.15 candela 2 steradian radian cd lux (lm/m ) lumen (cd·sr) 2 2 (m/m = 1) lx lm sr (m /m = 1) rad LUMINOUS INTENSITY ILLUMINANCE LUMINOUS SOLID ANGLE PLANE ANGLE FLUX The diagram above shows graphically how the 22 SI derived units with special names and symbols are related to the seven SI base units. In the first column, the symbols of the SI base units are shown in rectangles, with the name of the unit shown toward the upper left of the rectangle and the name of the associated base quantity shown in italic type below the rectangle. -
Relative Permeability Measurements for Metal-Detector Research
NATL INST. OF STAND & TECH MIST 1""""""""" PUBUCATI0N8 National Institute of Standards and Technology Technology Administration, U.S. Department of Commerce NIST Technical Note 1532 Relative Permeability Measurements for Metal-Detector Research Michael D. Janezic James Baker-Jarvis /oo NIST Technical Note 1532 Relative Permeability Measurements For Metal-Detector Research Michael D. Janezic James Baker-Jarvis Radio-Frequency Technology Division Electronics and Electrical Engineering Laboratory National Institute of Standards and Technology Boulder, CO 80305 April 2004 U.S. Department of Commerce Donald L. Evans, Secretary Technology Administration Phillip J. Bond, Under Secretary for Technology National Institute of Standards and Technology Arden L. Bement, Jr., Director National Institute of Standards U.S. Government Printing Office For sale by the and Technology Washington: 2004 Superintendent of Documents Technical Note 1532 U.S. Government Printing Office Natl. Inst. Stand. Technol. Stop SSOP Tech. Note 1532 Washington, DC 20402-0001 1 6 Pages (April 2004) Phone: (202) 512-1 800 CODEN: NTNOEF Fax: (202) 512-2250 Internet: bookstore.gpo.gov Contents 1 Introduction 1 2 Overview and Definitions 2 3 Toroid Meeisurement Technique 4 3.0.1 Relative Permeability Model Excluding Toroid Conductivity 4 3.0.2 Relative Permittivity Model Including Toroid Conductivity 5 4 Measurements of Relative Permeability 7 5 Conclusions 11 6 References 12 Relative Permeability Measurements for Metal-Detector Research Michael D. Janezic and James Baker- Jarvis Electromagnetics Division, National Institute of Standards and Technology, Boulder, CO 80305 We examine a measurement method for characterizing the low-frequency relative per- meability of ferromagnetic metals commonly used in the manufacture of weapons. -
The International System of Units (SI)
NAT'L INST. OF STAND & TECH NIST National Institute of Standards and Technology Technology Administration, U.S. Department of Commerce NIST Special Publication 330 2001 Edition The International System of Units (SI) 4. Barry N. Taylor, Editor r A o o L57 330 2oOI rhe National Institute of Standards and Technology was established in 1988 by Congress to "assist industry in the development of technology . needed to improve product quality, to modernize manufacturing processes, to ensure product reliability . and to facilitate rapid commercialization ... of products based on new scientific discoveries." NIST, originally founded as the National Bureau of Standards in 1901, works to strengthen U.S. industry's competitiveness; advance science and engineering; and improve public health, safety, and the environment. One of the agency's basic functions is to develop, maintain, and retain custody of the national standards of measurement, and provide the means and methods for comparing standards used in science, engineering, manufacturing, commerce, industry, and education with the standards adopted or recognized by the Federal Government. As an agency of the U.S. Commerce Department's Technology Administration, NIST conducts basic and applied research in the physical sciences and engineering, and develops measurement techniques, test methods, standards, and related services. The Institute does generic and precompetitive work on new and advanced technologies. NIST's research facilities are located at Gaithersburg, MD 20899, and at Boulder, CO 80303. -
Atomic Weights and Isotopic Abundances*
Pure&App/. Chem., Vol. 64, No. 10, pp. 1535-1543, 1992. Printed in Great Britain. @ 1992 IUPAC INTERNATIONAL UNION OF PURE AND APPLIED CHEMISTRY INORGANIC CHEMISTRY DIVISION COMMISSION ON ATOMIC WEIGHTS AND ISOTOPIC ABUNDANCES* 'ATOMIC WEIGHT' -THE NAME, ITS HISTORY, DEFINITION, AND UNITS Prepared for publication by P. DE BIEVRE' and H. S. PEISER2 'Central Bureau for Nuclear Measurements (CBNM), Commission of the European Communities-JRC, B-2440 Geel, Belgium 2638 Blossom Drive, Rockville, MD 20850, USA *Membership of the Commission for the period 1989-1991 was as follows: J. R. De Laeter (Australia, Chairman); K. G. Heumann (FRG, Secretary); R. C. Barber (Canada, Associate); J. CCsario (France, Titular); T. B. Coplen (USA, Titular); H. J. Dietze (FRG, Associate); J. W. Gramlich (USA, Associate); H. S. Hertz (USA, Associate); H. R. Krouse (Canada, Titular); A. Lamberty (Belgium, Associate); T. J. Murphy (USA, Associate); K. J. R. Rosman (Australia, Titular); M. P. Seyfried (FRG, Associate); M. Shima (Japan, Titular); K. Wade (UK, Associate); P. De Bi&vre(Belgium, National Representative); N. N. Greenwood (UK, National Representative); H. S. Peiser (USA, National Representative); N. K. Rao (India, National Representative). Republication of this report is permitted without the need for formal IUPAC permission on condition that an acknowledgement, with full reference together with IUPAC copyright symbol (01992 IUPAC), is printed. Publication of a translation into another language is subject to the additional condition of prior approval from the relevant IUPAC National Adhering Organization. ’Atomic weight‘: The name, its history, definition, and units Abstract-The widely used term “atomic weight” and its acceptance within the international system for measurements has been the subject of debate. -
Chapter 6 Inductance, Capacitance, and Mutual Inductance
Chapter 6 Inductance, Capacitance, and Mutual Inductance 6.1 The inductor 6.2 The capacitor 6.3 Series-parallel combinations of inductance and capacitance 6.4 Mutual inductance 6.5 Closer look at mutual inductance 1 Overview In addition to voltage sources, current sources, resistors, here we will discuss the remaining 2 types of basic elements: inductors, capacitors. Inductors and capacitors cannot generate nor dissipate but store energy. Their current-voltage (i-v) relations involve with integral and derivative of time, thus more complicated than resistors. 2 Key points di Why the i-v relation of an inductor isv L ? dt dv Why the i-v relation of a capacitor isi C ? dt Why the energies stored in an inductor and a capacitor are: 1 1 w Li, 2 , 2 Cv respectively? 2 2 3 Section 6.1 The Inductor 1. Physics 2. i-v relation and behaviors 3. Power and energy 4 Fundamentals An inductor of inductance L is symbolized by a solenoidal coil. Typical inductance L ranges from 10 H to 10 mH. The i-v relation of an inductor (under the passive sign convention) is: di v L , dt 5 Physics of self-inductance (1) Consider an N1 -turn coil C1 carrying current I1 . The resulting magnetic fieldB 1() r 1 N 1(Biot- I will pass through Savart law) C1 itself, causing a flux linkage 1 , where B1() r 1 N 1 , 1 B1 r1() d s1 P 1, 1 N I S 1 P1 is the permeance. 2 1 PNI 1 11. 6 Physics of self-inductance (2) The ratio of flux linkage to the driving current is defined as the self inductance of the loop: 1 2 L1NP 1 1, I1 which describes how easy a coil current can introduce magnetic flux over the coil itself.