Gauss and Weber's Creation of the Absolute System of Units Inphysics
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Basic Magnetic Measurement Methods
Basic magnetic measurement methods Magnetic measurements in nanoelectronics 1. Vibrating sample magnetometry and related methods 2. Magnetooptical methods 3. Other methods Introduction Magnetization is a quantity of interest in many measurements involving spintronic materials ● Biot-Savart law (1820) (Jean-Baptiste Biot (1774-1862), Félix Savart (1791-1841)) Magnetic field (the proper name is magnetic flux density [1]*) of a current carrying piece of conductor is given by: μ 0 I dl̂ ×⃗r − − ⃗ 7 1 - vacuum permeability d B= μ 0=4 π10 Hm 4 π ∣⃗r∣3 ● The unit of the magnetic flux density, Tesla (1 T=1 Wb/m2), as a derive unit of Si must be based on some measurement (force, magnetic resonance) *the alternative name is magnetic induction Introduction Magnetization is a quantity of interest in many measurements involving spintronic materials ● Biot-Savart law (1820) (Jean-Baptiste Biot (1774-1862), Félix Savart (1791-1841)) Magnetic field (the proper name is magnetic flux density [1]*) of a current carrying piece of conductor is given by: μ 0 I dl̂ ×⃗r − − ⃗ 7 1 - vacuum permeability d B= μ 0=4 π10 Hm 4 π ∣⃗r∣3 ● The Physikalisch-Technische Bundesanstalt (German national metrology institute) maintains a unit Tesla in form of coils with coil constant k (ratio of the magnetic flux density to the coil current) determined based on NMR measurements graphics from: http://www.ptb.de/cms/fileadmin/internet/fachabteilungen/abteilung_2/2.5_halbleiterphysik_und_magnetismus/2.51/realization.pdf *the alternative name is magnetic induction Introduction It -
The Magnetic Moment of a Bar Magnet and the Horizontal Component of the Earth’S Magnetic Field
260 16-1 EXPERIMENT 16 THE MAGNETIC MOMENT OF A BAR MAGNET AND THE HORIZONTAL COMPONENT OF THE EARTH’S MAGNETIC FIELD I. THEORY The purpose of this experiment is to measure the magnetic moment μ of a bar magnet and the horizontal component BE of the earth's magnetic field. Since there are two unknown quantities, μ and BE, we need two independent equations containing the two unknowns. We will carry out two separate procedures: The first procedure will yield the ratio of the two unknowns; the second will yield the product. We will then solve the two equations simultaneously. The pole strength of a bar magnet may be determined by measuring the force F exerted on one pole of the magnet by an external magnetic field B0. The pole strength is then defined by p = F/B0 Note the similarity between this equation and q = F/E for electric charges. In Experiment 3 we learned that the magnitude of the magnetic field, B, due to a single magnetic pole varies as the inverse square of the distance from the pole. k′ p B = r 2 in which k' is defined to be 10-7 N/A2. Consider a bar magnet with poles a distance 2x apart. Consider also a point P, located a distance r from the center of the magnet, along a straight line which passes from the center of the magnet through the North pole. Assume that r is much larger than x. The resultant magnetic field Bm at P due to the magnet is the vector sum of a field BN directed away from the North pole, and a field BS directed toward the South pole. -
PH585: Magnetic Dipoles and So Forth
PH585: Magnetic dipoles and so forth 1 Magnetic Moments Magnetic moments ~µ are analogous to dipole moments ~p in electrostatics. There are two sorts of magnetic dipoles we will consider: a dipole consisting of two magnetic charges p separated by a distance d (a true dipole), and a current loop of area A (an approximate dipole). N p d -p I S Figure 1: (left) A magnetic dipole, consisting of two magnetic charges p separated by a distance d. The dipole moment is |~µ| = pd. (right) An approximate magnetic dipole, consisting of a loop with current I and area A. The dipole moment is |~µ| = IA. In the case of two separated magnetic charges, the dipole moment is trivially calculated by comparison with an electric dipole – substitute ~µ for ~p and p for q.i In the case of the current loop, a bit more work is required to find the moment. We will come to this shortly, for now we just quote the result ~µ=IA nˆ, where nˆ is a unit vector normal to the surface of the loop. 2 An Electrostatics Refresher In order to appreciate the magnetic dipole, we should remind ourselves first how one arrives at the field for an electric dipole. Recall Maxwell’s first equation (in the absence of polarization density): ρ ∇~ · E~ = (1) r0 If we assume that the fields are static, we can also write: ∂B~ ∇~ × E~ = − (2) ∂t This means, as you discovered in your last homework, that E~ can be written as the gradient of a scalar function ϕ, the electric potential: E~ = −∇~ ϕ (3) This lets us rewrite Eq. -
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. -
On the Covariant Representation of Integral Equations of the Electromagnetic Field
On the covariant representation of integral equations of the electromagnetic field Sergey G. Fedosin PO box 614088, Sviazeva str. 22-79, Perm, Perm Krai, Russia E-mail: [email protected] Gauss integral theorems for electric and magnetic fields, Faraday’s law of electromagnetic induction, magnetic field circulation theorem, theorems on the flux and circulation of vector potential, which are valid in curved spacetime, are presented in a covariant form. Covariant formulas for magnetic and electric fluxes, for electromotive force and circulation of the vector potential are provided. In particular, the electromotive force is expressed by a line integral over a closed curve, while in the integral, in addition to the vortex electric field strength, a determinant of the metric tensor also appears. Similarly, the magnetic flux is expressed by a surface integral from the product of magnetic field induction by the determinant of the metric tensor. A new physical quantity is introduced – the integral scalar potential, the rate of change of which over time determines the flux of vector potential through a closed surface. It is shown that the commonly used four-dimensional Kelvin-Stokes theorem does not allow one to deduce fully the integral laws of the electromagnetic field and in the covariant notation requires the addition of determinant of the metric tensor, besides the validity of the Kelvin-Stokes theorem is limited to the cases when determinant of metric tensor and the contour area are independent from time. This disadvantage is not present in the approach that uses the divergence theorem and equation for the dual electromagnetic field tensor. -
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. -
Units and Magnitudes (Lecture Notes)
physics 8.701 topic 2 Frank Wilczek Units and Magnitudes (lecture notes) This lecture has two parts. The first part is mainly a practical guide to the measurement units that dominate the particle physics literature, and culture. The second part is a quasi-philosophical discussion of deep issues around unit systems, including a comparison of atomic, particle ("strong") and Planck units. For a more extended, profound treatment of the second part issues, see arxiv.org/pdf/0708.4361v1.pdf . Because special relativity and quantum mechanics permeate modern particle physics, it is useful to employ units so that c = ħ = 1. In other words, we report velocities as multiples the speed of light c, and actions (or equivalently angular momenta) as multiples of the rationalized Planck's constant ħ, which is the original Planck constant h divided by 2π. 27 August 2013 physics 8.701 topic 2 Frank Wilczek In classical physics one usually keeps separate units for mass, length and time. I invite you to think about why! (I'll give you my take on it later.) To bring out the "dimensional" features of particle physics units without excess baggage, it is helpful to keep track of powers of mass M, length L, and time T without regard to magnitudes, in the form When these are both set equal to 1, the M, L, T system collapses to just one independent dimension. So we can - and usually do - consider everything as having the units of some power of mass. Thus for energy we have while for momentum 27 August 2013 physics 8.701 topic 2 Frank Wilczek and for length so that energy and momentum have the units of mass, while length has the units of inverse mass. -
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. -
Weberˇs Planetary Model of the Atom
Weber’s Planetary Model of the Atom Bearbeitet von Andre Koch Torres Assis, Gudrun Wolfschmidt, Karl Heinrich Wiederkehr 1. Auflage 2011. Taschenbuch. 184 S. Paperback ISBN 978 3 8424 0241 6 Format (B x L): 17 x 22 cm Weitere Fachgebiete > Physik, Astronomie > Physik Allgemein schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, eBooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte. Weber’s Planetary Model of the Atom Figure 0.1: Wilhelm Eduard Weber (1804–1891) Foto: Gudrun Wolfschmidt in der Sternwarte in Göttingen 2 Nuncius Hamburgensis Beiträge zur Geschichte der Naturwissenschaften Band 19 Andre Koch Torres Assis, Karl Heinrich Wiederkehr and Gudrun Wolfschmidt Weber’s Planetary Model of the Atom Ed. by Gudrun Wolfschmidt Hamburg: tredition science 2011 Nuncius Hamburgensis Beiträge zur Geschichte der Naturwissenschaften Hg. von Gudrun Wolfschmidt, Geschichte der Naturwissenschaften, Mathematik und Technik, Universität Hamburg – ISSN 1610-6164 Diese Reihe „Nuncius Hamburgensis“ wird gefördert von der Hans Schimank-Gedächtnisstiftung. Dieser Titel wurde inspiriert von „Sidereus Nuncius“ und von „Wandsbeker Bote“. Andre Koch Torres Assis, Karl Heinrich Wiederkehr and Gudrun Wolfschmidt: Weber’s Planetary Model of the Atom. Ed. by Gudrun Wolfschmidt. Nuncius Hamburgensis – Beiträge zur Geschichte der Naturwissenschaften, Band 19. Hamburg: tredition science 2011. Abbildung auf dem Cover vorne und Titelblatt: Wilhelm Weber (Kohlrausch, F. (Oswalds Klassiker Nr. 142) 1904, Frontispiz) Frontispiz: Wilhelm Weber (1804–1891) (Feyerabend 1933, nach S. -
Permanent Magnet DC Motors Catalog
Catalog DC05EN Permanent Magnet DC Motors Drives DirectPower Series DA-Series DirectPower Plus Series SC-Series PRO Series www.electrocraft.com www.electrocraft.com For over 60 years, ElectroCraft has been helping engineers translate innovative ideas into reality – one reliable motor at a time. As a global specialist in custom motor and motion technology, we provide the engineering capabilities and worldwide resources you need to succeed. This guide has been developed as a quick reference tool for ElectroCraft products. It is not intended to replace technical documentation or proper use of standards and codes in installation of product. Because of the variety of uses for the products described in this publication, those responsible for the application and use of this product must satisfy themselves that all necessary steps have been taken to ensure that each application and use meets all performance and safety requirements, including all applicable laws, regulations, codes and standards. Reproduction of the contents of this copyrighted publication, in whole or in part without written permission of ElectroCraft is prohibited. Designed by stilbruch · www.stilbruch.me ElectroCraft DirectPower™, DirectPower™ Plus, DA-Series, SC-Series & PRO Series Drives 2 Table of Contents Typical Applications . 3 Which PMDC Motor . 5 PMDC Drive Product Matrix . .6 DirectPower Series . 7 DP20 . 7 DP25 . 9 DP DP30 . 11 DirectPower Plus Series . 13 DPP240 . 13 DPP640 . 15 DPP DPP680 . 17 DPP700 . 19 DPP720 . 21 DA-Series. 23 DA43 . 23 DA DA47 . 25 SC-Series . .27 SCA-L . .27 SCA-S . .29 SC SCA-SS . 31 PRO Series . 33 PRO-A04V36 . 35 PRO-A08V48 . 37 PRO PRO-A10V80 . -
The Concept of Field in the History of Electromagnetism
The concept of field in the history of electromagnetism Giovanni Miano Department of Electrical Engineering University of Naples Federico II ET2011-XXVII Riunione Annuale dei Ricercatori di Elettrotecnica Bologna 16-17 giugno 2011 Celebration of the 150th Birthday of Maxwell’s Equations 150 years ago (on March 1861) a young Maxwell (30 years old) published the first part of the paper On physical lines of force in which he wrote down the equations that, by bringing together the physics of electricity and magnetism, laid the foundations for electromagnetism and modern physics. Statue of Maxwell with its dog Toby. Plaque on E-side of the statue. Edinburgh, George Street. Talk Outline ! A brief survey of the birth of the electromagnetism: a long and intriguing story ! A rapid comparison of Weber’s electrodynamics and Maxwell’s theory: “direct action at distance” and “field theory” General References E. T. Wittaker, Theories of Aether and Electricity, Longam, Green and Co., London, 1910. O. Darrigol, Electrodynamics from Ampère to Einste in, Oxford University Press, 2000. O. M. Bucci, The Genesis of Maxwell’s Equations, in “History of Wireless”, T. K. Sarkar et al. Eds., Wiley-Interscience, 2006. Magnetism and Electricity In 1600 Gilbert published the “De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure” (On the Magnet and Magnetic Bodies, and on That Great Magnet the Earth). ! The Earth is magnetic ()*+(,-.*, Magnesia ad Sipylum) and this is why a compass points north. ! In a quite large class of bodies (glass, sulphur, …) the friction induces the same effect observed in the amber (!"#$%&'(, Elektron). Gilbert gave to it the name “electricus”. -
08. Ampère and Faraday Darrigol (2000), Chap 1
08. Ampère and Faraday Darrigol (2000), Chap 1. A. Pre-1820. (1) Electrostatics (frictional electricity) • 1780s. Coulomb's description: ! Two electric fluids: positive and negative. ! Inverse square law: It follows therefore from these three tests, that the repulsive force that the two balls -- [which were] electrified with the same kind of electricity -- exert on each other, Charles-Augustin de Coulomb follows the inverse proportion of (1736-1806) the square of the distance."" (2) Magnetism: Coulomb's description: • Two fluids ("astral" and "boreal") obeying inverse square law. • No magnetic monopoles: fluids are imprisoned in molecules of magnetic bodies. (3) Galvanism • 1770s. Galvani's frog legs. "Animal electricity": phenomenon belongs to biology. • 1800. Volta's ("volatic") pile. Luigi Galvani (1737-1798) • Pile consists of alternating copper and • Charged rod connected zinc plates separated by to inner foil. brine-soaked cloth. • Outer foil grounded. • A "battery" of Leyden • Inner and outer jars that can surfaces store equal spontaeously recharge but opposite charges. themselves. 1745 Leyden jar. • Volta: Pile is an electric phenomenon and belongs to physics. • But: Nicholson and Carlisle use voltaic current to decompose Alessandro Volta water into hydrogen and oxygen. Pile belongs to chemistry! (1745-1827) • Are electricity and magnetism different phenomena? ! Electricity involves violent actions and effects: sparks, thunder, etc. ! Magnetism is more quiet... Hans Christian • 1820. Oersted's Experimenta circa effectum conflictus elecrici in Oersted (1777-1851) acum magneticam ("Experiments on the effect of an electric conflict on the magnetic needle"). ! Galvanic current = an "electric conflict" between decompositions and recompositions of positive and negative electricities. ! Experiments with a galvanic source, connecting wire, and rotating magnetic needle: Needle moves in presence of pile! "Otherwise one could not understand how Oersted's Claims the same portion of the wire drives the • Electric conflict acts on magnetic poles.