Experiment IV: Magnetic Fields and Inductance
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Magnetic Fields Magnetism Magnetic Field
PHY2061 Enriched Physics 2 Lecture Notes Magnetic Fields Magnetic Fields Disclaimer: These lecture notes are not meant to replace the course textbook. The content may be incomplete. Some topics may be unclear. These notes are only meant to be a study aid and a supplement to your own notes. Please report any inaccuracies to the professor. Magnetism Is ubiquitous in every-day life! • Refrigerator magnets (who could live without them?) • Coils that deflect the electron beam in a CRT television or monitor • Cassette tape storage (audio or digital) • Computer disk drive storage • Electromagnet for Magnetic Resonant Imaging (MRI) Magnetic Field Magnets contain two poles: “north” and “south”. The force between like-poles repels (north-north, south-south), while opposite poles attract (north-south). This is reminiscent of the electric force between two charged objects (which can have positive or negative charge). Recall that the electric field was invoked to explain the “action at a distance” effect of the electric force, and was defined by: F E = qel where qel is electric charge of a positive test charge and F is the force acting on it. We might be tempted to define the same for the magnetic field, and write: F B = qmag where qmag is the “magnetic charge” of a positive test charge and F is the force acting on it. However, such a single magnetic charge, a “magnetic monopole,” has never been observed experimentally! You cannot break a bar magnet in half to get just a north pole or a south pole. As far as we know, no such single magnetic charges exist in the universe, D. -
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. -
Chapter 7 Magnetism and Electromagnetism
Chapter 7 Magnetism and Electromagnetism Objectives • Explain the principles of the magnetic field • Explain the principles of electromagnetism • Describe the principle of operation for several types of electromagnetic devices • Explain magnetic hysteresis • Discuss the principle of electromagnetic induction • Describe some applications of electromagnetic induction 1 The Magnetic Field • A permanent magnet has a magnetic field surrounding it • A magnetic field is envisioned to consist of lines of force that radiate from the north pole to the south pole and back to the north pole through the magnetic material Attraction and Repulsion • Unlike magnetic poles have an attractive force between them • Two like poles repel each other 2 Altering a Magnetic Field • When nonmagnetic materials such as paper, glass, wood or plastic are placed in a magnetic field, the lines of force are unaltered • When a magnetic material such as iron is placed in a magnetic field, the lines of force tend to be altered to pass through the magnetic material Magnetic Flux • The force lines going from the north pole to the south pole of a magnet are called magnetic flux (φ); units: weber (Wb) •The magnetic flux density (B) is the amount of flux per unit area perpendicular to the magnetic field; units: tesla (T) 3 Magnetizing Materials • Ferromagnetic materials such as iron, nickel and cobalt have randomly oriented magnetic domains, which become aligned when placed in a magnetic field, thus they effectively become magnets Electromagnetism • Electromagnetism is the production -
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 22 Magnetism
Chapter 22 Magnetism 22.1 The Magnetic Field 22.2 The Magnetic Force on Moving Charges 22.3 The Motion of Charged particles in a Magnetic Field 22.4 The Magnetic Force Exerted on a Current- Carrying Wire 22.5 Loops of Current and Magnetic Torque 22.6 Electric Current, Magnetic Fields, and Ampere’s Law Magnetism – Is this a new force? Bar magnets (compass needle) align themselves in a north-south direction. Poles: Unlike poles attract, like poles repel Magnet has NO effect on an electroscope and is not influenced by gravity Magnets attract only some objects (iron, nickel etc) No magnets ever repel non magnets Magnets have no effect on things like copper or brass Cut a bar magnet-you get two smaller magnets (no magnetic monopoles) Earth is like a huge bar magnet Figure 22–1 The force between two bar magnets (a) Opposite poles attract each other. (b) The force between like poles is repulsive. Figure 22–2 Magnets always have two poles When a bar magnet is broken in half two new poles appear. Each half has both a north pole and a south pole, just like any other bar magnet. Figure 22–4 Magnetic field lines for a bar magnet The field lines are closely spaced near the poles, where the magnetic field B is most intense. In addition, the lines form closed loops that leave at the north pole of the magnet and enter at the south pole. Magnetic Field Lines If a compass is placed in a magnetic field the needle lines up with the field. -
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. -
Revision Pack Topic 7- Magnetism & Electromagnetism
Revision Pack Topic 7- Magnetism & Electromagnetism Permanent and induced magnetism, magnetic forces and fields R/A/G Poles of a magnet The poles of a magnet are the places where the magnetic forces are strongest. When two magnets are brought close together they exert a force on each other. Two like poles repel each other. Two unlike poles attract each other. Attraction and repulsion between two magnetic poles are examples of non-contact force. A permanent magnet produces its own magnetic field. An induced magnet is a material that becomes a magnet when it is placed in a magnetic field. Induced magnetism always causes a force of attraction. When removed from the magnetic field an induced magnet loses most/all of its magnetism quickly. Magnetic fields The region around a magnet where a force acts on another magnet or on a magnetic material (iron, steel, cobalt and nickel) is called the magnetic field. The force between a magnet and a magnetic material is always one of attraction. The strength of the magnetic field depends on the distance from the magnet. The field is strongest at the poles of the magnet. The direction of the magnetic field at any point is given by the direction of the force that would act on another north pole placed at that point. The direction of a magnetic field line is from the north (seeking) pole of a magnet to the south (seeking) pole of the magnet. A magnetic compass contains a small bar magnet. The Earth has a magnetic field. The compass needle points in the direction of the Earth’s magnetic field. -
Electricity and Magnetism Inductance Transformers Maxwell's Laws
Electricity and Magnetism Inductance Transformers Maxwell's Laws Lana Sheridan De Anza College Dec 1, 2015 Last time • Ampere's law • Faraday's law • Lenz's law Overview • induction and energy transfer • induced electric fields • inductance • self-induction • RL Circuits Inductors A capacitor is a device that stores an electric field as a component of a circuit. inductor a device that stores a magnetic field in a circuit It is typically a coil of wire. 782 Chapter 26 Capacitance and Dielectrics ▸ 26.2 continued Categorize Because of the spherical symmetry of the sys- ϪQ tem, we can use results from previous studies of spherical Figure 26.5 (Example 26.2) systems to find the capacitance. A spherical capacitor consists of an inner sphere of radius a sur- ϩQ a Analyze As shown in Chapter 24, the direction of the rounded by a concentric spherical electric field outside a spherically symmetric charge shell of radius b. The electric field b distribution is radial and its magnitude is given by the between the spheres is directed expression E 5 k Q /r 2. In this case, this result applies to radially outward when the inner e sphere is positively charged. 820 the field Cbetweenhapter 27 the C spheresurrent and (a R esistance, r , b). b S Write an expression for the potential difference between 2 52 ? S 782 Chapter 26 Capacitance and DielectricsTable 27.3 CriticalVb TemperaturesVa 3 E d s a the two conductors from Equation 25.3: for Various Superconductors ▸ 26.2 continued Material Tc (K) b b dr 1 b ApplyCategorize the result Because of Example of the spherical 24.3 forsymmetry the electric ofHgBa the sys 2fieldCa- 2Cu 3O8 2 52134 52 Ϫ5Q Vb Va 3 Er dr ke Q 3 2 ke Q Tl—Ba—Ca—Cu—O 125a a r r a outsidetem, wea sphericallycan use results symmetric from previous charge studies distribution of spherical Figure 26.5 (Example 26.2) systems to findS the capacitance. -
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. -
Magnetism in Transition Metal Complexes
Magnetism for Chemists I. Introduction to Magnetism II. Survey of Magnetic Behavior III. Van Vleck’s Equation III. Applications A. Complexed ions and SOC B. Inter-Atomic Magnetic “Exchange” Interactions © 2012, K.S. Suslick Magnetism Intro 1. Magnetic properties depend on # of unpaired e- and how they interact with one another. 2. Magnetic susceptibility measures ease of alignment of electron spins in an external magnetic field . 3. Magnetic response of e- to an external magnetic field ~ 1000 times that of even the most magnetic nuclei. 4. Best definition of a magnet: a solid in which more electrons point in one direction than in any other direction © 2012, K.S. Suslick 1 Uses of Magnetic Susceptibility 1. Determine # of unpaired e- 2. Magnitude of Spin-Orbit Coupling. 3. Thermal populations of low lying excited states (e.g., spin-crossover complexes). 4. Intra- and Inter- Molecular magnetic exchange interactions. © 2012, K.S. Suslick Response to a Magnetic Field • For a given Hexternal, the magnetic field in the material is B B = Magnetic Induction (tesla) inside the material current I • Magnetic susceptibility, (dimensionless) B > 0 measures the vacuum = 0 material response < 0 relative to a vacuum. H © 2012, K.S. Suslick 2 Magnetic field definitions B – magnetic induction Two quantities H – magnetic intensity describing a magnetic field (Système Internationale, SI) In vacuum: B = µ0H -7 -2 µ0 = 4π · 10 N A - the permeability of free space (the permeability constant) B = H (cgs: centimeter, gram, second) © 2012, K.S. Suslick Magnetism: Definitions The magnetic field inside a substance differs from the free- space value of the applied field: → → → H = H0 + ∆H inside sample applied field shielding/deshielding due to induced internal field Usually, this equation is rewritten as (physicists use B for H): → → → B = H0 + 4 π M magnetic induction magnetization (mag.