Electromagnetic Fields Fact Sheet
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Electrostatics Voltage Source
012-07038B Instruction Sheet for the PASCO Model ES-9077 ELECTROSTATICS VOLTAGE SOURCE Specifications Ranges: • Fixed 1000, 2000, 3000 VDC ±10%, unregulated (maximum short circuit current less than 0.01 mA). • 30 VDC ±5%, 1mA max. Power: • 110-130 VDC, 60 Hz, ES-9077 • 220/240 VDC, 50 Hz, ES-9077-220 Dimensions: Introduction • 5 1/2” X 5” X 1”, plus AC adapter and red/black The ES-9077 is a high voltage, low current power cable set supply designed exclusively for experiments in electrostatics. It has outputs at 30 volts DC for IMPORTANT: To prevent the risk of capacitor plate experiments, and fixed 1 kV, 2 kV, and electric shock, do not remove the cover 3 kV outputs for Faraday ice pail and conducting on the unit. There are no user sphere experiments. With the exception of the 30 volt serviceable parts inside. Refer servicing output, all of the voltage outputs have a series to qualified service personnel. resistance associated with them which limit the available short-circuit output current to about 8.3 microamps. The 30 volt output is regulated but is Operation capable of delivering only about 1 milliamp before When using the Electrostatics Voltage Source to power falling out of regulation. other electric circuits, (like RC networks), use only the 30V output (Remember that the maximum drain is 1 Equipment Included: mA.). • Voltage Source Use the special high-voltage leads that are supplied with • Red/black, banana plug to spade lug cable the ES-9077 to make connections. Use of other leads • 9 VDC power supply may allow significant leakage from the leads to ground and negatively affect output voltage accuracy. -
The Lorentz Force
CLASSICAL CONCEPT REVIEW 14 The Lorentz Force We can find empirically that a particle with mass m and electric charge q in an elec- tric field E experiences a force FE given by FE = q E LF-1 It is apparent from Equation LF-1 that, if q is a positive charge (e.g., a proton), FE is parallel to, that is, in the direction of E and if q is a negative charge (e.g., an electron), FE is antiparallel to, that is, opposite to the direction of E (see Figure LF-1). A posi- tive charge moving parallel to E or a negative charge moving antiparallel to E is, in the absence of other forces of significance, accelerated according to Newton’s second law: q F q E m a a E LF-2 E = = 1 = m Equation LF-2 is, of course, not relativistically correct. The relativistically correct force is given by d g mu u2 -3 2 du u2 -3 2 FE = q E = = m 1 - = m 1 - a LF-3 dt c2 > dt c2 > 1 2 a b a b 3 Classically, for example, suppose a proton initially moving at v0 = 10 m s enters a region of uniform electric field of magnitude E = 500 V m antiparallel to the direction of E (see Figure LF-2a). How far does it travel before coming (instanta> - neously) to rest? From Equation LF-2 the acceleration slowing the proton> is q 1.60 * 10-19 C 500 V m a = - E = - = -4.79 * 1010 m s2 m 1.67 * 10-27 kg 1 2 1 > 2 E > The distance Dx traveled by the proton until it comes to rest with vf 0 is given by FE • –q +q • FE 2 2 3 2 vf - v0 0 - 10 m s Dx = = 2a 2 4.79 1010 m s2 - 1* > 2 1 > 2 Dx 1.04 10-5 m 1.04 10-3 cm Ϸ 0.01 mm = * = * LF-1 A positively charged particle in an electric field experiences a If the same proton is injected into the field perpendicular to E (or at some angle force in the direction of the field. -
Quantum Mechanics Electromotive Force
Quantum Mechanics_Electromotive force . Electromotive force, also called emf[1] (denoted and measured in volts), is the voltage developed by any source of electrical energy such as a batteryor dynamo.[2] The word "force" in this case is not used to mean mechanical force, measured in newtons, but a potential, or energy per unit of charge, measured involts. In electromagnetic induction, emf can be defined around a closed loop as the electromagnetic workthat would be transferred to a unit of charge if it travels once around that loop.[3] (While the charge travels around the loop, it can simultaneously lose the energy via resistance into thermal energy.) For a time-varying magnetic flux impinging a loop, theElectric potential scalar field is not defined due to circulating electric vector field, but nevertheless an emf does work that can be measured as a virtual electric potential around that loop.[4] In a two-terminal device (such as an electrochemical cell or electromagnetic generator), the emf can be measured as the open-circuit potential difference across the two terminals. The potential difference thus created drives current flow if an external circuit is attached to the source of emf. When current flows, however, the potential difference across the terminals is no longer equal to the emf, but will be smaller because of the voltage drop within the device due to its internal resistance. Devices that can provide emf includeelectrochemical cells, thermoelectric devices, solar cells and photodiodes, electrical generators,transformers, and even Van de Graaff generators.[4][5] In nature, emf is generated whenever magnetic field fluctuations occur through a surface. -
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. -
Capacitance and Dielectrics Capacitance
Capacitance and Dielectrics Capacitance General Definition: C === q /V Special case for parallel plates: εεε A C === 0 d Potential Energy • I must do work to charge up a capacitor. • This energy is stored in the form of electric potential energy. Q2 • We showed that this is U === 2C • Then we saw that this energy is stored in the electric field, with a volume energy density 1 2 u === 2 εεε0 E Potential difference and Electric field Since potential difference is work per unit charge, b ∆∆∆V === Edx ∫∫∫a For the parallel-plate capacitor E is uniform, so V === Ed Also for parallel-plate case Gauss’s Law gives Q Q εεε0 A E === σσσ /εεε0 === === Vd so C === === εεε0 A V d Spherical example A spherical capacitor has inner radius a = 3mm, outer radius b = 6mm. The charge on the inner sphere is q = 2 C. What is the potential difference? kq From Gauss’s Law or the Shell E === Theorem, the field inside is r 2 From definition of b kq 1 1 V === dr === kq −−− potential difference 2 ∫∫∫a r a b 1 1 1 1 === 9 ×××109 ××× 2 ×××10−−−9 −−− === 18 ×××103 −−− === 3 ×××103 V −−−3 −−−3 3 ×××10 6 ×××10 3 6 What is the capacitance? C === Q /V === 2( C) /(3000V ) === 7.6 ×××10−−−4 F A capacitor has capacitance C = 6 µF and charge Q = 2 nC. If the charge is Q.25-1 increased to 4 nC what will be the new capacitance? (1) 3 µF (2) 6 µF (3) 12 µF (4) 24 µF Q. -
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. -
Measuring Electricity Voltage Current Voltage Current
Measuring Electricity Electricity makes our lives easier, but it can seem like a mysterious force. Measuring electricity is confusing because we cannot see it. We are familiar with terms such as watt, volt, and amp, but we do not have a clear understanding of these terms. We buy a 60-watt lightbulb, a tool that needs 120 volts, or a vacuum cleaner that uses 8.8 amps, and dont think about what those units mean. Using the flow of water as an analogy can make Voltage electricity easier to understand. The flow of electrons in a circuit is similar to water flowing through a hose. If you could look into a hose at a given point, you would see a certain amount of water passing that point each second. The amount of water depends on how much pressure is being applied how hard the water is being pushed. It also depends on the diameter of the hose. The harder the pressure and the larger the diameter of the hose, the more water passes each second. The flow of electrons through a wire depends on the electrical pressure pushing the electrons and on the Current cross-sectional area of the wire. The flow of electrons can be compared to the flow of Voltage water. The water current is the number of molecules flowing past a fixed point; electrical current is the The pressure that pushes electrons in a circuit is number of electrons flowing past a fixed point. called voltage. Using the water analogy, if a tank of Electrical current (I) is defined as electrons flowing water were suspended one meter above the ground between two points having a difference in voltage. -
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. -
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. -
Minutes of Claremore Public Works Authority Meeting Council Chambers, City Hall, 104 S
MINUTES OF CLAREMORE PUBLIC WORKS AUTHORITY MEETING COUNCIL CHAMBERS, CITY HALL, 104 S. MUSKOGEE, CLAREMORE, OKLAHOMA MARCH 03, 2008 CALL TO ORDER Meeting called to order by Mayor Brant Shallenburger at 6:00 P.M. ROLL CALL Nan Pope called roll. The following were: Present: Brant Shallenburger, Buddy Robertson, Tony Mullenger, Flo Guthrie, Mick Webber, Terry Chase, Tom Lehman, Paula Watson Absent: Don Myers Staff Present: City Manager Troy Powell, Nan Pope, Serena Kauk, Matt Mueller, Randy Elliott, Cassie Sowers, Phil Stowell, Steve Lett, Daryl Golbek, Joe Kays, Gene Edwards, Tim Miller, Tamryn Cluck, Mark Dowler Pledge of Allegiance by all. Invocation by James Graham, Verdigris United Methodist Church. ACCEPTANCE OF AGENDA Motion by Mullenger, second by Lehman that the agenda for the regular CPWA meeting of March 03, 2008, be approved as written. 8 yes, Mullenger, Lehman, Robertson, Guthrie, Shallenburger, Webber, Chase, Watson. ITEMS UNFORESEEN AT THE TIME AGENDA WAS POSTED None CALL TO THE PUBLIC None CURRENT BUSINESS Motion by Mullenger, second by Lehman to approve the following consent items: (a) Minutes of Claremore Public Works Authority meeting on February 18, 2008, as printed. (b) All claims as printed. (c) Approve budget supplement for upgrading the electric distribution system and adding an additional Substation for the new Oklahoma Plaza Development - $586,985 - Leasehold improvements to new project number assignment. (Serena Kauk) (d) Approve budget supplement for purchase of an additional concrete control house for new Substation #5 for Oklahoma Plaza Development - $93,946 - Leasehold improvements to new project number assignment. (Serena Kauk) (e) Approve budget supplement for electrical engineering contract with Ledbetter, Corner and Associates for engineering design phase for Substation #5 - Oklahoma Plaza Development - $198,488 - Leasehold improvements to new project number assignment. -
Paul Hertz Astrophysics Subcommittee
Paul Hertz Astrophysics Subcommittee February 23, 2012 Agenda • Science Highlights • Organizational Changes • Program Update • President’s FY13 Budget Request • Addressing Decadal Survey Priorities 2 Chandra Finds Milky Way’s Black Hole Grazing on Asteroids • The giant black hole at the center of the Milky Way may be vaporizing and devouring asteroids, which could explain the frequent flares observed, according to astronomers using data from NASA's Chandra X-ray Observatory. For several years Chandra has detected X-ray flares about once a day from the supermassive black hole known as Sagittarius A*, or "Sgr A*" for short. The flares last a few hours with brightness ranging from a few times to nearly one hundred times that of the black hole's regular output. The flares also have been seen in infrared data from ESO's Very Large Telescope in Chile. • Scientists suggest there is a cloud around Sgr A* containing trillions of asteroids and comets, stripped from their parent stars. Asteroids passing within about 100 million miles of the black hole, roughly the distance between the Earth and the sun, would be torn into pieces by the tidal forces from the black hole. • These fragments then would be vaporized by friction as they pass through the hot, thin gas flowing onto Sgr A*, similar to a meteor heating up and glowing as it falls through Earth's atmosphere. A flare is produced and the remains of the asteroid are eventually swallowed by the black hole. • The authors estimate that it would take asteroids larger than about six miles in radius to generate the flares observed by Chandra. -
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.