Earth's Vertical Electric Field Introduction
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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. -
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. -
Chapter 5 Capacitance and Dielectrics
Chapter 5 Capacitance and Dielectrics 5.1 Introduction...........................................................................................................5-3 5.2 Calculation of Capacitance ...................................................................................5-4 Example 5.1: Parallel-Plate Capacitor ....................................................................5-4 Interactive Simulation 5.1: Parallel-Plate Capacitor ...........................................5-6 Example 5.2: Cylindrical Capacitor........................................................................5-6 Example 5.3: Spherical Capacitor...........................................................................5-8 5.3 Capacitors in Electric Circuits ..............................................................................5-9 5.3.1 Parallel Connection......................................................................................5-10 5.3.2 Series Connection ........................................................................................5-11 Example 5.4: Equivalent Capacitance ..................................................................5-12 5.4 Storing Energy in a Capacitor.............................................................................5-13 5.4.1 Energy Density of the Electric Field............................................................5-14 Interactive Simulation 5.2: Charge Placed between Capacitor Plates..............5-14 Example 5.5: Electric Energy Density of Dry Air................................................5-15 -
Electromagnetic Hypersensitivity
Electromagnetic Hypersensitivity Proceedings International Workshop on EMF Hypersensitivity Prague, Czech Republic October 25-27, 2004 Editors Kjell Hansson Mild Mike Repacholi Emilie van Deventer Paolo Ravazzani WHO Library Cataloguing-in-Publication Data: International Workshop on Electromagnetic Field Hypersensitivity (2004 : Prague, Czech Republic) Electromagnetic Hypersensitivity : proceedings, International Workshop on Electromagnetic Field Hypersensitivity, Prague, Czech Republic, October 25-27, 2004 / editors, Kjell Hansson Mild, Mike Repacholi, Emilie van Deventer, and Paolo Ravazzani. 1.Electromagnetic fields - adverse effects. 2.Hypersensitivity. 3.Environmental exposure. 4.Psychophysiologic disorders. I.Mild, Kjell Hansson. II.Repacholi, Michael H. III.Deventer, Emilie van. IV.Ravazzani, Paolo. V.World Health Organization. VI.Title. VII.Title: Proceedings, International Workshop on Electromagnetic Field Hypersensitivity, Prague, Czech Republic, October 25-27, 2004. ISBN 92 4 159412 8 (NLM classification: QT 34) ISBN 978 92 4 159412 7 © World Health Organization 2006 All rights reserved. Publications of the World Health Organization can be obtained from WHO Press, World Health Organization, 20 Avenue Appia, 1211 Geneva 27, Switzerland (tel: +41 22 791 3264; fax: +41 22 791 4857; email: [email protected]). Requests for permission to reproduce or translate WHO publications – whether for sale or for noncommercial distribution – should be addressed to WHO Press, at the above address (fax: +41 22 791 4806; email: [email protected]). The designations employed and the presentation of the material in this publication do not imply the expression of any opinion whatsoever on the part of the World Health Organization concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. -
Electric Potential
Electric Potential • Electric Potential energy: b U F dl elec elec a • Electric Potential: b V E dl a Field is the (negative of) the Gradient of Potential dU dV F E x dx x dx dU dV F UF E VE y dy y dy dU dV F E z dz z dz In what direction can you move relative to an electric field so that the electric potential does not change? 1)parallel to the electric field 2)perpendicular to the electric field 3)Some other direction. 4)The answer depends on the symmetry of the situation. Electric field of single point charge kq E = rˆ r2 Electric potential of single point charge b V E dl a kq Er ˆ r 2 b kq V rˆ dl 2 a r Electric potential of single point charge b V E dl a kq Er ˆ r 2 b kq V rˆ dl 2 a r kq kq VVV ba rrba kq V const. r 0 by convention Potential for Multiple Charges EEEE1 2 3 b V E dl a b b b E dl E dl E dl 1 2 3 a a a VVVV 1 2 3 Charges Q and q (Q ≠ q), separated by a distance d, produce a potential VP = 0 at point P. This means that 1) no force is acting on a test charge placed at point P. 2) Q and q must have the same sign. 3) the electric field must be zero at point P. 4) the net work in bringing Q to distance d from q is zero. -
Handbook of Induction Heating Theoretical Background
This article was downloaded by: 10.3.98.104 On: 28 Sep 2021 Access details: subscription number Publisher: CRC Press Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: 5 Howick Place, London SW1P 1WG, UK Handbook of Induction Heating Valery Rudnev, Don Loveless, Raymond L. Cook Theoretical Background Publication details https://www.routledgehandbooks.com/doi/10.1201/9781315117485-3 Valery Rudnev, Don Loveless, Raymond L. Cook Published online on: 11 Jul 2017 How to cite :- Valery Rudnev, Don Loveless, Raymond L. Cook. 11 Jul 2017, Theoretical Background from: Handbook of Induction Heating CRC Press Accessed on: 28 Sep 2021 https://www.routledgehandbooks.com/doi/10.1201/9781315117485-3 PLEASE SCROLL DOWN FOR DOCUMENT Full terms and conditions of use: https://www.routledgehandbooks.com/legal-notices/terms This Document PDF may be used for research, teaching and private study purposes. Any substantial or systematic reproductions, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The publisher shall not be liable for an loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. 3 Theoretical Background Induction heating (IH) is a multiphysical phenomenon comprising a complex interac- tion of electromagnetic, heat transfer, metallurgical phenomena, and circuit analysis that are tightly interrelated and highly nonlinear because the physical properties of materi- als depend on magnetic field intensity, temperature, and microstructure. -
Physics 2102 Lecture 2
Physics 2102 Jonathan Dowling PPhhyyssicicss 22110022 LLeeccttuurree 22 Charles-Augustin de Coulomb EElleeccttrriicc FFiieellddss (1736-1806) January 17, 07 Version: 1/17/07 WWhhaatt aarree wwee ggooiinngg ttoo lleeaarrnn?? AA rrooaadd mmaapp • Electric charge Electric force on other electric charges Electric field, and electric potential • Moving electric charges : current • Electronic circuit components: batteries, resistors, capacitors • Electric currents Magnetic field Magnetic force on moving charges • Time-varying magnetic field Electric Field • More circuit components: inductors. • Electromagnetic waves light waves • Geometrical Optics (light rays). • Physical optics (light waves) CoulombCoulomb’’ss lawlaw +q1 F12 F21 !q2 r12 For charges in a k | q || q | VACUUM | F | 1 2 12 = 2 2 N m r k = 8.99 !109 12 C 2 Often, we write k as: 2 1 !12 C k = with #0 = 8.85"10 2 4$#0 N m EEleleccttrricic FFieieldldss • Electric field E at some point in space is defined as the force experienced by an imaginary point charge of +1 C, divided by Electric field of a point charge 1 C. • Note that E is a VECTOR. +1 C • Since E is the force per unit q charge, it is measured in units of E N/C. • We measure the electric field R using very small “test charges”, and dividing the measured force k | q | by the magnitude of the charge. | E |= R2 SSuuppeerrppoossititioionn • Question: How do we figure out the field due to several point charges? • Answer: consider one charge at a time, calculate the field (a vector!) produced by each charge, and then add all the vectors! (“superposition”) • Useful to look out for SYMMETRY to simplify calculations! Example Total electric field +q -2q • 4 charges are placed at the corners of a square as shown. -
Upward Electrical Discharges from Thunderstorm Tops
UPWARD ELECTRICAL DISCHARGES FROM THUNDERSTORM TOPS BY WALTER A. LYONS, CCM, THOMAS E. NELSON, RUSSELL A. ARMSTRONG, VICTOR P. PASKO, AND MARK A. STANLEY Mesospheric lightning-related sprites and elves, not attached to their parent thunderstorm’s tops, are being joined by a family of upward electrical discharges, including blue jets, emerging directly from thunderstorm tops. or over 100 years, persistent eyewitness reports in (Wilson 1956). On the night of 6 July 1989, while the scientific literature have recounted a variety testing a low-light television camera (LLTV) for an Fof brief atmospheric electrical phenomena above upcoming rocket launch, the late Prof. John R. thunderstorms (Lyons et al. 2000). The startled ob- Winckler of the University of Minnesota made a most servers, not possessing a technical vocabulary with serendipitous observation. Replay of the video tape which to report their observations, used terms as var- revealed two frames showing brilliant columns of ied as “rocket lightning,” “cloud-to-stratosphere light extending far into the stratosphere above dis- lightning,” “upward lightning,” and even “cloud-to- tant thunderstorms (Franz et al. 1990). This single space lightning” (Fig. 1). Absent hard documenta- observation has energized specialists in scientific dis- tion, the atmospheric electricity community gave ciplines as diverse as space physics, radio science, at- little credence to such anecdotal reports, even one mospheric electricity, atmospheric acoustics, and originating with a Nobel Prize winner in physics -
Electrical Structure of the Stratosphere and Mesophere
1969 (6th) Vol. 1 Space, Technology, and The Space Congress® Proceedings Society Apr 1st, 8:00 AM Electrical Structure of the Stratosphere and Mesophere Willis L. Webb U.S. Army Electronics Command Follow this and additional works at: https://commons.erau.edu/space-congress-proceedings Scholarly Commons Citation Webb, Willis L., "Electrical Structure of the Stratosphere and Mesophere" (1969). The Space Congress® Proceedings. 1. https://commons.erau.edu/space-congress-proceedings/proceedings-1969-6th-v1/session-16/1 This Event is brought to you for free and open access by the Conferences at Scholarly Commons. It has been accepted for inclusion in The Space Congress® Proceedings by an authorized administrator of Scholarly Commons. For more information, please contact [email protected]. ELECTRICAL STRUCTURE OF THE STRATOSPHERE AND MESOSPHERE Will is L. V/ebb Atmospheric Sciences Laboratory U S Army Electronics Command White Sands Missile Range, New Mexico Synoptic rocket exploration of the strato exploration of the earth's upper atmosphere using spheric circulation has revealed the presence of small rocket vehicles was initiated to extend the hemispheric tidal circulations that are indicated region of meteorological study to higher alti to be in part characterized by systematic vertical tudes* . This meteorological rocket network (MRN) motions in low latitudes of the sunlit hemisphere. has expanded the atmospheric volume currently sub These vertical motions are powered by meridional ject to meteorological scrutiny from limitations oscillations in the stratospheric circulation pro of the order of 30-km peak altitude to a current duced by solar heating of the stratopause region synoptic data ceiling of the order of 80 km. -
Frequency Dependence of the Permittivity
Frequency dependence of the permittivity February 7, 2016 In materials, the dielectric “constant” and permeability are actually frequency dependent. This does not affect our results for single frequency modes, but when we have a superposition of frequencies it leads to dispersion. We begin with a simple model for this behavior. The variation of the permeability is often quite weak, and we may take µ = µ0. 1 Frequency dependence of the permittivity 1.1 Permittivity produced by a static field The electrostatic treatment of the dielectric constant begins with the electric dipole moment produced by 2 an electron in a static electric field E. The electron experiences a linear restoring force, F = −m!0x, 2 eE = m!0x where !0 characterizes the strength of the atom’s restoring potential. The resulting displacement of charge, eE x = 2 , produces a molecular polarization m!0 pmol = ex eE = 2 m!0 Then, if there are N molecules per unit volume with Z electrons per molecule, the dipole moment per unit volume is P = NZpmol ≡ 0χeE so that NZe2 0χe = 2 m!0 Next, using D = 0E + P E = 0E + 0χeE the relative dielectric constant is = = 1 + χe 0 NZe2 = 1 + 2 m!00 This result changes when there is time dependence to the electric field, with the dielectric constant showing frequency dependence. 1 1.2 Permittivity in the presence of an oscillating electric field Suppose the material is sufficiently diffuse that the applied electric field is about equal to the electric field at each atom, and that the response of the atomic electrons may be modeled as harmonic. -
Magnetic Fields and Forces
Magnetic Fields and Forces (1) Magnetic Fields are produced by moving charges. (2) Magnetic Fields exert forces on moving charges. (3) Stationary Charges do not produce magnetic fields. (4) Stationary Charges are not affected by stationary magnetic fields. Permanent Magnets There are naturally occurring magnetic substances. These were long used for navigation. As a result, we speak of “north” and “south” magnetic poles, instead of positive and negative magnetic charges. Permanent magnets can also be made by people from raw materials. These magnetic poles also respect an “opposites attract” rule: N S N S attraction N S S N repulsion Earth: North and South Revisited The ancients defined the “north” end of a permanent magnet as the end that is attracted to the “north” pole of the earth. points north S N S Therefore the north geographic pole of earth is a south magnetic pole. N Magnetic Field of a Bar Magnet This is a magnetic dipole field, very similar to the electric dipole field of two opposite electric charges. Note that magnetic field lines are all closed loops, unlike electric field lines that must start and stop on a charge. Important: There is no magnetic “monopole.” N Such a thing has never been observed. North and South magnetic poles always come in pairs of equal strength. Properties of the magnetic force on a charge moving in a B field 1. The magnetic force is proportional to the charge q and speed v of the particle 2. The magnitude and direction of the magnetic force depend on the velocity of the particle and on the magnitude and direction of the magnetic field. -
The Dipole Moment.Doc 1/6
10/26/2004 The Dipole Moment.doc 1/6 The Dipole Moment Note that the dipole solutions: Qd cosθ V ()r = 2 4πε0 r and Qd 1 =+⎡ θθˆˆ⎤ E ()r2cossin3 ⎣ aar θ ⎦ 4πε0 r provide the fields produced by an electric dipole that is: 1. Centered at the origin. 2. Aligned with the z-axis. Q: Well isn’t that just grand. I suppose these equations are thus completely useless if the dipole is not centered at the origin and/or is not aligned with the z-axis !*!@! A: That is indeed correct! The expressions above are only valid for a dipole centered at the origin and aligned with the z- axis. Jim Stiles The Univ. of Kansas Dept. of EECS 10/26/2004 The Dipole Moment.doc 2/6 To determine the fields produced by a more general case (i.e., arbitrary location and alignment), we first need to define a new quantity p, called the dipole moment: pd= Q Note the dipole moment is a vector quantity, as the d is a vector quantity. Q: But what the heck is vector d ?? A: Vector d is a directed distance that extends from the location of the negative charge, to the location of the positive charge. This directed distance vector d thus describes the distance between the dipole charges (vector magnitude), as well as the orientation of the charges (vector direction). Therefore dd= aˆ , where: Q d ddistance= d between charges d and − Q ˆ ad = the orientation of the dipole Jim Stiles The Univ. of Kansas Dept. of EECS 10/26/2004 The Dipole Moment.doc 3/6 Note if the dipole is aligned with the z-axis, we find that d = daˆz .