Conductors and Electric Fields in Static Equilibrium

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On the Segregation of Genetically Modified, Conventional, and Organic Products in European Agriculture: A Multi-market Equilibrium Analysis GianCarlo Moschini, Harun Bulut, and Luigi Cembalo Working Paper 05-WP 411 October 2005 Center for Agricultural and Rural Development Iowa State University Ames, Iowa 50011-1070 www.card.iastate.edu GianCarlo Moschini is a professor of economics and Pioneer Endowed Chair in Science and Technology Policy, Harun Bulut is a post-doctoral fellow, and Luigi Cembalo was a visiting scientist, all with the Department of Economics at Iowa State University. Moschini and Bulut developed, calibrated and simulated the model and wrote the paper. Cembalo assembled the data used in the calibration. The support of the U.S. Department of Agriculture, through a National Research Initiative grant, is gratefully acknowledged. This paper is available online on the CARD Web site: www.card.iastate.edu. Permission is granted to reproduce this information with appropriate attribution to the authors. Questions or comments about the contents of this paper should be directed to GianCarlo Moschini, 583 Heady Hall, Iowa State University, Ames, IA 50011-1070; Ph: (515) 294-5761; Fax: (515) 294-6336; E-mail: moschini@iastate.edu. The U.S. Department of Agriculture (USDA) prohibits discrimination in all its programs and activities on the basis of race, color, national origin, gender, religion, age, disability, political beliefs, sexual orientation, and marital or family status. (Not all prohibited bases apply to all programs.) Persons with disabilities who require alternative means for communication of program information (Braille, large print, audiotape, etc.) should contact USDA’s TARGET Center at (202) 720-2600 (voice and TDD). To file a complaint of discrimination, write USDA, Director, Office of Civil Rights, Room 326-W, Whitten Building, 14th and Independence Avenue, SW, Washington, DC 20250-9410 or call (202) 720-5964 (voice and TDD). USDA is an equal opportunity provider and employer. Iowa State University does not discriminate on the basis of race, color, age, religion, national origin, sexual orientation, gender identity, sex, marital status, disability, or status as a U.S. veteran. Inquiries can be directed to the Director of Equal Opportunity and Diversity, 3680 Beardshear Hall, (515) 294-7612. Abstract Evaluating the possible benefits of the introduction of genetically modified (GM) crops must address the issue of consumer resistance as well as the complex regulation that has ensued. In the European Union (EU) this regulation envisions the “co-existence” of GM food with conventional and quality-enhanced products, mandates the labelling and traceability of GM products, and allows only a stringent adventitious presence of GM content in other products. All these elements are brought together within a partial equilibrium model of the EU agricultural food sector. The model comprises conventional, GM and organic food. Demand is modelled in a novel fashion, whereby organic and conventional products are treated as horizontally differentiated but GM products are vertically differentiated (weakly inferior) relative to conventional ones. Supply accounts explicitly for the land constraint at the sector level and for the need for additional resources to produce organic E ∥ F Conductors and Electric Fields in Static Equilibrium Conductors and Electric Fields in Static Equilibrium Bởi: OpenStaxCollege Conductors contain free charges that move easily When excess charge is placed on a conductor or the conductor is put into a static electric field, charges in the conductor quickly respond to reach a steady state called electrostatic equilibrium [link] shows the effect of an electric field on free charges in a conductor The free charges move until the field is perpendicular to the conductor’s surface There can be no component of the field parallel to the surface in electrostatic equilibrium, since, if there were, it would produce further movement of charge A positive free charge is shown, but free charges can be either positive or negative and are, in fact, negative in metals The motion of a positive charge is equivalent to the motion of a negative charge in the opposite direction When an electric field is applied to a conductor, free charges inside the conductor move until the field is perpendicular to the surface (a) The electric field is a vector quantity, with both parallel and perpendicular components The parallel component ( ) exerts a force ( ) on the free charge q, which moves the charge until = (b) The resulting field is perpendicular 1/12 Conductors and Electric Fields in Static Equilibrium to the surface The free charge has been brought to the conductor’s surface, leaving electrostatic forces in equilibrium A conductor placed in an electric field will be polarized [link] shows the result of placing a neutral conductor in an originally uniform electric field The field becomes stronger near the conductor but entirely disappears inside it This illustration shows a spherical conductor in static equilibrium with an originally uniform electric field Free charges move within the conductor, polarizing it, until the electric field lines are perpendicular to the surface The field lines end on excess negative charge on one section of the surface and begin again on excess positive charge on the opposite side No electric field exists inside the conductor, since free charges in the conductor would continue moving in response to any field until it was neutralized Misconception Alert: Electric Field inside a Conductor Excess charges placed on a spherical conductor repel and move until they are evenly distributed, as shown in [link] Excess charge is forced to the surface until the field inside the conductor is zero Outside the conductor, the field is exactly the same as if the conductor were replaced by a point charge at its center equal to the excess charge The mutual repulsion of excess positive charges on a spherical conductor distributes them uniformly on its surface The resulting electric field is perpendicular to the surface and zero inside Outside the conductor, the field is identical to that of a point charge at the center equal to the excess charge Properties of a Conductor in Electrostatic Equilibrium The electric field is zero inside a conductor Just outside a conductor, the electric field lines are perpendicular to its surface, ending or beginning on charges on the surface 2/12 Conductors and Electric Fields in Static Equilibrium Any excess charge resides entirely on the surface or surfaces of a conductor The properties of a conductor are consistent with the situations already discussed and can be used to analyze any conductor in electrostatic equilibrium This can lead to some interesting new insights, such as described below How can a very uniform electric field be created? Consider a system of two metal plates with opposite charges on them, as shown in [link] The properties of conductors in electrostatic equilibrium indicate that the electric field between the plates will be uniform in strength and direction Except near the edges, the excess charges distribute themselves uniformly, producing field lines that are uniformly spaced (hence uniform in strength) and perpendicular to the surfaces (hence uniform in direction, since the plates are flat) The edge effects are less important when the plates are close together Two metal plates with equal, but opposite, excess charges The field between them is uniform in strength and direction except near the edges One use of such a field is to produce uniform acceleration of charges between the plates, such as in the electron gun of a TV tube Earth’s Electric Field A near uniform electric field of approximately 150 N/C, directed downward, surrounds Earth, with the magnitude increasing slightly as we get closer to the surface What causes the electric field? At around 100 km above the surface of Earth we have a layer of charged particles, called the ionosphere The ionosphere is responsible for a range of phenomena including the electric field surrounding Earth In fair weather the ionosphere is positive and the Earth largely negative, maintaining the electric field ([link](a)) In storm conditions clouds form and localized electric ...Dielectrics in Electric Fields Gorur G. Raju University of Windsor- Windsor, Ontario, Canada MARCEL MARCEL DEKKER, INC. DEKKER NEW YORK BASEL Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN: 0-8247-0864-4 This book is printed on acid-free paper Headquarters Marcel Dekker, Inc 270 Madison Avenue, New York, NY 10016 tel 212-696-9000, fax 212-685-4540 Eastern Hemisphere Distribution Marcel Dekker AG Hutgasse4, Postfach 812, CH-4001 Basel, Switzerland tel 41-61-260-6300, fax 41-61-260-6333 World Wide Web http //www dekker com The publisher offers discounts on this book when ordered in bulk quantities For more information, write to Special Sales/Professional Marketing at the headquarters address above Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher Current printing (last digit) 10 987654321 PRINTED IN THE UNITED STATES OF AMERICA TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. POWER ENGINEERING Series Editor H. Lee Willis ABB Inc. Raleigh, North Carolina 1. Power Distribution Planning Reference Book, H. Lee Willis 2. Transmission Network Protection: Theory and Practice, Y. G. Paithan- kar 3. Electrical Insulation in Power Systems, N. H. Malik, A. A. AI-Arainy, and M. I. Qureshi 4. Electrical Power Equipment Maintenance and Testing, Paul Gill 5. Protective Relaying: Principles and Applications, Second Edition, J. Lewis Blackburn 6. Understanding Electric Utilities and De-Regulation, Lorrin Philipson and H. Lee Willis 7. 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Lee Willis 19. Dielectrics in Electric Fields, GorurG. Raju 20. Protection Devices and Systems for High-Voltage Applications, Vladimir Gurevich ADDITIONAL VOLUMES IN PREPARATION TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. TO MY PARENTS. MY WIFE, PADMINI, AND OUR SON, ANAND WHO GA VE ME ALL I VALUE. SOME DEBTS ARE NEVER REPAID IN FULL MEASURE. TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. SERIES INTRODUCTION Power engineering is the oldest and most traditional of the various areas within electrical engineering, yet no other facet of modern technology is currently undergoing a more dramatic revolution in both technology and industry structure. This addition to Marcel Dekker's Power Engineering Series addresses a fundamental element The rich and the poor are two locked caskets of which each contains the key to the other. Karen Blixen (Danish Writer) 1 INTRODUCTORY CONCEPTS I n this Chapter we recapitulate some basic concepts that are used in several chapters that follow. Theorems on electrostatics are included as an introduction to the study of the influence of electric fields on dielectric materials. The solution of Laplace's equation to find the electric field within and without dielectric combinations yield expressions which help to develop the various dielectric theories discussed in subsequent chapters. The band theory of solids is discussed briefly to assist in understanding the electronic structure of dielectrics and a fundamental knowledge of this topic is essential to understand the conduction and breakdown in dielectrics. The energy distribution of charged particles is one of the most basic aspects that are required for a proper understanding of structure of the condensed phase and electrical discharges in gases. Certain theorems are merely mentioned without a rigorous proof and the student should consult a book on electrostatics to supplement the reading. 1.1 A DIPOLE A pair of equal and opposite charges situated close enough compared with the distance to an observer is called an electric dipole. The quantity » = Qd (1.1) where d is the distance between the two charges is called the electric dipole moment, u. is a vector quantity the direction of which is taken from the negative to the positive •jr. charge and has the unit of C m. A unit of dipole moment is 1 Debye = 3.33 xlO" C m. TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. 1.2 THE POTENTIAL DUE TO A DIPOLE Let two point charges of equal magnitude and opposite polarity, +Q and -Q be situated d meters apart. It is required to calculate the electric potential at point P, which is situated at a distance of R from the midpoint of the axis of the dipole. Let R + and R . be the distance of the point from the positive and negative charge respectively (fig. 1.1). Let R make an angle 6 with the axis of the dipole. R Fig. 1.1 Potential at a far away point P due to a dipole. The potential at P is equal to Q R_ (1.2) Starting from this equation the potential due to the dipole is , QdcosQ (1.3) TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. Three other forms of equation (1.3) are often useful. They are (1.4) (1.5) (1.6) The potential due to a dipole decreases more rapidly than that due to a single charge as the distance is increased. Hence equation (1.3) should not be used when R « d. To determine its accuracy relative to eq. (1.2) consider a point along the axis of the dipole at a distance of R=d from the positive charge. Since 6 = 0 in this case, (f> = Qd/4ns 0 (1.5d) =Q/9ns 0 d according to (1.3). If we use equation (1.2) instead, the potential is Q/8ns 0 d, an error of about 12%. The electric field due to a dipole in spherical coordinates with two variables (r, 0 ) is given as: 17 r n _!_ n l-—*r-—* 9 (iy) Partial differentiation of equation (1.3) leads to Equation (1.7) may be written more concisely as: TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. (1.10) Substituting for § from equation (1.5) and changing the variable to r from R we get 1 1 47TGQ r r We may now make the substitution r r 3r ^ r Equation (1.12) now becomes 3//vT (1.11) (1.12) (1.13) Fig. 1.2 The two components of the electric field due to a dipole with moment TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. The electric field at P has two components. The first term in Seek simplicity, and distrust it. -Alfred North Whitehead POLARIZATION and STATIC DIELECTRIC CONSTANT T he purposes of this chapter are (i) to develop equations relating the macroscopic properties (dielectric constant, density, etc.) with microscopic quantities such as the atomic radius and the dipole moment, (ii) to discuss the various mechanisms by which a dielectric is polarized when under the influence of a static electric field and (iii) to discuss the relation of the dielectric constant with the refractive index. The earliest equation relating the macroscopic and microscopic quantities leads to the so-called Clausius-Mosotti equation and it may be derived by the approach adopted in the previous chapter, i.e., finding an analytical solution of the electric field. This leads to the concept of the internal field which is higher than the applied field for all dielectrics except vacuum. The study of the various mechanisms responsible for polarizations lead to the Debye equation and Onsager theory. There are important modifications like Kirkwood theory which will be explained with sufficient details for practical applications. Methods of Applications of the formulas have been demonstrated by choosing relatively simple molecules without the necessity of advanced knowledge of chemistry. A comprehensive list of formulas for the calculation of the dielectric constants is given and the special cases of heterogeneous media of several components and liquid mixtures are also presented. 2.1 POLARIZATION AND DIELECTRIC CONSTANT Consider a vacuum capacitor consisting of a pair of parallel electrodes having an area of cross section A m 2 and spaced d m apart. When a potential difference V is applied between the two electrodes, the electric field intensity at any point between the electrodes, perpendicular to the plates, neglecting the edge effects, is E=V/d. The TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. 36 Chapter! capacitance of the vacuum capacitor is Co = So A/d and the charge stored in the capacitor is Qo=A£oE (2.1) in which e 0 is the permittivity of free space. If a homogeneous dielectric is introduced between the plates keeping the potential constant the charge stored is given by Q = s Q sAE (2.2) where s is the dielectric constant of the material. Since s is always greater than unity Qi > Q and there is an increase in the stored charge given by *-l) (2-3) This increase may be attributed to the appearance of charges on the dielectric surfaces. Negative charges appear on the surface opposite to the positive plate and vice-versa (Fig. 2. 1) 1 . This system of charges is apparently neutral and possesses a dipole moment (2.4) Since the volume of the dielectric is v =Ad the dipole moment per unit volume is P = -^ = Ee 0 (e-l) = X e 0 E (2.5) Ad The quantity P, is the polarization of the dielectric and denotes the dipole moment per fj _ unit volume. It is expressed in C/m . The constant yj= (e-1) is called the susceptability of the medium. The flux density D defined by D = £ Q sE (2.6) becomes, because of equation (2.5), D = s 0 £ + P (2.7) TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. Polarization 37 hi±J bill bill Ei±l hl±Ihl±Jhl±!H±l till H±J bill EH 3 3 3 3 a Free charge Bound chorye Fig. 2.1 Schematic representation of dielectric polarization [von Hippel, 1954]. (With permission of John Wiley & Sons, New York) Polarization of a dielectric may be classified according to 1. Electronic or Optical Polarization 2. Orientational Polarization 3. Atomic or Ionic Polarization 4. Interfacial Polarization. We shall consider the first three LWT - Food Science and Technology 42 (2009) 735–739 Contents lists available at ScienceDirect LWT - Food Science and Technology journal homepage: www.elsevier.com/locate/lwt Shelf life of whole milk processed by pulsed electric fields in combination with PEF-generated heat David R Sepulveda a, Marı´a M Go´ngora-Nieto c, Jose´ A Guerrero b, Gustavo V Barbosa-Ca´novas c, * a ´ n en Alimentacio ´n y Desarrollo (CIAD), A.C., Av Rı´o Conchos S/N, Parque Industrial, Cd Cuahute´moc, Chihuahua, Mexico Centro de Investigacio Departamento de Ingenierı´a Quı´mica y Alimentos, Universidad de las Ame´ricas-Puebla, Cholula, Puebla 72820, Mexico c Biological Systems Engineering Department, Washington State University, Pullman 99164-6120, WA, USA b a r t i c l e i n f o a b s t r a c t Article history: Received January 2008 Received in revised form 29 September 2008 Accepted October 2008 Application of pulsed electric fields (PEF) in combination with mild thermal treatment was studied to extend the shelf life of whole milk Five pulses with peak electric field strength of 35 kV/cm and pulse width of around 2.3 ms were applied to milk at 65  C and sustained for less than 10 s Shelf life of the milk was extended by a minimum of 24 days A synergistic interaction between PEF and mild thermal treatment was found Neither the severe PEF treatment applied at lower temperatures, nor the mild thermal treatment equivalent, including longer treatment times than used in this study, could significantly extend the shelf life of milk However, the combination of both PEF and mild temperature extended milk’s shelf life adequately The use of a thermal regeneration system improved the energy efficiency of the studied preservation process making it highly competitive with pasteurization Ó 2008 Published by Elsevier Ltd on behalf of Swiss Society of Food Science and Technology Keywords: Pulsed Electric Fields PEF Whole moilk Thermization Introduction Thermal pasteurization of milk is a preservation technique that has been employed commercially and enforced in the U.S for more than fifty years, and has been used successfully to control milktransmitted diseases (Steele, 2000) Besides eradicating pathogenic bacteria, thermal pasteurization also can extend the shelf life of refrigerated milk for up to three weeks Nevertheless, after the storage period the high microbial content and/or other undesirable characteristics (sensory) make the milk unacceptable for human consumption (Richter, Ledford, & Murphy, 1992) The development of a suitable technology capable of substituting such a well-established preservation process involves identifying a process capable of producing microbiologically safe products with extended shelf life and superior quality attributes This alternative preservation technique needs to be accomplished at a reasonable energy expenditure level PEF treatment is a novel food preservation process valued for its ability to eliminate bacteria from foods without increasing their temperature (Barbosa-Ca´novas, Go´ngoraNieto, Pothakamury, & Swanson, 1999) Preservation of milk and fluid dairy products seems to be one of the main market niches for PEF technology since it is mainly intended for preservation of pumpable fluid or semi-fluid foods (Qin, Pothakamury, Barbosa* Corresponding author Tel.: þ1 509 335 6188; fax: þ1 509 335 2722 E-mail address: barbosa@wsu.edu (G.V Barbosa-Ca´novas) Ca´novas, & Swanson, 1996) Commercial application of PEF technology, however, has not been implemented yet, mainly due to lack of ... the electric field lines in the vicinity of the charged insulator in [link] noting its nonuniform charge distribution 9/12 Conductors and Electric Fields in Static Equilibrium A charged insulating... zero, other than at infinity? (Hint: A graphing calculator can yield considerable insight in this problem.) 10/12 Conductors and Electric Fields in Static Equilibrium (a) Find the total Coulomb... ions and electrons recombine, and we get discharge in the form of lightning sparks and corona discharge 3/12 ∥ F Conductors and Electric Fields in Static Equilibrium Earth’s electric field (a) Fair