Coulomb Force

12 Key excerpts on "Coulomb Force"

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  eBook - ePub

  Molecular Driving Forces

  Statistical Thermodynamics in Biology, Chemistry, Physics, and Nanoscience

  • Ken Dill, Sarina Bromberg(Authors)
  • 2010(Publication Date)
  • Garland Science

    (Publisher)

  20 Coulomb’s Law of Electrostatic Forces Charge Interactions Are Described by Coulomb’s Law

  Electrical interactions between charges govern much of physics, chemistry, and biology. They are the basis for chemical bonding, weak and strong. Salts dissolve in water to form the solutions of charged ions that cover three-quarters of the Earth’s surface. Salt water forms the working fluid of living cells. pH and salts regulate the associations of proteins, DNA, cells, and colloids, and the conformations of biopolymers. Nervous systems would not function without ion fluxes. Electrostatic interactions are also important in batteries, corrosion, and electroplating.

  Charge interactions obey Coulomb’s law. When more than two charged particles interact, the energies are sums of Coulombic interactions. To calculate such sums, we introduce the concepts of the electric field, Gauss’s law, and the electrostatic potential. With these tools, you can determine the electrostatic force exerted by one charged object on another, as when an ion interacts with a protein, DNA molecule, or membrane, or when a charged polymer changes conformation.

  Coulomb’s law was discovered in careful experiments by H Cavendish (1731–1810), J Priestley (1733–1804), and CA Coulomb (1736–1806) on macroscopic objects such as magnets, glass rods, charged spheres, and silk cloths. Coulomb’s law applies to a wide range of size scales, including atoms, molecules, and biological cells. It states that the interaction energy u(r) between two charges in a vacuum is

  u ( r ) = C q 1 q 2 r ,

  (20.1)

  where q1 and q2 are the magnitudes of the two charges, r is the distance separating them, and

  C = 1 / 4 π

  ε 0

  is a proportionality constant (see box below).

  Units

  The proportionality constant C in Equation (20.1) depends on the units used to measure the charge and the distance. In the older c.g.s. system, the units were defined so that

  C = 1

  . We use the SI system, in which the unit of charge is the coulomb C, the unit of energy is the joule J, and the unit of distance is the meter m. The corresponding constant C equals (4πε0 )−1 . The factor ε0 is called the permittivity of the vacuum. In SI units, ε0 = 8.85 × 10−12 Fm−1 . The farad F is the SI unit of capacitance, equal to 1 C V−1 . The volt V is the SI unit of electrical potential, which is equal to 1 JC−1 . So ε0 = 8.85 × 10−12 C2 J−1 m−1 . In c.g.s. units, the unit of charge is 1 statcoulomb or 1 esu = 3.00 × 109 C, the unit of potential is 1 statvolt = (1/300) V, and the unit of capacitance is 1 statfarad = 9 × 1011

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  Physics for Students of Science and Engineering

  • A. L. Stanford, J. M. Tanner(Authors)
  • 2014(Publication Date)
  • Academic Press

    (Publisher)

  11

  Electric Charge and Electric Fields

  Publisher Summary

  This chapter begins our study of electric and magnetic phenomena, collectively called electromagnetism . Electromagnetic forces, like gravitational forces, are fundamental interactions that occur between particles. Just as mass is that property of matter that engenders gravitational attraction, electric charge is a property of certain fundamental particles, like electrons and protons, that causes electromagnetic interaction. Our investigation of electrostatics , the analysis of interactions between charges at rest, is based on a force law for charges and on the concept of electric fields. The force law for charges, called Coulomb’s law, is the electrical analogue of the law of universal gravitation. The electric field is an abstract concept used to characterize how the presence of charge alters the properties of the space around that charge.

  11.1 Electric Charge and Coulomb’s Law

  Electric charges exist in two forms, called positive charge and negative charge . The natural unit of charge is the positive charge of a proton or the negative charge of an electron. The SI unit of charge is the coulomb (C), which will be defined later in terms of electric current. This unusual definition is used because of the difficulty of making reproducible measurements on quantities of charge. For now, we will use as a measure of charge the experimentally obtained value for e , the magnitude of the charge of an electron or proton:

  e = 1.60 ×

  10

  − 19

  C

  (11-1)

  (11-1)

  Equivalently, a coulomb is the quantity of charge carried by 6.25 × 1018 electrons.

  An electron (or proton) bears the smallest unit of charge found in nature, so any quantity of charge q occurs as an integral number n of the basic charge e , or q = ne . Thus, as with any physical quantity made up of a number of “minimum parcels,” we say that electric charge is quantized; the least quantity that occurs, the quantum of charge, is the electronic charge e

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  Electromagnetism

  • I. S. Grant, W. R. Phillips(Authors)
  • 2013(Publication Date)
  • Wiley

    (Publisher)

  1 is

  In general, the force Fj on a charge

  qj

  due to a number of other charges

  qi

  is

  The symbol i ≠ j under the summation signs indicates that the summation for charge i is over all the other charges j , but of course not including charge i itself. This equation can be written in another way in terms of the position vectors of the charges with respect to a fixed origin O. If the position vectors of the charges q 1 , q 2 … q i … are r1 , r2 … ri … then the vector joining charges i and j is rij = rj – ri . The total force on

  qj

  is thus

  (1.3)

  A trivial example of the application of Equation (1.3) is in working out the electrostatic forces exerted by atomic nuclei containing many protons on the electrons surrounding them. Nuclei are much smaller than atoms, and for this purpose can be regarded as point charges. Equation (1.3) then tells us that the attractive force between an electron and a nucleus containing Z protons is Z times as great as that between an electron and a single proton.

  It turns out that apart from the sign, the charge carried by electrons and protons is the same, and has the magnitude e = 1.602 × 10−19 coulombs* : the charge on the proton is +e , that on the electron is – e . The strength of atomic interactions is governed by the size of the electronic charge e . Although e

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  Fundamentals of Physics

  • David Halliday, Robert Resnick, Jearl Walker(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  ● Coulomb’s law describes the electrostatic force (or electric force) between two charged particles. If the Coulomb’s Law C H A P T E R 2 1 642 CHAPTER 21 COULOMB’S LAW What Is Physics? You are surrounded by devices that depend on the physics of electromagnetism, which is the combination of electric and magnetic phenomena. This physics is at the root of computers, television, radio, telecommunications, household light- ing, and even the ability of food wrap to cling to a container. This physics is also the basis of the natural world. Not only does it hold together all the atoms and molecules in the world, it also produces lightning, auroras, and rainbows. The physics of electromagnetism was first studied by the early Greek philos- ophers, who discovered that if a piece of amber is rubbed and then brought near bits of straw, the straw will jump to the amber. We now know that the attraction between amber and straw is due to an electric force. The Greek philosophers also discovered that if a certain type of stone (a naturally occurring magnet) is brought near bits of iron, the iron will jump to the stone. We now know that the attraction between magnet and iron is due to a magnetic force. From these modest origins with the Greek philosophers, the sciences of electricity and magnetism developed separately for centuries—until 1820, in fact, when Hans Christian Oersted found a connection between them: An electric cur- rent in a wire can deflect a magnetic compass needle. Interestingly enough, Oer- sted made this discovery, a big surprise, while preparing a lecture demonstration for his physics students. The new science of electromagnetism was developed further by workers in many countries. One of the best was Michael Faraday, a truly gifted experimenter with a talent for physical intuition and visualization. That talent is attested to by the fact that his collected laboratory notebooks do not contain a single equation.

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  Principles of Physics: Extended, International Adaptation

  • David Halliday, Robert Resnick, Jearl Walker(Authors)
  • 2023(Publication Date)
  • Wiley

    (Publisher)

  The forces push the particles apart. But here the forces pull the particles together. Here too. FIGURE 21.1.5 Two charged particles repel each other if they have the same sign of charge, either (a) both positive or (b) both negative. (c) They attract each other if they have opposite signs of charge. FIGURE 21.1.6 The electrostatic force on particle 1 can be described in terms of a unit vector r ̂ along an axis through the two particles, radially away from particle 2. r q 1 q 2 F ˆ r 612 CHAPTER 21 Coulomb’s Law CHECKPOINT 21.1.1 The figure shows five pairs of plates: A, B, and D are charged plastic plates and C is an electrically neu- tral copper plate. The electrostatic forces between the pairs of plates are shown for three of the pairs. For the remaining two pairs, do the plates repel or attract each other? A C C D B B A D A D An Aside. Here is something that is very curious. The form of Eq. 21.1.1 is the same as that of Newton’s equation (Eq. 13.1.3) for the gravitational force between two particles with masses m 1 and m 2 and separation r : F → = G m 1 m 2 ______ r 2 r ̂ (Newton’s law), (21.1.2) where G is the gravitational constant. Although the two types of forces are wildly different, both equations describe inverse square laws (the 1/r 2 dependences) that involve a product of a property of the interacting particles—the charge in one case and the mass in the other. However, the laws differ in that gravitational forces are always attractive but electrostatic forces may be either attractive or repulsive, depending on the signs of the charges. This difference arises from the fact that there is only one type of mass but two types of charge. Unit. The SI unit of charge is the coulomb. For practical reasons having to do with the accuracy of measurements, the coulomb unit is derived from the SI unit ampere for electric current i.

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  Principles of Electric Methods in Surface and Borehole Geophysics

  • Alex Kaufman, B. Anderson, Alex A. Kaufman(Authors)
  • 2010(Publication Date)
  • Elsevier Science

    (Publisher)

  This chapter introduces the theory of stationary electric fields—that is, the theory of electric fields that do not vary with time—starting from Coulomb’s law of force between electric charges and the principle of superposition. The concepts of electric field and electric potential are then developed, along with the general equations that these fields satisfy and their solutions in simple configurations. The material developed here will be used repeatedly in subsequent chapters to study the applications of stationary electric fields in surface and borehole methods of geophysics.

  1.1 INTERACTION OF ELECTRIC CHARGES AND COULOMB’S LAW

  The force of interaction between electric charges is, like the force of gravity, one of the fundamental concepts of physics. The French physicist Charles-Augustin de Coulomb (1736–1806) was the first to study quantitatively this remarkable phenomenon in experiments carried out at the end of eighteenth century. In this chapter, we consider these concepts only at the “macroscopic” level, which means that the dimensions of regions where “elementary” charges are located are assumed to be much smaller than the distances between these regions, while elementary charges themselves can have an arbitrary value. Coulomb’s law then states that the force acting on an elementary charge located at the point p , caused by a second elementary charge located at the point q , is given by the simple expression:

  F ( p ) =

  1

  4 π

  ε 0

  d e ( q ) d e ( p )

  L qp 3

  L qp

  .

    [1.1]

  Here de (p ) and de (q ) are the numerical values of the elementary charges, L qp is the vector directed from the point q to the point p , L qp is the distance between these points, and ε 0 is a constant of nature. In the standard International System of units (S.I. units), force is measured in “newtons” (N), which according to Newton’s Second Law has dimensions of mass times acceleration, or kilogram–meter per second squared (kg m s− 2 ); charge is measured in “coulombs” (C); and distance is measured in meters. The constant ε 0 then has the value

  ε 0

  =

  1

  36 π

  10

  − 9

  F

  m

  − 1

  ,

  where “F” is a unit called the “farad.” Its dimensions can be worked out from Eq. [1.1] , but will later be expressed more simply after some further electrical units are introduced. Noting that the vector separation L qp

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  Halliday's Fundamentals of Physics, 1st Australian & New Zealand Edition

  • David Halliday, Jearl Walker, Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons, Dipesh Bhattarai(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  The ratio 1/4 0 is often replaced with the electrostatic constant (or Coulomb constant) k = 8.99 × 10 9 N ⋅ m 2 /C 2 . • The electrostatic force vector acting on a charged particle due to a second charged particle is either directly towards the second particle (opposite signs of charge) or directly away from it (same sign of charge). • As with other types of forces, if multiple electrostatic forces act on a particle, the net force is the vector sum (not scalar sum) of the individual forces. • Shell theorem 1: a charged particle outside a shell with charge uniformly distributed on its surface is attracted or repelled as if the shell’s charge were concentrated as a particle at its centre. • Shell theorem 2: a charged particle inside a shell with charge uniformly distributed on its surface has no net force acting on it due to the shell. • Charge on a conducting spherical shell spreads uniformly over the (external) surface. Why study physics? In New Zealand and Australia, domestic and industrial electrostatic precipitators capture particulates in dust, smoke and exhaust fumes. As particulates pass through the system they become negatively charged. Positively charged collection plates attract the particulates and the exhaust gases continue on to be filtered or released. Periodically, the collection plates are vibrated to detach the particulates into a collection bin for disposal. You are surrounded by devices that depend on the physics of electromagnetism, which is the combination of electric and magnetic phenomena. Our discussion of electromagnetism is spread through the next 16 chapters. We begin with electrical phenomena, and our first step is to discuss the nature of electric charge and electric force. Electric charge Demonstration 1 After rubbing a glass rod with a silk cloth (on a day with low humidity), we hang the rod by means of a thread tied around its centre. Then we rub a second glass rod with the silk cloth and bring it near the hanging rod.

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  Electrostatic Dust Mitigation and Manipulation Techniques for Planetary Dust

  • Nima Gharib, Javad Farrokhi Derakhshandeh, Peter Radziszewski(Authors)
  • 2022(Publication Date)
  • Elsevier

    (Publisher)

  Coulomb's law and electric field 3.1. Coulomb's law The basic electromagnetic concepts are studied one by one in sequence. A dimensional description will suffice in the vast majority of cases; the latter will be deduced from their relationship via the theory's basic equations, which will be tested experimentally. The next section will take place immediately after the current enumeration of essential concepts. To understand how much force does a single point charge q exert on a test charge Q while it is at rest r distance away, Coulomb's law can evaluate the answer as follows: (3.1) The constant ε 0 = (8.85 × 10 − 12 C 2 /N m 2) is referred to as open space permittivity (ludicrously). In SI units, newton (N) denotes force, meter (m) denotes distance, and coulomb denotes charge (C). In other words, the force is proportional to the charge product and inversely proportional to the square of the separation distance. Here, item Δ r is the separation vector with magnitude of r. The force is directed down the line q-Q ; it is repulsive if q and Q have the same sign, and attractive if they have the opposite sign. Coulomb's law and the principle of superposition provide the physical basis for electrostatics; all else is mathematical development of these basic laws, with the exception of a few specific features and elaboration these rules. 3.2. The electric field If there are many point charges, such as q 1, q 2, …, q n at distances r 1, r 2, …, r n from Q, the total force on Q is then equal to (3.2) or (3.3) Here, (3.4) Factor E (r) is referred to as the source of electric field charge, which is a function of position (r), since the separation vectors r i are location-dependent. However, it makes no mention of the test charge Q. The electric field is a vector quantity that varies across points and is governed by the arrangement of source charges as shown in Fig. 3.1 ; physically, E (r) is the force per unit charge that would be exerted on a test charge if placed at P. 4

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  Electromagnetism

  Maxwell Equations, Wave Propagation and Emission

  • Tamer Becherrawy(Author)
  • 2013(Publication Date)
  • Wiley-ISTE

    (Publisher)

  Chapter 2

  Electrostatics in Vacuum

  The interaction of electric charges, as expressed by Coulomb Force, is formulated according to the Newtonian concept of action-at-a-distance: if a charge q′ is produced at r′ at a time t′, a charge q located at r feels the action of q′ instantaneously, whatever the distance |r − r′| and the medium that separates the charges. The concept of field was developed by Faraday, Maxwell, Lorentz, Einstein, and many others. In modern physics, all interactions are conceived as local, i.e. involving quantities defined at the same point r and at the same time t. Fields are physical entities that are endowed with energy, momentum, etc., and they may propagate with some finite speed as waves. Furthermore, in quantum theory, the same objects (electrons for instance) have both particle and wave properties.

  In this chapter, we introduce the concepts of electric field and potential, we derive the fundamental equations of electrostatics in vacuum, and we discuss some of their properties and the concept of electrostatic energy.

  2.1. Electric forces and field

  In a famous experiment, Coulomb used a torsion balance to measure the force of interaction of electric charges. He verified that a small charge q1 acts on a small charge q2 situated at a distance r with a force FE = Ko q1 q2 /r2 oriented along the line joining the charges. This force is repulsive between like charges and attractive between unlike charges. It has a similar mathematical form to Newton's law of universal gravitation To specify both the direction and the magnitude, we write

  [2.1 ]

  Coulomb's force obeys the principle of action and reaction. Ko is a constant that depends on the adopted unit of charge. Using the coulomb (C) as the unit of charge and the Heaviside or rationalized system, we write

  [2.2]

  εo is the permittivity of vacuum. The factor 4π is introduced to simplify the writing of equations. The electric force is much more intense than the gravitational force and the coulomb is an enormous charge on the human scale: electric sparks are produced by less than one microcoulomb and rubbing produces a charge of the order of the nanocoulomb per square centimeter

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  College Physics

  • Paul Peter Urone, Roger Hinrichs(Authors)
  • 2012(Publication Date)
  • Openstax

    (Publisher)

  If the answer is unreasonable, look for what specifically could cause the identified difficulty. Usually, the manner in which the answer is unreasonable is an indication of the difficulty. For example, an extremely large Coulomb Force could be due to the assumption of an excessively large separated charge. Glossary a material that allows electrons to move separately from their atomic orbits an object with properties that allow charges to move about freely within it another term for the electrostatic force the interaction between two charged particles generated by the Coulomb Forces they exert on one another the mathematical equation calculating the electrostatic force vector between two charged particles a molecule’s lack of symmetrical charge distribution, causing one side to be more positive and another to be more negative a physical property of an object that causes it to be attracted toward or repelled from another charged object; each charged object generates and is influenced by a force called an electromagnetic force a three-dimensional map of the electric force extended out into space from a point charge 720 Chapter 18 | Electric Charge and Electric Field This OpenStax book is available for free at http://cnx.org/content/col11406/1.9

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  Halliday and Resnick's Principles of Physics

  • David Halliday, Robert Resnick, Jearl Walker(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  If the par- ticles have charges q 1 and q 2 , are separated by distance r, and are at rest (or moving only slowly) relative to each other, then the magni- tude of the force acting on each due to the other is given by F = 1 4πε 0 | q 1 || q 2 | r 2 (Coulomb’s law), (21-4) where ε 0 = 8.85 × 10 −12 C 2 /N · m 2 is the permittivity constant. The ratio 1/4πε 0 is often replaced with the electrostatic constant (or Coulomb constant) k = 8.99 × 10 9 N · m 2 /C 2 . Review & Summary The electrostatic force vector acting on a charged particle due to a second charged particle is either directly toward the second particle (opposite signs of charge) or directly away from it (same sign of charge). As with other types of forces, if multiple electrostatic forces act on a particle, the net force is the vector sum (not scalar sum) of the individual forces. The two shell theories for electrostatics are Shell theorem 1: A charged particle outside a shell with charge uniformly distributed on its surface is attracted or repelled as if the shell’s charge were concentrated as a particle at its center. Shell theorem 2: A charged particle inside a shell with charge uniformly distributed on its surface has no net force acting on it due to the shell. Charge on a conducting spherical shell spreads uniformly over the (external) surface. The Elementary Charge Electric charge is quantized (restricted to certain values). The charge of a particle can be writ- ten as ne, where n is a positive or negative integer and e is the elementary charge, which is the magnitude of the charge of the electron and proton (≈ 1.602 × 10 −19 C). Conservation of Charge The net electric charge of any iso- lated system is always conserved. 541 PROBLEMS 1 In Fig. 21-11, four particles form a square. The charges are q 1 = q 4 = Q and q 2 = q 3 = 7.90 fC.

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  Electromagnetism for Engineers

  An Introductory Course

  • P. Hammond(Author)
  • 2013(Publication Date)
  • Pergamon

    (Publisher)

  Since the current is measured in amperes, the unit of charge is the ampere-second and its special name is the coulomb. As we have also mentioned the forces due to the motion of charges are much smaller than those due to position. It is therefore convenient to choose the unit as involving the motion of a very large number of electrons. Thus in the SI system the electronic charge is chosen as 1-60 X 10 coulombs. The constant is experimental and is found to be 9 X 10^ (within 2 parts in 1,000). It is interesting to compare the electric and gravitational forces between two electrons. At a distance of 1 mm the gravitational force is an attraction of Electric Charges at Rest—I 11 because the subject of electrostatics had developed long before there was any knowledge of neutrons, protons and electrons. He will also have some misgivings that in our discussion we have included gravitational and electrostatic forces but have left out the short-range forces which bind the particles together in the atomic nucleus. Moreover he might rightly be suspicious about the exact nature of the experiments which supposedly led to the results described. It must at once be acknowledged that we have not followed the historical sequence. Many books on electricity have been written without reference to the fundamental particles, but since there are such particles there seems every reason to start our discussion by considering them. Nevertheless the laws of electromagnetism were originally applied to aggregates of electric particles and not to isolated particles or to nuclear structure. Additional considerations and laws have to be introduced when dealing with individual atoms. In this book we shall limit ourselves to the study of macroscopic phenomena and we shall treat electricity as a continuous fluid rather than as an assembly of discrete charges.

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