Physics
Coulomb's Law
Coulomb's Law describes the electrostatic force between two charged particles. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically, it is expressed as F = k * (|q1 * q2|) / r^2, where F is the force, q1 and q2 are the charges, r is the distance between them, and k is the Coulomb's constant.
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12 Key excerpts on "Coulomb's Law"
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 3 Laws and Theories of Electricity, Quantum Mechanics and Particle Physics Laws of Electricity 1. Coulomb's Law Coulomb's Law is a law of physics describing the electrostatic interaction between electrically charged particles. It was studied and first published in 1783 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism. Nevertheless, the dependence of the electric force with distance (inverse square law) had been proposed previously by Joseph Priestley and the dependence with both distance and charge had been discovered, but not published, by Henry Cavendish, prior to Coulomb's works. ________________________ WORLD TECHNOLOGIES ________________________ Basic Equation Diagram describing the basic mechanism of Coulomb's Law; like charges repel each other and opposite charges attract each other. ________________________ WORLD TECHNOLOGIES ________________________ Coulomb's torsion balance The scalar form of Coulomb's Law is an expression for the magnitude and sign of the electrostatic force between two idealized point charges , small in size compared to their separation. This force ( F ) acting simultaneously on point charges ( q 1 ) and ( q 2 ), is given by where r is the separation distance and k e is a proportionality constant. A positive force implies it is repulsive, while a negative force implies it is attractive. The proportionality constant k e , called the Coulomb constant (sometimes called the Coulomb force constant ), is related to defined properties of space and can be calculated based on knowledge of empirical measurements of the speed of light:
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 12 Laws and Theories of Electricity, Quantum Mechanics and Particle Physics Laws of Electricity 1. Coulomb's Law Coulomb's Law is a law of physics describing the electrostatic interaction between electrically charged particles. It was studied and first published in 1783 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism. Nevertheless, the dependence of the electric force with distance (inverse square law) had been proposed previously by Joseph Priestley and the dependence with both distance and charge had been discovered, but not published, by Henry Cavendish, prior to Coulomb's works. Basic Equation Diagram describing the basic mechanism of Coulomb's Law; like charges repel each other and opposite charges attract each other. ________________________ WORLD TECHNOLOGIES ________________________ Coulomb's torsion balance The scalar form of Coulomb's Law is an expression for the magnitude and sign of the electrostatic force between two idealized point charges , small in size compared to their separation. This force ( F ) acting simultaneously on point charges ( q 1 ) and ( q 2 ), is given by where r is the separation distance and k e is a proportionality constant. A positive force implies it is repulsive, while a negative force implies it is attractive. The proportionality constant k e , called the Coulomb constant (sometimes called the Coulomb force ________________________ WORLD TECHNOLOGIES ________________________ constant ), is related to defined properties of space and can be calculated based on knowledge of empirical measurements of the speed of light: In SI units, the speed of light in vacuum (or electromagnetic waves, in general), denoted c , to nine significant figures has been determined experimentally to be 299,792,458 m·s −1 , and the magnetic constant ( μ 0 ) is set at 4π × 10 −7 H·m −1 .
- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
Coulomb’s Law Now we come to the equation for Coulomb’s law, but first a caution. This equa- tion works for only charged particles (and a few other things that can be treated as particles). For extended objects, with charge located in many different places, we need more powerful techniques. So, here we consider just charged particles and not, say, two charged cats. If two charged particles are brought near each other, they each exert an elec- trostatic force on the other. The direction of the force vectors depends on the signs of the charges. If the particles have the same sign of charge, they repel each other. That means that the force vector on each is directly away from the other particle (Figs. 21.1.5a and b). If we release the particles, they accelerate away from each other. If, instead, the particles have opposite signs of charge, they attract each other. That means that the force vector on each is directly toward the other particle (Fig. 21.1.5c). If we release the particles, they accelerate toward each other. The equation for the electrostatic forces acting on the particles is called Coulomb’s law after Charles-Augustin de Coulomb, whose experiments in 1785 led him to it. Let’s write the equation in vector form and in terms of the particles shown in Fig. 21.1.6, where particle 1 has charge q 1 and particle 2 has charge q 2 . (These symbols can represent either positive or negative charge.) Let’s also focus on particle 1 and write the force acting on it in terms of a unit vector r ̂ that points along a radial axis extending through the two particles, radially away from parti- cle 2.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
If the particles 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), 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 con- stant (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 toward the second particle (opposite signs of charge) or directly away from it (same sign of charge). ● If multiple electrostatic forces act on a particle, the net force is the vector sum (not scalar sum) of the individual forces. Key Ideas Learning Objectives 610 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.
- S. B. Lal Seksena, Kaustuv Dasgupta(Authors)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
3.2 Coulomb’s Law and Its Application Let us illustrate a system consisting of two one-dimensional charged bodies (point charge) having static charge q 1 and q 2 . These are separated by a distance vector r – *. O r 1 r 2 r Fig. 3.1: Coulomb’s law Electrostatic 131 Now, these two charges will create an electrostatic field. Both the charges will experience a force due to the field created by them. Let us assign the origin of the plane containing q 1 and q 2 at O. Therefore, the position vector of q 1 and q 2 with respect to the origin O is r – 1 and r – 2 respectively, following the vector algebra we can write, ∴ r – = r – 1 – r – 2 .......... 3.1 In the year of 1785 a French Physicist Charles Augustin de Coulomb had published a report where he had derived this force. F – , both qualitatively and quantitatively. We can summarize what he had concluded a. About the magnitude of the force (Quantitive) i. The magnitude of the force is directly proportional to the product of both the charges. |F| α q 1 q 2 ii. The magnitude of the force is inversely proportional to the square of the distance by which the charges are separated (i.e. the magnitude of the distance vector) |F| α 1 |r – | 2 b. About the direction of the force (Qualititive) i. The direction of the force depends on the nature of the charges. If q 1 and q 2 are of same type (i.e., +ve and +ve or –ve and –ve) the force is repulsive. And if q 1 and q 2 are of opposite type (i.e. +ve and –ve) the force is attractive one. ii. The force is along with the distance vector r – So the force |F| can be expressed as: F 1 4 q q r 1 2 = πε r 2 ˆ .......... 3.2 r F 1 4 q q r 1 2 = πε r 1 2 2 circumflex.titling -..........
eBook - PDFSteady Electric Fields and Currents
Elementary Electromagnetic Theory
- B. H. Chirgwin, C. Plumpton, C. W. Kilmister(Authors)
- 2013(Publication Date)
- Pergamon(Publisher)
30 ELEMENTARY ELECTROMAGNETIC THEORY The force exerted by one point charge on another is directly propor-tional to the product of the magnitudes of the charges, is inversely pro-portional to the square of the distance between them, acts along the line joining them, and is a repulsion when the charges have the same sign, and is an attraction when they have opposite signs. We can represent this by the relation F ~ -^ r , (2.11) where F is the force between the charges, Qx and Q% are the strengths of the charges, r is the position vector of the charge experiencing the force referred to the other charge as origin, and r = | r |. FIG. 2.3 This law was verified approximately by direct measurement by Coulomb (hence the name) and also by Cavendish. It has been verified subsequently to a high degree of accuracy, directly and indirectly by a variety of experiments. Coulomb's Law enables us to relate the vector D to the sources of a field and hence to obtain the complete chain of interaction between the sources of a field and an object charge. In the situation contemplated by Coulomb's Law we regard one of the charges, say Qx, as the source of the field and we regard the other, Q 2 , as a test charge which experiences the force but does not disturb the field. We choose Qx as the origin of coordinates (Fig. 2.3). We may write eqn. (2.11) as where k is a constant of proportionality. Therefore This result shows that the vector D (and E) arising from Qx has spherical symmetry, the lines of force being everywhere radial. These lines arise from § 2.4 THE INVERSE SQUARE LAW IN ELECTROSTATICS 31 β ι at O and must end on — Q x dispersed at infinity, so that the total displace-ment across a sphere of radius r centred on O is βι. Therefore Q ± = 4nr 2 D = 4πή D r = AneJcQu 1 Γ βιβ: 2 * = * F = -^ ± ; -r , 4πεο ' 4πε 0 Γ 3 D = -ß^r = eoE. (2.12) Equation (2.12) gives the displacement at any point produced by a point charge βι at the origin.
- 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)
Particles with the same sign of electrical charge repel each other, and particles with opposite signs attract each other. Below we shall put this rule into quantitative form as Coulomb’s law of electrostatic force (or electric force) between charged particles. The term electrostatic means that, relative to each other, the particles are either stationary or moving only very slowly. But before we get to the equations, let’s use the rule to remove some of the magic from our two demonstrations. Demonstration 1 with signs When we rub the glass rod with a silk cloth, a small number of negative particles move from the rod to the silk (a charge transfer like that between you and a carpet), leaving the rod with a small amount of excess positive charge. (Which way the negative particles move is not obvious and requires experimen- tation.) We rub the silk over the rod to increase the number of contact points and thus the amount of transferred charge. Pdf_Folio:459 CHAPTER 21 Coulomb’s law 459 FIGURE 21.3 Two charged rods of the same sign repel each other. Glass Glass + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + F - F We hang the rod from the thread so as to elec- trically isolate it from its surroundings, so that the surroundings have no chance to neutralise the rod. When we rub the second rod with the silk cloth, it too becomes positively charged. So when we bring it near the first rod, the two rods repel each other because they have the same sign of excess charge (figure 21.3). We cannot see the charged particles, only the resulting motion, so the motion looks magical. Demonstration 2 with signs When we rub the plastic rod with fur, the rod gains excess negative charge. (Again, the transfer direc- tion is learned through many experiments.) When we bring the plastic rod (negatively charged) near the hanging rod (positively charged), the rods are attracted to each other because they have excess charges of opposite signs (figure 21.4).
eBook - PDF- David Halliday, Robert Resnick, Kenneth S. Krane(Authors)
- 2019(Publication Date)
- Wiley(Publisher)
14 N. (8.99 10 9 N m 2 /C 2 )(1.60 10 19 C) 2 (4 10 15 m) 2 F 1 4 0 e 2 r 2 574 Chapter 25 / Electric Charge and Coulomb’s Law Here r 12 represents the magnitude of the vector and indicates the unit vector in the direction of That is, (25-6) We used a form similar to Eq. 25-5 to express the gravita- tional force (see Eqs. 14-2 and 14-3). One other feature is apparent from Fig. 25-9. According to Newton’s third law, the force exerted on particle 2 by particle 1, is opposite to This force can then be expressed in eactly the same form: (25-7) Here is a unit vector that points from particle 1 to parti- cle 2; that is, it would be the unit vector in the direction of particle 2 if the origin of coordinates were at the location of particle 1. The vector form of Coulomb’s law is useful because it carries within it the directional information about and whether the force is attractive or repulsive. Using the vector form is of critical importance when we consider the forces acting on an assembly of more than two charges. In this case, Eq. 25-5 would hold for every pair of charges, and the total force on any one charge would be found by taking the vector sum of the forces due to each of the other charges. For example, the force on particle 1 in an assembly would be (25-8) where is the force on particle 1 from particle 2, is the force on particle 1 from particle 3, and so on. Equation 25-8 is the mathematical representation of the principle of superposition applied to electric forces. It asserts that the force acting on one charge due to another is independent of whether or not other charges are present, and therefore we F B 13 F B 12 F B 1 F B 12 F B 13 F B 14 , F B r ˆ 21 F B 21 1 4 0 q 1 q 2 r 2 21 r ˆ 21 . F B 12 . F B 21 , r ˆ 12 r B 12 r 12 . r B 12 . r ˆ 12 r B 12 , can calculate the force separately for each pair of charges and then take their vector sum to find the net force on any charge.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
542 CHAPTER 21 COULOMB’S LAW 21 We know that the negative charge on the electron and the positive charge on the proton are equal. Suppose, however, that these magnitudes differ from each other by 0.00010%. With what force would two copper coins, placed 1.0 m apart, repel each other? Assume that each coin contains 3 × 10 22 copper atoms. (Hint: A neutral copper atom contains 29 protons and 29 electrons.) What do you conclude? 22 Of the charge Q on a tiny sphere, a fraction α is to be trans- ferred to a second, nearby sphere. The spheres can be treated as particles. (a) What value of α maximizes the magnitude F of the elec- trostatic force between the two spheres? What are the (b) smaller and (c) larger values of α that put F at half the maximum magnitude? 23 If a cat repeatedly rubs against your cotton slacks on a dry day, the charge transfer between the cat hair and the cotton can leave you with an excess charge of −2.00 μC. (a) How many elec- trons are transferred between you and the cat? You will gradually discharge via the floor, but if instead of waiting, you immediately reach toward a faucet, a painful spark can suddenly appear as your fingers near the faucet. (b) In that spark, do electrons flow from you to the faucet or vice versa? (c) Just before the spark appears, do you induce positive or neg- ative charge in the faucet? (d) If, instead, the cat reaches a paw toward the faucet, which way do electrons flow in the resulting spark? (e) If you stroke a cat with a bare hand on a dry day, you should take care not to bring your fingers near the cat’s nose or you will hurt it with a spark. Considering that cat hair is an insulator, explain how the spark can appear. 24 In Fig. 21-15, three charged particles lie on an x axis. Par- ticles 1 and 2 are fixed in place. Particle 3 is free to move, but the net electrostatic force on it from particles 1 and 2 happens to be zero.
eBook - PDFElectromagnetism for Engineers
An Introductory Course
- P. Hammond(Author)
- 2013(Publication Date)
- Pergamon(Publisher)
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. This means that the smallest drop of our fluid must contain some thousands of electrons and the shortest distance between our charges must be about a thousand times the diameter of an atom. Thus distances of about 10 ^ m are admissible and the restriction is hardly a severe one. Within this limitation we shall be able to speak of point charges, meaning by this term not a mathematical point of zero dimension but a region of 10 m diameter. Moreover the experiments that we shall cite in the construction of the theory of electromagnetism will deal with currents and charges containing large numbers of electrons. The inverse square law is in fact as old as 1767, when Joseph Priestley suggested it. Priestley found that there was no electric force inside a metal cup which had been connected to an electric friction machine. This reminded him of a theorem of Newton's that inside a hollow sphere of gravitating matter there would be no gravitational force. Newton's experiment was an impossible one, at least at the time, because it would have had to be carried out in space away from other masses, but Priestley saw that his electrical experiment was strictly analogous; hence his suggestion of an inverse square law. Priestley's friend Cavendish built an apparatus consisting of two concentric spherical conductors joined by a wire. The spheres were first charged, then the connecting wire was withdrawn and after the outer sphere had been earthed a pith-ball electroscope was used to explore the charge on the inner sphere.
eBook - PDF- Paul Peter Urone, Roger Hinrichs(Authors)
- 2012(Publication Date)
- Openstax(Publisher)
• A conductor is a substance that allows charge to flow freely through its atomic structure. • An insulator holds charge within its atomic structure. • Objects with like charges repel each other, while those with unlike charges attract each other. • A conducting object is said to be grounded if it is connected to the Earth through a conductor. Grounding allows transfer of charge to and from the earth’s large reservoir. • Objects can be charged by contact with another charged object and obtain the same sign charge. • If an object is temporarily grounded, it can be charged by induction, and obtains the opposite sign charge. • Polarized objects have their positive and negative charges concentrated in different areas, giving them a non-symmetrical charge. • Polar molecules have an inherent separation of charge. 18.3 Coulomb’s Law • Frenchman Charles Coulomb was the first to publish the mathematical equation that describes the electrostatic force between two objects. • Coulomb’s law gives the magnitude of the force between point charges. It is F = k | q 1 q 2| r 2 , where q 1 and q 2 are two point charges separated by a distance r , and k ≈ 8.99×10 9 N · m 2 / C 2 • This Coulomb force is extremely basic, since most charges are due to point-like particles. It is responsible for all electrostatic effects and underlies most macroscopic forces. • The Coulomb force is extraordinarily strong compared with the gravitational force, another basic force—but unlike gravitational force it can cancel, since it can be either attractive or repulsive. • The electrostatic force between two subatomic particles is far greater than the gravitational force between the same two particles. 18.4 Electric Field: Concept of a Field Revisited • The electrostatic force field surrounding a charged object extends out into space in all directions.
eBook - PDF- Saad Osman Bashir(Author)
- 2015(Publication Date)
- IntechOpen(Publisher)
Chapter 3 The Electromagnetic Force between Two Parallel Current Conductors Explained Using Coulomb’s Law Jan Olof Jonson Additional information is available at the end of the chapter http://dx.doi.org/10.5772/61221 Abstract In this book chapter the electromagnetic force between two parallel electric conduc‐ tors has been derived, applying thereby the effects of propagation delay and the Spe‐ cial Relativity theory, taking thereby also into count the thus far neglected effects introduced by the voltage sources of both circuits. This has been done for a specific case consisting of two rectangular circuits, aligned to each other along one of the long sides, at a distance that is short compared to the long sides. The intention in doing so is to make a meaningful application of the concept of “two parallel conductors of in‐ finite length”, so that it is possible to make a complete calculation of the force between the two circuits, avoiding thus making a vague claim as for example Maxwell, saying that the other parts of the conductors do not contribute to the force. What is radically new in this interpretation is that it is Coulomb’s law that is responsible for the force. Keywords: Ampère’s Bridge, Ampère’s Law, Coulomb’s Law, electromagnetic force, Lorentz force, Lorentz transformation, parallel conductors, propagation delay, retard‐ ed action, Special Relativity theory, Sagnac effect, time dilatation 1. Introduction In several papers evidence has been presented that is able to refute the widely recognized electromagnetic theory of today [1-5]. One such fundamental law is Lorentz’ force law. Already 1997 a paper presented mathematical proofs showing that this law is unable to explain the repulsive force between collinear currents, demonstrated in the case of Ampère’s bridge [1]. Even Graneau’s exploding wires and Hering’s pump cause difficulties, when trying to use Lorentz’ force law in order to explain the effects that have been registered [6-11].
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