Physics
Electrostatics
Electrostatics is the study of stationary electric charges and the forces they exert. It deals with phenomena such as electric fields, electric potential, and the behavior of conductors and insulators in the presence of electric charges. The principles of electrostatics are fundamental to understanding the behavior of electrically charged particles and the interactions between them.
Written by Perlego with AI-assistance
Related key terms
1 of 5
12 Key excerpts on "Electrostatics"
eBook - PDF- Bhag Singh Guru, Hüseyin R. Hiziroglu(Authors)
- 2009(Publication Date)
- Cambridge University Press(Publisher)
3 Electrostatics 3.1 Introduction ................................. Armed with the necessary tools of vector operations and vector calculus, we are now ready to explore electromagnetic field theory. In this chapter, we study static electric fields (Electrostatics), due to charges at rest. A charge can be either concentrated at a point or distributed in some fashion. In any case, the charge is assumed to be constant in time. We begin our discussion by stating Coulomb’s law of electrostatic force between two point charges fixed in space. We define the electric field intensity as the force per unit charge. We then want to establish that a) The electric field intensity is irrotational or conservative, and b) The work done in moving a charge from one point to another in an electrostatic field is independent of the path taken and depends only upon the endpoints of the path. We will express the electric field intensity in terms of electric potential and deduce an expression for the energy required to move a charge from one location to another in an electrostatic field. We will also explore the influence of the medium on electrostatic fields and define bound charge densities ; examine several methods (Gauss’s law, Poisson’s and Laplace’s equations, method of images) of solving electrostatic field problems ; and develop the concept of ca-pacitance and obtain an equation for the energy stored in a capacitor. Some aspects of electrostatic fields discussed in this chapter may appear to be a repetition of what you have already studied in physics. Some repetition is necessary, not only to maintain a continuous link from one section to another, but also to motivate the learning process. We are convinced that a discerning student will find this repetition helpful. 3.2 Coulomb’s law ................................. Electrostatics is based upon the quantitative and experimentally veri-fiable statement of Coulomb’s law pertaining to the electric force that 70
- Harald J W M??ller-Kirsten(Author)
- 2004(Publication Date)
- WSPC(Publisher)
Chapter 2 Electrostatics - Basic Aspects 2.1 Introductory Remarks In this chapter the Coulomb law is introduced, and various static conse- quences are investigated, such as electrical screening and diverse applica- tions. The latter require also the introduction of essential mathematics, in particular that of the delta distribution. 2.2 The Coulomb Law Electrostatics is the theory of static charges, which means that moving charges, i.e. currents, are not considered. The fundamental phenomeno- logical law which is the basis of Electrostatics is Coulomb’s law, which deter- mines the force acting between two point charges q1, q2 and which in vacuum is given by q1q2 r. F12 = k- 7-3 Here r = r l - r2 is the vectorial separation of the charges qi at positions ri. k is the constant fixed by the choice of units. In the ISU, as explained in Chapter 1, 1 k=- in vacuum. The force is given in newtons (N), the charge in coulombs (C) and the separation in meters (m). The electric field strength E(r) at a point r as in Fig. 2.1 is defined as the Coulomb force acting on a unit charge (+1C) 4TEo 9 10 CHAPTER 2. Electrostatics - BASIC ASPECTS at this point, i.e. In the ISU or MKSA-system of units the electric field strength is given in units of N/C or V/m. In the Gaussian system the charge is given in stat- coulombs, the distance in cm, the force in dynes, and the electric field strength in statvolt/cm (1 C = 3 x lo9 statcoulombs, 1 statcoulomb = 10 e.s.u.; 1 newton = lo5 dynes). Fig. 2.1 Point charges q1 and $1. It should be remembered that a charge q can be positive or negative. Con- ventionally electric lines of force are drawn as leaving positive charges and directed towards negative charges. In this sense positive charges are regarded as sources of the electric fields and negative charges as sinks. One distinguishes between discrete charge distributions (charges at dis- tinct points) and continuous charge distributions (charges spread over spatial domains).
- Lawrence N. Dworsky(Author)
- 2014(Publication Date)
- Wiley-IEEE Press(Publisher)
1 A Review of Basic ElectrostaticsElectric and magnetic phenomena, including electromagnetic wave propagation, are described by Maxwell’s equations.1 When nothing is changing with time, that is, when all derivatives with respect to time are zero, the electric and the magnetic phenomena decouple and become separate electric and magnetic phenomena. These are referred to respectively as Electrostatics, which describes the properties of systems with separated static regions of positive and negative electric charge (although the entire system is charge-neutral), and magnetostatics, which describes the properties of systems with electric currents and/or magnetized materials.In this book we shall consider only Electrostatics. This subset of a subset of topics describes a vast number of real-world situations. Chapter 2 describes some practical needs and uses of electrostatic analyses, the remainder of the book will be dedicated to examining several techniques for performing these analyses.The materials to follow are intended to be a quick review of the relationships that will be used throughout this book. The intent here is to provide a consistent set of notation using all the relationships that will be needed going forward. Many of these relationships are stated without derivation or proof. A more complete Electrostatics theory text is recommended for newcomers to the subject. There are very many excellent texts available. The references list at the end of this chapter is certainly not exhaustive, but the texts cited are considered standards in the field.1.1 Charge, Force, and the Electric Field
Electric charges exert forces on one another. This is the basis of Electrostatics. The characteristics of these forces are summarized in Coulomb’s law:- Electric charge carries a polarity, or sign. The choice of sign was originally arbitrary, but now is established by tradition—the electron, the most common charged subatomic particle, carries a negative charge.
eBook - PDF- Pierluigi Zotto, Sergio Lo Russo, Paolo Sartori(Authors)
- 2022(Publication Date)
- Società Editrice Esculapio(Publisher)
Electrostatic Field and Electrostatic Potential 2.1 Introduction Electrostatic force, as defined by Coulomb’s law, is formally identical to gravitational force, as expressed by Newton’s law, with the mere substitution of the mass of the bodies with their charge. It is therefore possible to define an electrostatic field, in full analogy with respect to the gravitational field definition, as the region of the space where an electrostatic force is exerted and it is also possible to associate an electrostatic potential with each point of this region. The general properties of an electrostatic force and of a gravitational force are obviously the same. 2.2 Electrostatic field Consider a point-like particle of mass m, charged with an amount of electric charge q, which lies in an empty space, that is in a region of the space where all the other bodies are placed at a very large distance from the selected body. Bring from infinite distance another point-like body which carries a charge ′ q (usually called test-charge) into this empty space and measure the intensity and the direction of the force being exerted between the two charges q and ′ q in each point P which belongs to this space. This operation draws a map of the electrostatic force vector F = 1 4πε 0 q ′ q r 2 u r , where u r is the unit vector of a polar coordinate reference system whose origin is chosen in point O, where body m is placed. Such a map is correct only if the size of body m with respect to the distance from point P, where charge ′ q is placed, is truly negligible, because electrostatic induction causes charge displacement both inside the body and on its surface. The map is therefore exact in the whole space only if the charge ′ q has a negligible value and therefore it cannot generate any relevant displacement of charge q which modifies how it is distributed in a body.
- Nima Gharib, Javad Farrokhi Derakhshandeh, Peter Radziszewski(Authors)
- 2022(Publication Date)
- Elsevier(Publisher)
Chapter 3: Fundamentals of electrodynamics
Abstract
This chapter focuses on the fundamentals of Electrostatics for particles. Important ideas and terminologies are introduced for subsequent debate. In addition, we present essential equations and mathematical tools to emphasize the physical nature of the issues. The offered contents in this chapter will serve as a strong basis for investigations into related applications of Electrostatics of particles.Keywords
Charge Distribution; Electric Charge; Electromotive Force; Electrostatics of Particles; Farday's Law; Ohm's Law; Tribocharging1. Introduction to Electrostatics of particles
The introduction and fundamentals of electrodynamics theory were published by David Griffiths (2021) with a clear and accessible explanation for undergraduate and postgraduate levels in the Fourth Edition. It is good to emphasize that the textbook published by David has been designed with the conceptual difficulties frequently encountered by scholars and researchers, including students and senior researchers, which offer the theoretical phases with carefully selected examples and thorough illustrations. Therefore, the main relative sections of this chapter, which relate to the Electrostatics of particles, are chosen from the textbook of Introduction to Electrodynamics (Griffiths, 2021 ). The presented materials in this chapter will serve as a solid foundation for studies of related applications of Electrostatics of particles.For the majority of engineering applications, Newtonian mechanics is sufficient. However, when applied to objects moving at high velocities (close to the speed of light), it is incorrect and must be replaced by special relativity (introduced by Einstein in 1905); when applied to extremely small objects (close to the size of atoms), it fails for a variety of reasons and must be replaced by quantum mechanics (developed by Bohr, Schrödinger, Heisenberg, and many others). Because modern particle physics deals with extremely fast and extremely small objects, a mechanics that incorporates both relativity and quantum principles is required, which is known as quantum field theory; it was developed in the 1930 and 1940s but is still not considered a fully satisfactory system today. Therefore, considering some assumptions and simplifications, electrodynamic phenomenon can be considered by classical mechanics. Mechanics describes how a system will act under the influence of a specific force. There are just four fundamental forces that physics is now aware of, which are listed as follows in decreasing order of strength: (1) strong, (2) electromagnetic, (3) weak, and (4) gravitational. Categorizing forces according to the aforementioned list may generate the following questions: Where is the point of contention? Where is the “normal” force that prevents you from collapsing? Where are the chemical forces that connect molecules? Where does the impact force between two colliding billiard balls originate? The explanation is that they are all electromagnetic forces. Indeed, it is not hyperbolic to assert that we live in an electromagnetic world—nearly every force encountered in daily life, with the exception of gravity, is electromagnetic in origin. Because the strong forces that keep protons and neutrons together in the atomic nucleus have an incredibly narrow range, humans do not “feel” them, despite their hundredfold greater strength than electrical forces. Weak forces, which are responsible for some types of radioactive decay, are likewise short-ranged and significantly weaker than electromagnetic forces. Gravity, on the other hand, is so pitifully weak (in comparison to the others) that we only sense it in the presence of massive mass concentrations (such as the earth and the sun). The electrical attraction between two electrons is (10e42
eBook - PDF- Michael Neidle(Author)
- 2013(Publication Date)
- Butterworth-Heinemann(Publisher)
Chapter 3 STATIC ELECTRICITY Static electricity refers to electricity 4 at rest' on an insulator in contrast to current electricity where the electrons are in continuous movement through a conductor. A common effect of static electricity occurs when a portion of insulation being stripped from a p.v.c.-insulated cable flies off and clings to a wall. If a fountain pen is rubbed, it is found to pick up small pieces of light materials such as paper, etc. During dry cold winters, office workers walking on nylon carpets have been known to feel a prickle and even see sparks coming from their fingers when approaching hot-water radiators. These are all simple examples of electric charges that have been built up. An understanding of them helps to explain electrical applications of great practical importance. 3.1. Charges The atoms which comprise all matter, i.e. everything which occu-pies space, are ultimately electrical in nature. The simple hydrogen atom indicates the general pattern. The inner core or nucleus contains the positively-charged proton ; orbiting round the nucleus is the single negatively-charged electron. Unimaginably small as is the atom—smaller than 10 6 millimetres in diameter—its structure contains the neutron, which possesses no charge, and many other sub-atomic particles. Fortunately, most of our electrical theory can be explained in terms of the proton and electron parts of the atom alone. Normal materials, such as the book you are reading, are electric-ally neutral, i.e., they show no external electricity because the proton and electron charges exactly balance or cancel each other out. An atom is positively charged when electrons are lost and negatively charged when an atom possesses surplus electrons. Sometimes the process is known as ionisation. Atoms which are deficient in electrons are called positive ions and those which have gained electrons, negative ions.
eBook - PDF- Paul Peter Urone, Roger Hinrichs(Authors)
- 2012(Publication Date)
- Openstax(Publisher)
electric field lines: electromagnetic force: electron: electrostatic equilibrium: electrostatic force: electrostatic precipitators: electrostatic repulsion: Electrostatics: Faraday cage: field: free charge: free electron: grounded: grounded: induction: ink-jet printer: insulator: ionosphere: laser printer: law of conservation of charge: photoconductor: point charge: polar molecule: polarization: polarized: proton: screening: static electricity: test charge: Van de Graaff generator: vector: vector addition: a series of lines drawn from a point charge representing the magnitude and direction of force exerted by that charge one of the four fundamental forces of nature; the electromagnetic force consists of static electricity, moving electricity and magnetism a particle orbiting the nucleus of an atom and carrying the smallest unit of negative charge an electrostatically balanced state in which all free electrical charges have stopped moving about the amount and direction of attraction or repulsion between two charged bodies filters that apply charges to particles in the air, then attract those charges to a filter, removing them from the airstream the phenomenon of two objects with like charges repelling each other the study of electric forces that are static or slow-moving a metal shield which prevents electric charge from penetrating its surface a map of the amount and direction of a force acting on other objects, extending out into space an electrical charge (either positive or negative) which can move about separately from its base molecule an electron that is free to move away from its atomic orbit when a conductor is connected to the Earth, allowing charge to freely flow to and from Earth’s unlimited reservoir connected to the ground with a conductor, so that charge flows freely to and from the Earth to the grounded object the process by which an electrically
eBook - PDF- Michael Neidle(Author)
- 2016(Publication Date)
- Butterworth-Heinemann(Publisher)
Chapter 3 STATIC ELECTRICITY Static electricity refers to electricity 'at rest' on an insulator in contrast to current electricity where the electrons are in continuous movement through a conductor. A common effect of static electricity occurs when a portion of insulation being stripped from a p.v.c.-insulated cable flies off and clings to a wall. If a fountain pen is rubbed, it is found to pick up small pieces of light materials such as paper, etc. During dry cold winters, office workers walking on nylon carpets have been known to feel a prickle and even see sparks coming from their fingers when approaching hot-water radiators. These are all simple examples of electric charges that have been built up. An understanding of them helps to explain electrical applications of great practical importance. 3.1. Charges The atoms which comprise all matter, i.e. everything which occu-pies space, are ultimately electrical in nature. The simple hydrogen atom indicates the general pattern. The inner core or nucleus contains the positively-charged proton ; orbiting round the nucleus is the single negatively-charged electron. Unimaginably small as is the atom—smaller than 10^ millimetres in diameter—its structure contains the neutron, which possesses no charge, and many other sub-atomic particles. Fortunately, most of our electrical theory can be explained in terms of the proton and electron parts of the atom alone. Normal materials, such as the book you are reading, are electric-ally neutral, i.e., they show no external electricity because the proton and electron charges exactly balance or cancel each other out. An atom is positively charged when electrons are lost and negatively charged when an atom possesses surplus electrons. Sometimes the process is known as ionisation. Atoms which are deficient in electrons are called positive ions and those which have gained electrons, negative ions.
eBook - PDF- Y K Lim(Author)
- 1986(Publication Date)
- WSPC(Publisher)
Chapter I FUNDAMENTAL CONCEPTS AND EXPERIMENTAL LAWS Electrodynamics deals with the fields and radiation of moving charges. In describing the interaction between charges it is convenient, both mathematically and physically, to consider it, not as forces that act at a distance, but as the force exerted by the field set up by one charge on the other. This approach is in fact essential for charges in relative motion as electromagnetic effects are found to propagate with finite velocity. The four field vectors, Ej B, D and H, which are fundamental in Maxwell's electro-magnetic theory are introduced and discussed in this chapter in a phenomenologiaal manner. In addition, a short review is made of the experimental laws which lead to Maxwell's equations. 1.1 Electric Field Intensity E Electric field is said to exist at a point where a stationary particle experiences a force on account of its charge. The electric field intensity or electric field strength E is defined as the force per unit charge acting on a small positive charge q' introduced at that point. Let F be the electric force acting on the test charge, then by definition 2 . E - lim -L . (1.1) q' + OQ' The limit q' + Q is required in order that the introduction of the test charge will not significantly Influence the source; the field can then be described independently of the presence of a test charge. The finite magnitude of the elementary charge e does not permit the limiting process to be realized even in principle. The definition applies, therefore, to macroscopic phenomena only. For microscopic processes, the field is usually defined in terms of its source, assuming that the macroscopic laws governing the field-source relationship still apply. The simplest type of electric field is one that is set up by stationary charges, the electrostatic field. We shall confine ourselves in the first instance to free space.
eBook - PDF- David J. Griffiths(Author)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
C H A P T E R 2 Electrostatics 2.1 THE ELECTRIC FIELD 2.1.1 Introduction The fundamental problem electrodynamics hopes to solve is this (Fig. 2.1): We have some electric charges, q 1 , q 2 , q 3 , . . . (call them source charges); what force do they exert on another charge, Q (call it the test charge)? The positions of the source charges are given (as functions of time); the trajectory of the test particle is to be calculated. In general, both the source charges and the test charge are in motion. The solution to this problem is facilitated by the principle of superposition, which states that the interaction between any two charges is completely unaffected by the presence of others. This means that to determine the force on Q, we can first compute the force F 1 , due to q 1 alone (ignoring all the others); then we compute the force F 2 , due to q 2 alone; and so on. Finally, we take the vector sum of all these individual forces: F = F 1 + F 2 + F 3 + . . . Thus, if we can find the force on Q due to a single source charge q , we are, in principle, done (the rest is just a question of repeating the same operation over and over, and adding it all up). 1 Well, at first sight this looks very easy: Why don’t I just write down the formula for the force on Q due to q , and be done with it? I could, and in Chapter 10 I shall, but you would be shocked to see it at this stage, for not only does the force on Q depend on the separation distance r between the charges (Fig. 2.2), it also q 2 Q “Source” charges “Test” charge q 1 q i FIGURE 2.1 Q q r FIGURE 2.2 1 The principle of superposition may seem “obvious” to you, but it did not have to be so simple: if the electromagnetic force were proportional to the square of the total source charge, for instance, the principle of superposition would not hold, since (q 1 + q 2 ) 2 = q 2 1 + q 2 2 (there would be “cross terms” to consider). Superposition is not a logical necessity, but an experimental fact. 59
eBook - PDFEngineering Electromagnetics
Pergamon Unified Engineering Series
- David T. Thomas, Thomas F. Irvine, James P. Hartnett, William F. Hughes(Authors)
- 2013(Publication Date)
- Pergamon(Publisher)
3 Techniques for the Electrostatic Field INTRODUCTION One might suppose from the simple appearance of Maxwell's Equations that solutions might be readily available for even the most general of problems. Unfortunately (or fortunately 1 ) such is not the case; in fact, almost the opposite is true. We find that solutions are possible only in simple, greatly idealized problems in which a mathematical model of the actual problem is solved. It is this process of simplifying and idealizing problems which is the heart of engineering. The pruning of irrelevant information, the neglecting of influences which produce small effects, and approximating still further in order to simplify the model all precede the actual solution of the problem. Only a reasonable facsimile of the original problem is ever actually solved. Yet from these reason-able facsimiles we produce theories of the behavior of electromagnetic fields, and from the ever ongoing experiments we substantiate these theories. ELECTROSTATIC FIELD EQUATIONS AND DEFINITIONS Electromagnetic problems are divided into many groups or categories of idealized problems. Within each group many problems are solved in detail and studied for physical interpretation and generalization. Gradually, problems on the fringes of each group are studied to enlarge our knowledge of more general problems which may some day be solved. The initial group of problems to be discussed here are electrostatic problems. The term electrostatic implies that the problem to be worked satisfies two restrictions: 1. There is no time dependence (static). 2. Only electric fields (E, D and of course sources) are considered. *It is fortunate in that there are problems yet to be solved by those of you just beginning your lifelong affair with Maxwell's Equations and the beauties of electromagnetics. 57 58 Techniques for the Electrostatic Field Restriction No.
eBook - PDF- Yung-Kuo Lim(Author)
- 1993(Publication Date)
- WSPC(Publisher)
PART 1 Electrostatics 1. BASIC LAWS OF Electrostatics (1001-1023) 1001 A static charge distribution produces a radial electric field e-k E = A-e, , r where A and b are constants. (a) What is the charge density? Sketch it. (b) What is the total charge Q? Solution: (a) The charge density is given by Maxwell’s equation p = V . D = BOV .E. AS V. uv = VU * V + UV ’v, Making use of Dirac’s delta function 6(r) with properties 6(r)=O for r#O, =oo for r=O, J, 6(r)dV = 1 if v encloses r = 0, = 0 if otherwise, Thus 3 4 Problems U Solmiionr on Elcdromagnciirm Hence the charge distribution consists of a positive charge 4rsoA at the origin and a spherically symmetric negative charge distribution in the sur- rounding space, as shown in Fig. 1.1. Fig. 1.1 (b) The total charge is It can also be obtained from Gauss' flux theorem: Q= r-wx lim faoE-dS in agreement with the above. 1002 Suppose that, instead of the Coulomb force law, one found experimen- tally that the force between any two charges q1 and 42 was where a is a constant. (a) Write down the appropriate electric field E surrounding a point charge q. (b) Choose a path around this point charge and calculate the line integral f E - dl. Compare with the Coulomb result. (c) Find f En dS over a spherical surface of radius r1 with the point charge at this center. Compare with the Coulomb result. (d) Repeat (c) at radius r1 +A and find V .E at a distance rl from the point charge. Compare with the Coulomb result. Note that A is a small quantity. ( Wisconsin) Solution: (a) The electric field surrounding the point charge q is E(r) = -- I (I - f i l e r , h e 0 r2 where r is the distance between a space point and the point charge q, and er is a unit vector directed from q to the space point. Fig. 1.2 (b) As in Fig. 1.2, for the closed path L we find 6 Problemr d Solviionr on Eleciromrgnciirm and From Coulomb’s law Fl2 = a e r , z t we can obtain the electric field ! ? of the point charge E(r) = - 4mOr2 er * Clearly, one has A E .
Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
