Physics
Conservation of Charge
The principle of conservation of charge states that the total electric charge in an isolated system remains constant over time. This means that charge cannot be created or destroyed, only transferred from one object to another. It is a fundamental principle in physics and is closely related to the law of conservation of energy.
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12 Key excerpts on "Conservation of Charge"
eBook - PDF- Edward Purcell(Author)
- 2011(Publication Date)
- Cambridge University Press(Publisher)
But the product of two charges is not a charge; there is no comparison. Two other properties of electric charge are essential in the elec- trical structure of matter: Charge is conserved, and charge is quan- tized. These properties involve quantity of charge and thus imply a measurement of charge. Presently we shall state precisely how charge can be measured in terms of the force between charges a certain dis- tance apart, and so on. But let us take this for granted for the time being, so that we may talk freely about these fundamental facts. Conservation of Charge 1.2 The total charge in an isolated system never changes. By iso- lated we mean that no matter is allowed to cross the boundary of the system. We could let light pass into or out of the system, since the "particles" of light, called photons, carry no charge at all. Within the system charged particles may vanish or reappear, but they always do so in pairs of equal and opposite charge. For instance, a thin-walled box in a vacuum exposed to gamma rays might become the scene of a "pair-creation" event in which a high-energy photon ends its exis- tence with the creation of an electron and a positron (Fig. l.l). Two electrically charged particles have been newly created, but the net change in total charge, in and on the box, is zero. An event that would violate the law we have just stated would be the creation of a positively charged particle without the simultaneous creation of a negatively charged particle. Such an occurrence has never been observed. Of course, if the electric charges of an electron and a positron ELECTROSTATICS: CHARGES AND. were not precisely equal in magnitude, pair creation would still violate the strict law of charge conservation. That equality is a manifestation of the particle-antiparticle duality already mentioned, a universal symmetry of nature.
eBook - PDF- Paul Peter Urone, Roger Hinrichs(Authors)
- 2012(Publication Date)
- Openstax(Publisher)
The law of Conservation of Charge is absolute—it has never been observed to be violated. Charge, then, is a special physical quantity, joining a very short list of other quantities in nature that are always conserved. Other conserved quantities include energy, momentum, and angular momentum. PhET Explorations: Balloons and Static Electricity Why does a balloon stick to your sweater? Rub a balloon on a sweater, then let go of the balloon and it flies over and sticks to the sweater. View the charges in the sweater, balloons, and the wall. Figure 18.10 Balloons and Static Electricity (http://cnx.org/content/m42300/1.5/balloons_en.jar) 18.2 Conductors and Insulators Figure 18.11 This power adapter uses metal wires and connectors to conduct electricity from the wall socket to a laptop computer. The conducting wires allow electrons to move freely through the cables, which are shielded by rubber and plastic. These materials act as insulators that don’t allow electric charge to escape outward. (credit: Evan-Amos, Wikimedia Commons) Some substances, such as metals and salty water, allow charges to move through them with relative ease. Some of the electrons in metals and similar conductors are not bound to individual atoms or sites in the material. These free electrons can Chapter 18 | Electric Charge and Electric Field 699 move through the material much as air moves through loose sand. Any substance that has free electrons and allows charge to move relatively freely through it is called a conductor. The moving electrons may collide with fixed atoms and molecules, losing some energy, but they can move in a conductor. Superconductors allow the movement of charge without any loss of energy. Salty water and other similar conducting materials contain free ions that can move through them. An ion is an atom or molecule having a positive or negative (nonzero) total charge. In other words, the total number of electrons is not equal to the total number of protons.
eBook - PDF- David J. Griffiths(Author)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
C H A P T E R 8 Conservation Laws 8.1 CHARGE AND ENERGY 8.1.1 The Continuity Equation In this chapter we study conservation of energy, momentum, and angular momen- tum, in electrodynamics. But I want to begin by reviewing the Conservation of Charge, because it is the paradigm for all conservation laws. What precisely does Conservation of Charge tell us? That the total charge in the universe is constant? Well, sure—that’s global Conservation of Charge. But local Conservation of Charge is a much stronger statement: If the charge in some region changes, then exactly that amount of charge must have passed in or out through the surface. The tiger can’t simply rematerialize outside the cage; if it got from inside to outside it must have slipped through a hole in the fence. Formally, the charge in a volume V is Q(t ) = V ρ(r, t ) d τ, (8.1) and the current flowing out through the boundary S is S J · d a, so local conser- vation of charge says dQ dt = − S J · d a. (8.2) Using Eq. 8.1 to rewrite the left side, and invoking the divergence theorem on the right, we have V ∂ρ ∂ t d τ = − V ∇ · J d τ, (8.3) and since this is true for any volume, it follows that ∂ρ ∂ t = −∇ · J. (8.4) This is the continuity equation—the precise mathematical statement of lo- cal Conservation of Charge. It can be derived from Maxwell’s equations— Conservation of Charge is not an independent assumption; it is built into the laws 356 8.1 Charge and Energy 357 of electrodynamics. It serves as a constraint on the sources (ρ and J). They can’t be just any old functions—they have to respect Conservation of Charge. 1 The purpose of this chapter is to develop the corresponding equations for local conservation of energy and momentum. In the process (and perhaps more impor- tant) we will learn how to express the energy density and the momentum density (the analogs to ρ ), as well as the energy “current” and the momentum “current” (analogous to J).
eBook - PDF- David Halliday, Robert Resnick, Kenneth S. Krane(Authors)
- 2019(Publication Date)
- Wiley(Publisher)
25-6 Conservation of Charge When a glass rod is rubbed with silk, a positive charge ap- pears on the rod. Measurement shows that a corresponding negative charge appears on the silk. This suggests that rub- bing does not create charge but merely transfers it from one object to another, disturbing slightly the electrical neutrality of each. This hypothesis of the Conservation of Charge has stood up under careful experimental tests both for large- scale objects and for atoms, nuclei, and elementary parti- cles. No exceptions have ever been found. In analogy with other conservation laws, such as conser- vation of momentum or conservation of energy, we can ex- press conservation of electric charge as (25-18) In any process occurring in an isolated system the net initial charge must equal the net final charge. In finding the net charge, it is important to take into account the signs of the individual charges. An interesting example of charge conservation comes about when an electron (charge e) and an antielectron q constant or q i q f . F(R/2) F(R) 1 16 . q R/2 0 dV R/2 0 Zer R 4 4 r 2 dr Ze 16 . or positron (charge e) are brought close to each other. The two particles may annihilate one another, converting all their rest energy into radiant energy. The radiant energy may appear in the form of two gamma rays (high-energy packets of electromagnetic radiation, which are charge- less): The net charge is zero both before and after the event, and charge is conserved. Certain uncharged particles, such as the neutral me- son, sometimes decay into two gamma rays: This decay conserves charge, the total charge again being 0 before and after the decay. For another example, a neu- tron (q 0) decays into a proton (q e) and an elec- tron (q e) plus another neutral particle, a neutrino (q 0): The total charge is zero, both before and after the decay, and charge is conserved.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
The electrostatic force, on the other hand, is repulsive for charges of the same sign, so it is unable to collect either positive charge or negative charge into large concen- trations that would then exert large electrostatic forces. Charge Is Conserved If you rub a glass rod with silk, a positive charge appears on the rod. Measure- ment shows that a negative charge of equal magnitude appears on the silk. This suggests that rubbing does not create charge but only transfers it from one body to another, upsetting the electrical neutrality of each body during the process. This hypothesis of Conservation of Charge, first put forward by Benjamin Franklin, has stood up under close examination, both for large-scale charged bodies and for atoms, nuclei, and elementary particles. No exceptions have ever been found. Thus, we add electric charge to our list of quantities — including energy and both linear momentum and angular momentum — that obey a conservation law. Important examples of the Conservation of Charge occur in the radioactive decay of nuclei, in which a nucleus transforms into (becomes) a different type of nucleus. For example, a uranium-238 nucleus ( 238 U) transforms into a thorium-234 nucleus ( 234 Th) by emitting an alpha particle. Because that particle has the same makeup as a helium-4 nucleus, it has the symbol 4 He. The number used in the name of a nucleus and as a superscript in the symbol for the nucleus is called the mass number and is the total number of the protons and neutrons in the nucleus. For example, the total number in 238 U is 238. The number of protons in a nucleus is the atomic number Z, which is listed for all the elements in Appendix F. From that list we find that in the decay 238 U → 234 Th + 4 He, (21-13) 540 CHAPTER 21 COULOMB’S LAW the parent nucleus 238 U contains 92 protons (a charge of +92e), the daughter nucleus 234 Th contains 90 protons (a charge of +90e), and the emitted alpha par- ticle 4 He contains 2 protons (a charge of +2e).
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
The electrostatic force, on the other hand, is repulsive for charges of the same sign, so it is unable to collect either positive charge or negative charge into large concen- trations that would then exert large electrostatic forces. Charge Is Conserved If you rub a glass rod with silk, a positive charge appears on the rod. Measure- ment shows that a negative charge of equal magnitude appears on the silk. This suggests that rubbing does not create charge but only transfers it from one body to another, upsetting the electrical neutrality of each body during the process. This hypothesis of Conservation of Charge, first put forward by Benjamin Franklin, has stood up under close examination, both for large-scale charged bodies and for atoms, nuclei, and elementary particles. No exceptions have ever been found. Thus, we add electric charge to our list of quantities — including energy and both linear momentum and angular momentum — that obey a conservation law. Important examples of the Conservation of Charge occur in the radioactive decay of nuclei, in which a nucleus transforms into (becomes) a different type of nucleus. For example, a uranium-238 nucleus ( 238 U) transforms into a thorium-234 nucleus ( 234 Th) by emitting an alpha particle. Because that particle has the same makeup as a helium-4 nucleus, it has the symbol 4 He. The number used in the name of a nucleus and as a superscript in the symbol for the nucleus is called the mass number and is the total number of the protons and neutrons in the nucleus. For example, the total number in 238 U is 238. The number of protons in a nucleus is the atomic number Z, which is listed for all the elements in Appendix F. From that list we find that in the decay 238 U → 234 Th + 4 He, (21-13) 622 CHAPTER 21 COULOMB’S LAW the parent nucleus 238 U contains 92 protons (a charge of +92e), the daughter nucleus 234 Th contains 90 protons (a charge of +90e), and the emitted alpha par- ticle 4 He contains 2 protons (a charge of +2e).
- Ribaric Marijan, Luka Sustersic(Authors)
- 1990(Publication Date)
- World Scientific(Publisher)
Parti CONSERVATION LAWS OF CLASSICAL ELECTRODYNAMICS In modern theoretical physics, symmetries and conservation laws play a leading role in constructing basic equations describing physical processes, e.g. fundamental interactions. When the basic equations are given, we try to gain an understanding of the physics they describe by seeking the physi-cally interpretable properties of their solutions, cf. Feynman, Leighton and Sands [1965, §§ 2.1 and 41-6]. The problem with classical electrodynamics, as stated by Jackson [1975, §17.1], is that we are able to obtain relevant solutions and study their properties only in two limiting cases: ... one in which the sources of charge and current are specified and the resulting electromagnetic fields are calculated, and the other in which the external electromagnetic fields are specified and the motion of charged particles or currents is calculated. Occasionally, ... , the two problems are com-bined. But the treatment is a step wise one—first the motion of the charged particle in the external field is determined, neglecting the emission of radi-ation; then the radiation is calculated from the trajectory as a given source distribution. It is evident that this manner of handling problems in elec-trodynamics can be of only approximate validity. As a consequence, we do not yet have physical understanding of those electromechanical systems where we cannot neglect the mutual interaction between electric charges and currents, and the electromagnetic field emitted by them; witness the absence of any generally accepted equation of motion for pointlike charged particles. To alleviate this situation we propose to study electrodynamic conservation laws and conserved quantities, because we hope with Rohrlich [1965, §3-17], that The understanding of a physical system is greatly aided by the knowledge of those physical quantities that do not change during this development.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
The electrostatic force, on the other hand, is repulsive for charges of the same sign, so it is unable to collect either positive charge or negative charge into large concentrations that would then exert large electrostatic forces. Additional examples, video, and practice available at WileyPLUS 21.3 CHARGE IS CONSERVED Learning Objectives After reading this module, you should be able to . . . 21.3.1 Identify that in any isolated physical process, the net charge cannot change (the net charge is always conserved). 21.3.2 Identify an annihilation process of particles and a pair production of particles. 21.3.3 Identify mass number and atomic number in terms of the number of protons, neutrons, and electrons. Key Ideas ● The net electric charge of any isolated system is always conserved. ● If two charged particles undergo an annihilation process, they have opposite signs of charge. ● If two charged particles appear as a result of a pair production process, they have opposite signs of charge. 655 21.3 CHARGE IS CONSERVED Thus, we add electric charge to our list of quantities—including energy and both linear momentum and angular momentum—that obey a conservation law. Important examples of the Conservation of Charge occur in the radioactive decay of nuclei, said to be radionuclides. In the process, a nucleus transforms into (becomes) a different type of nucleus. For example, a uranium-238 nucleus ( 92 238 U) transforms into a thorium-234 nucleus ( 90 234 Th) by emitting an alpha par- ticle. That particle can be symbolized with α, but because it has the same makeup as a helium-4 nucleus, it can also be symbolized with 2 4 He. In these symbols, we use the chemical notation for the element. The superscript is the mass number A that gives the total number of protons and neutrons in the nucleus (collectively called the nucleons), and the subscript is the atomic number or charge number Z that gives the number of protons.
- Nima Gharib, Javad Farrokhi Derakhshandeh, Peter Radziszewski(Authors)
- 2022(Publication Date)
- Elsevier(Publisher)
Charge is classified into two types, which are referred to as “plus” and “minus,” since their effects tend to cancel out (having both+q and -q at the same spot electrically equals having no charge at all). This may seem self-evident; however, it is good to consider additional possibilities: what if there were eight or 10 distinct species of charge? (In reality, in chromodynamics, three variables comparable to electric charge exist, each of which may be either positive or negative). Or what if the two types did not tend to cancel each other out? The remarkable reality is that plus and minus charges exist in bulk matter in precisely equal numbers, to the extent that their effects are virtually totally canceled. Without this, we would be exposed to huge forces. For instance, if the cancellation was even one part in 10e10 off, a potato would explode severely.Charge is conserved: it cannot be generated or destroyed; what exists now existed before. (A plus charge may “annihilate” an equivalent minus charge, but a plus charge cannot just vanish; it must be picked up by something.) Thus, the universe's overall charge is fixed in time. This is referred to as global charge conservation. Indeed, we may state something much more emphatically: Global conservation would enable for a charge to vanish in one area/city and resurface instantaneously in another area/city (which would have no effect on the total), but we know this does not occur. If the charge originated in the first area/city and traveled to second area/city, it must have followed a continuous path between the two cities. This is referred to as local charge conservation.Charge is quantized. Although classical electrodynamics makes no such requirement, the truth is that electric charge exists only in discrete lumps—integer multiples of the fundamental unit of charge. If we call the charge on the proton+e, then the electron carries charge − e; the neutron charge zero; the pi mesons+e, 0, and −
eBook - ePub- L D Landau(Author)
- 2013(Publication Date)
- Pergamon(Publisher)
CHAPTER 3 CHARGES IN ELECTROMAGNETIC FIELDS Publisher Summary This chapter explores charge particles in electromagnetic fields. In the theory of relativity, elementary particles are considered as rigid bodies whose dimensions all remain unchanged in the reference system in which they are at rest. However, it is easy to see that the theory of relativity makes the existence of rigid bodies impossible in general. A charge located in a field not only is subjected to a force exerted by the field, but also in turn acts on the field, changing it. However, if the charge e is not large, the action of the charge on the field can be neglected. The equations of motion of a charge in an electromagnetic field are invariant with respect to a change in sign of the time, that is, the two time directions are equivalent. Thus, if a certain motion is possible according to the equations of mechanics, the reverse motion is also possible, in which the system passes through the same states in reverse order. Furthermore, the gauge invariance of the equations of electrodynamics and the Conservation of Charge are closely related to one another. The constancy of the acceleration of a charged particle is related to the fact that the electric field does not change for Lorentz transformations having velocities V along the direction of the field. § 15 Elementary particles in the theory of relativity The interaction of particles can be described with the help of the concept of a field of force. Namely, instead of saying that one particle acts on another, we may say that the particle creates a field around itself; a certain force then acts on every other particle located in this field. In classical mechanics, the field is merely a mode of description of the physical phenomenon—the interaction of particles. In the theory of relativity, because of the finite velocity of propagation of interactions, the situation is changed fundamentally
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
Like charges repel, unlike charges attract, and the force between charges decreases with the square of the distance. • The vast majority of positive charge in nature is carried by protons, whereas the vast majority of negative charge is carried by electrons. The electric charge of one electron is equal in magnitude and opposite in sign to the charge of one proton. • An ion is an atom or molecule that has nonzero total charge due to having unequal numbers of electrons and protons. • The SI unit for charge is the coulomb (C), with protons and electrons having charges of opposite sign but equal magnitude; the magnitude of this basic charge is e ≡ 1.602 × 10 −19 C Chapter 5 | Electric Charges and Fields 221 • Both positive and negative charges exist in neutral objects and can be separated by bringing the two objects into physical contact; rubbing the objects together can remove electrons from the bonds in one object and place them on the other object, increasing the charge separation. • For macroscopic objects, negatively charged means an excess of electrons and positively charged means a depletion of electrons. • The law of Conservation of Charge states that the net charge of a closed system is constant. 5.2 Conductors, Insulators, and Charging by Induction • A conductor is a substance that allows charge to flow freely through its atomic structure. • An insulator holds charge fixed in place. • Polarization is the separation of positive and negative charges in a neutral object. Polarized objects have their positive and negative charges concentrated in different areas, giving them a charge distribution. 5.3 Coulomb's Law • Coulomb’s law gives the magnitude of the force between point charges. It is F → 12 (r) = 1 4πε 0 q 1 q 2 r 12 2 r ^ 12 where q 2 and q 2 are two point charges separated by a distance r. This Coulomb force is extremely basic, since most charges are due to point-like particles.
- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
3. Conductors are materials in which a significant number of electrons are free to move. The charged particles in nonconductors (insulators) are not free to move. 4. Electric current i is the rate dq/dt at which charge passes a point: i = dq ___ dt . 5. Coulomb’s law describes the electrostatic force (or electric force) between two charged particles. 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 magnitude 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 constant (or Coulomb constant) k = 8.99 × 10 9 N · m 2 /C 2 . 6. 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). 7. If multiple electrostatic forces act on a particle, the net force is the vector sum (not scalar sum) of the individual forces. 8. 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. 9. Shell theorem 2: A charged particle inside a shell with charge uniformly dis- tributed on its surface has no net force acting on it due to the shell. 10. Charge on a conducting spherical shell spreads uniformly over the (external) surface. LEARNING OBJECTIVES 607 Coulomb’s Law 608 CHAPTER 21 Coulomb’s Law diagram, showing the electrostatic force (Coulomb force) on it and anchoring the tail of the force vector on that particle.
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