Physics
Electric Field Energy
Electric field energy refers to the potential energy associated with the arrangement of electric charges in an electric field. It is a measure of the work that can be done by the electric field on a charged particle. The energy stored in an electric field is proportional to the square of the electric field strength and the amount of charge present.
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11 Key excerpts on "Electric Field Energy"
eBook - PDF- Ruth W. Chabay, Bruce A. Sherwood(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
QUESTION Where is there a decrease of energy in the surroundings? Evidently the energy stored in the fields surrounding the two particles must decrease. Clearly, the electric field at any location in space does change as the positions of the particles change. The electric field in the region between the particles gets larger, but the electric field everywhere else in space decreases (since E dipole is proportional to s, the distance between the particles). It would be a somewhat daunting task to integrate E 2 over the volume of the Universe, with the additional complication that close to a charged particle E approaches infinity. However, we do not actually need to do this integral to figure out the change in energy of the electric field throughout space. Since ∆(Field energy) +∆K positron +∆K electron = 0 then ∆(Field energy) = -2(∆K electron ) In this example, the principle of conservation of energy leads us directly to the idea that energy must be stored in electric fields, since there is no other way to account for the decrease of energy in the surroundings. If we had chosen the electron plus the positron as our system, we would have found that ∆U el is equal to -2(∆K electron ). The change in potential energy for the two-particle system is the same as the change in the field energy. Evidently in a multiparticle system we can either consider a change in potential energy or a change in field energy (but not both); the quantities are equal. The idea of energy stored in fields is a general one. It is not only electric fields that carry energy, but magnetic fields and gravitational fields as well. 658 Chapter 16 Electric Potential 16.11 *POTENTIAL OF DISTRIBUTED CHARGES Potential Along the Axis of a Uniformly Charged Disk R z r Δr Figure 16.53 A ring of radius r and width ∆r makes a contribution V ring to the potential of the disk. Consider a disk of radius R (area A = πR 2 ) with charge Q uniformly distributed over its surface.
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
But energy and voltage are not the same thing. A motorcycle battery, for example, is small and would not be very successful in replacing a much larger car battery, yet each has the same voltage. In this chapter, we examine the relationship between voltage and electrical energy, and begin to explore some of the many applications of electricity. Chapter 7 | Electric Potential 285 7.1 | Electric Potential Energy Learning Objectives By the end of this section, you will be able to: • Define the work done by an electric force • Define electric potential energy • Apply work and potential energy in systems with electric charges When a free positive charge q is accelerated by an electric field, it is given kinetic energy (Figure 7.2). The process is analogous to an object being accelerated by a gravitational field, as if the charge were going down an electrical hill where its electric potential energy is converted into kinetic energy, although of course the sources of the forces are very different. Let us explore the work done on a charge q by the electric field in this process, so that we may develop a definition of electric potential energy. Figure 7.2 A charge accelerated by an electric field is analogous to a mass going down a hill. In both cases, potential energy decreases as kinetic energy increases, – ΔU = ΔK . Work is done by a force, but since this force is conservative, we can write W = – ΔU . The electrostatic or Coulomb force is conservative, which means that the work done on q is independent of the path taken, as we will demonstrate later. This is exactly analogous to the gravitational force. When a force is conservative, it is possible to define a potential energy associated with the force. It is usually easier to work with the potential energy (because it depends only on position) than to calculate the work directly.
- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
The conversion factor in the second set of parentheses comes from our definition of volt given above; that in the third set of parentheses is derived from the defini- tion of the joule. From now on, we shall express values of the electric field in volts per meter rather than in newtons per coulomb. Motion Through an Electric Field Change in Electric Potential. If we move from an initial point i to a second point f in the electric field of a charged object, the electric potential changes by Δ V = V f − V i . If we move a particle with charge q from i to f, then, from Eq. 24.1.3, the potential energy of the system changes by ΔU = q Δ V = q(V f – V i ). (24.1.4) The change can be positive or negative, depending on the signs of q and Δ V. It can also be zero, if there is no change in potential from i to f (the points have the same value of potential). Because the electric force is conservative, the change in potential energy ΔU between i and f is the same for all paths between those points (it is path independent). + Test charge q 0 at point P Charged object ( a) + + + + + + + + + + + Electric potential V at point P ( b ) + + + + + + + + + + + P The rod sets up an electric potential, which determines the potential energy. FIGURE 24.1.2 (a) A test charge has been brought in from infinity to point P in the electric field of the rod. (b) We define an electric potential V at P based on the potential energy of the configuration in (a). 690 CHAPTER 24 Electric Potential Work by the Field. We can relate the potential energy change ΔU to the work W done by the electric force as the particle moves from i to f by applying the general relation for a conservative force (Eq. 8.1.1): W = –ΔU (work, conservative force). (24.1.5) Next, we can relate that work to the change in the potential by substituting from Eq.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
578 CHAPTER 19 Electric Potential Energy and the Electric Potential 19.1 Potential Energy In Chapter 18 we discussed the electrostatic force that two point charges exert on each other, the magnitude of which is F = k∣q 1 ∣∣q 2 ∣/r 2 . The form of this equation is similar to the form for the gravitational force that two particles exert on each other, which is F = Gm 1 m 2 /r 2 , according to Newton’s law of universal gravitation (see Section 4.7). Both of these forces are conservative and, as Section 6.4 explains, a potential energy can be associated with a conservative force. Thus, an electric potential energy exists that is analogous to the gravitational potential energy. To Lightning permeates the sky around the ash plume above the Puyehue-Cordon Caulle volcano in south-central Chile in 2011. Unlike normal lightning associated with rain clouds, where static charges are produced by colliding ice particles, volcanic lightning, or “dirty thunderstorms,” can result from frictional charging between colliding ash and dust particles. The natural convective thermal currents in the hot ash cloud aid in the separation of charges. This creates extremely high differences in voltage, or potential, between different parts of the dust cloud or between the cloud and the ground. If the voltage difference is sufficiently large, the insulating properties of the air break down, and it conducts electricity in spectacular fashion. The electric potential, and its relationship to charge, will be one of the topics we study in this chapter. Carlos Gutierrez/Reuters LEARNING OBJECTIVES After reading this module, you should be able to... 19.1 Define electrical potential energy. 19.2 Solve problems involving electric potential and electric potential energy. 19.3 Calculate electric potential created by point charges. 19.4 Relate equipotential surfaces to the electric field. 19.5 Solve problems involving capacitors. 19.6 Describe biomedical applications of electric potential.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
LEARNING OBJECTIVES After reading this module, you should be able to... 19.1 Define electrical potential energy. 19.2 Solve problems involving electric potential and electric potential energy. 19.3 Calculate electric potential created by point charges. 19.4 Relate equipotential surfaces to the electric field. 19.5 Solve problems involving capacitors. 19.6 Describe biomedical applications of electric potential. DANIEL MIHAILESCU/AFP/Getty Images/NewsCom CHAPTER 19 Electric Potential Energy and the Electric Potential In the medical diagnostic technique of electroencephalography, electrodes placed at various points on the head detect the small voltages that exist between the points. The cap worn by the young man in this photograph facilitates the placement of a number of electrodes, so that the voltages created by different regions of the brain as he plays a flipper pinball game can be measured simultaneously. The voltage between two points is another name for the difference in electric potential between the points, which is related to the concept of electric potential energy. Electric potential energy and electric potential are the central ideas in this chapter. 19.1 Potential Energy In Chapter 18 we discussed the electrostatic force that two point charges exert on each other, the magnitude of which is F = k|q 1 ||q 2 |/r 2 . The form of this equation is similar to the form for the gravitational force that two particles exert on each other, which is F = Gm 1 m 2 /r 2 , according to Newton’s law of universal gravitation (see Section 4.7). Both of these forces are conservative and, as Section 6.4 explains, a potential energy can be asso- ciated with a conservative force. Thus, an electric potential energy exists that is analogous to the gravitational potential energy. To set the stage for a discussion of the electric poten- tial energy, let’s review some of the important aspects of the gravitational counterpart.
eBook - PDF- Paul Peter Urone, Roger Hinrichs(Authors)
- 2012(Publication Date)
- Openstax(Publisher)
19.1 Electric Potential Energy: Potential Difference When a free positive charge q is accelerated by an electric field, such as shown in Figure 19.2, it is given kinetic energy. The process is analogous to an object being accelerated by a gravitational field. It is as if the charge is going down an electrical hill where its electric potential energy is converted to kinetic energy. Let us explore the work done on a charge q by the electric field in this process, so that we may develop a definition of electric potential energy. Figure 19.2 A charge accelerated by an electric field is analogous to a mass going down a hill. In both cases potential energy is converted to another form. Work is done by a force, but since this force is conservative, we can write W = –ΔPE . The electrostatic or Coulomb force is conservative, which means that the work done on q is independent of the path taken. This is exactly analogous to the gravitational force in the absence of dissipative forces such as friction. When a force is conservative, it is possible to define a potential energy associated with the force, and it is usually easier to deal with the potential energy (because it depends only on position) than to calculate the work directly. We use the letters PE to denote electric potential energy, which has units of joules (J). The change in potential energy, ΔPE , is crucial, since the work done by a conservative force is the negative of the change in potential energy; that is, W = –ΔPE . For example, work W done to accelerate a positive charge from rest is positive and results from a loss in PE, or a negative ΔPE . There must be a minus sign in front of ΔPE to make W positive. PE can be found at any point by taking one point as a reference and calculating the work needed to move a charge to the other point. Potential Energy W = –ΔPE . For example, work W done to accelerate a positive charge from rest is positive and results from a loss in PE, or a negative ΔPE.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler, Heath Jones, Matthew Collins, John Daicopoulos, Boris Blankleider(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
CHAPTER 19 Electric potential energy and the electric potential LEARNING OBJECTIVES After reading this module, you should be able to: 19.1 define electrical potential energy 19.2 solve problems involving electric potential and electric potential energy 19.3 calculate electric potential created by point charges 19.4 relate equipotential surfaces to the electric field 19.5 solve problems involving capacitors 19.6 describe biomedical applications of electric potential. INTRODUCTION In the medical diagnostic technique of electroencephalography, electrodes placed at various points on the head detect the small voltages that exist between the points. The cap worn by the young man in this photograph facilitates the placement of a number of electrodes, so that the voltages created by different regions of the brain as he plays a flipper pinball game can be measured simultaneously. The voltage between two points is another name for the difference in electric potential between the points, which is related to the concept of electric potential energy. Electric potential energy and electric potential are the central ideas in this chapter. Source: DANIEL MIHAILESCU / AFP / Getty Images / NewsCom 19.1 Potential energy LEARNING OBJECTIVE 19.1 Define electrical potential energy. FIGURE 19.1 Gravity exerts a force, F = m g, on the basketball of mass m. Work is done by the gravitational force as the ball falls from A to B. h A F = mg F = mg h B A B In chapter 18 we discussed the electrostatic force that two point charges exert on each other, the magni- tude of which is F = k|q 1 ||q 2 |/r 2 . The form of this equation is similar to the form for the gravitational force that two particles exert on each other, which is F = Gm 1 m 2 /r 2 , according to Newton’s law of univer- sal gravitation (see section 4.7). Both of these forces are conservative and, as section 6.4 explains, a poten- tial energy can be associated with a conservative force.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
458 Chapter 19 | Electric Potential Energy and the Electric Potential Figure 19.2 clarifies the analogy between electric and gravitational potential energies. In this drawing a positive test charge 1q 0 is situated at point A between two oppositely charged plates. Because of the charges on the plates, an electric field E B exists in the region between the plates. Consequently, the test charge experiences an electric force, F B 5 q 0 E B (Equation 18.2), that is directed downward, toward the lower plate. (The gravitational force is being neglected here.) As the charge moves from A to B, work is done by this force, in a fashion analogous to the work done by the gravitational force in Figure 19.1. The work W AB done by the electric force equals the difference between the electric potential energy EPE at A and the electric potential energy at B: W AB 5 EPE A 2 EPE B (19.1) This expression is similar to Equation 6.4. The path along which the test charge moves from A to B is of no consequence because the electric force, like the gravitational force, is conservative. For such forces, the work W AB is the same for all paths (see Section 6.4). 19.2 | The Electric Potential Difference Since the electric force is F B 5 q 0 E B , the work that it does as the charge moves from A to B in Figure 19.2 depends on the charge q 0 . It is useful, therefore, to express this work on a per-unit-charge basis, by dividing both sides of Equation 19.1 by the charge: W AB q 0 5 EPE A q 0 2 EPE B q 0 (19.2) Notice that the right-hand side of this equation is the difference between two terms, each of which is an electric potential energy divided by the test charge, EPE/q 0 . The quantity EPE/q 0 is the electric potential energy per unit charge and is an important concept in electricity. It is called the electric potential or, simply, the potential and is referred to with the symbol V, as in Equation 19.3.
eBook - PDF- David Halliday, Robert Resnick, Kenneth S. Krane(Authors)
- 2019(Publication Date)
- Wiley(Publisher)
635 28-1 POTENTIAL ENERGY Many electrical phenomena are associated with the transfer of large quantities of energy. For example, when a lightning flash strikes the Earth from a cloud, an energy of typically 10 8 J is released in the form of light, sound, heat, and shock wave. Where does this energy come from, and how is it stored in clouds? To understand this question, we must con- sider the energy associated with electrical forces. The electrostatic force law is very similar to the gravita- tional force law: (28-1a) gravitational. (28-1b) Both forces depend on the inverse square of the separation distance between the two objects. When an object moves from place to place under the gravitational force of another object (which we assume to remain at rest), the work done by the gravitational force on the first object depends only on the starting and finishing points and does not depend on the path taken between the points. In Section 12-1 we de- scribed a force that has this special property as a conserva- F G m 1 m 2 r 2 F 1 4 0 q 1 q 2 r 2 electrostatic, tive force, and we concluded in Section 12-2 that for a con- servative force we could define a potential energy. The dif- ference in potential energy U of the system as the object moves from its initial to its final position is equal to the negative of the work done by the force: (28-2) where W if is the work done by the force when the object moves from i to f. In the case of the gravitational force, we showed in Section 14-6 that, when an object with mass m 2 moves from a distance r i from mass m 1 to a distance r f from m 1 , the potential energy difference is (28-3) This potential energy difference is associated with the en- tire system consisting of m 1 and m 2 , not with either object alone.
No longer available |Learn morePhysics for Scientists and Engineers
Foundations and Connections, Extended Version with Modern Physics
- Debora Katz(Author)
- 2016(Publication Date)
- Cengage Learning EMEA(Publisher)
The electric potential V E is a scalar that depends on the source’s charge. Although the terms electric potential and electric potential energy are similar, it is important to distinguish between them. Any type of potential energy is associated with a system, so it must involve properties of both the source and the subject. The term potential refers to a property of the source alone. In our Earth-spacecraft analogy (Fig. 26.1), the gravitational potential depends only on the mass of the Earth, whereas the gravitational potential energy depends on the masses of both the Earth and the spacecraft. A less formal term for electric potential is voltage. Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 Unless otherwise noted, all content on this page is © Cengage Learning. 26-4 Electric Potential V 797 To emphasize the distinction between electric potential and electric potential en- ergy in the next few paragraphs, we add the term voltage in parentheses whenever we refer to electric potential. In Figure 26.1, we found the gravitational potential by dividing the gravitational potential energy by the mass of a test subject. The electric potential (voltage) V E can be found from the electric potential energy in a similar way: Divide the electric po- tential energy U E by the charge q of a test subject: V E 5 U E q (26.6) The dimensions of electric potential (voltage) are energy per charge, so the SI units are joules per coulomb, or volts (V): 1 J / C 5 1 V Just as only changes in potential energy are physically important, only differences in electric potential (voltage) are physically important. The electric potential (voltage) at any particular point is assigned a convenient value by convention or by definition; then you measure the potential at some other point relative to this assigned potential (Fig. 26.9).
eBook - PDF- Michael Tammaro(Author)
- 2019(Publication Date)
- Wiley(Publisher)
If the charge is negative, then the potential energy increases—that is, U 0. ∆ > For a given displacement, therefore, the sign of U ∆ depends on the sign of the charge. The change in potential energy per unit charge, however, is equal to ∆ = − ∆ U q E s 0 / and depends only on E and s ∆ . This quantity is called electric potential and is denoted by the symbol V. In a uniform electric field, the change in electric potential V ∆ is defined as follows: starts from rest, so let ∆ = K mv 1 2 2 and use Equation 19.1.1 for the change in potential energy, ∆ = − ∆ U q E s 0 . Solve From ∆ = −∆ K U , we have = ∆ mv q E s 1 2 2 0 , from which we have to solve for v. Multiply- ing both sides by 2, dividing both sides by m, then taking the square root of both sides yields = ∆ v q E s m 2 0 / . The proton moves in the same direction as the electric field, so ∆ = + s 0.056 m. The mass and charge of the proton can be found in Appendix A, and we have ( )( )( ) = ∆ = × × × − − v q E s m 2 2 1.60 10 C 2.9 10 N C 0.056 m 1.67 10 kg 0 19 5 27 / = × 1.8 10 m s 6 / Interpret This is a high speed, but not unusual for elementary particles. An electron—having a much smaller mass than the proton, but the same charge—would achieve an even higher speed if it fell through the same potential difference. Electric Potential Difference in a Uniform Electric Field For a given displacement in a uniform electric field E , the electric potential difference V ∆ between the initial and final positions is given by V E s ∆ = − ∆ (19.1.2) where s ∆ is the component of the displacement parallel to the electric field, where the positive s direction is taken to be the direction of E . For brevity, electric potential may be referred to simply as potential. Electric potential, like potential energy, is a scalar quantity, so it has no direction. The SI unit of potential is joules per coulomb (J/C), which is called a volt (V), so = 1 J C 1 V / .
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