Physics
Electrostatic Potential Energy
Electrostatic potential energy is the energy stored in a system of charged particles due to their positions relative to each other. It is directly related to the amount of work required to assemble the system of charges. The formula for electrostatic potential energy is U = k * (q1 * q2) / r, where U is the potential energy, k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between the charges.
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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- 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, 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)
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 photo- graph 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 | 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 5 ku q 1 uu q 2 u /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 5 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 set the stage for a discus- sion of the electric potential energy, let’s review some of the important aspects of the gravitational counterpart. Figure 19.1, which is essentially Figure 6.10, shows a basketball of mass m falling from point A to point B. The gravitational force, m g B , is the only force acting on the ball, where g is the magnitude of the acceleration due to gravity.
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.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
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 photo- graph 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 | Electric Potential Energy and the Electric Potential Chapter | 19 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. 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 5 ku q 1 uu q 2 u /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 5 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 set the stage for a discus- sion of the electric potential energy, let’s review some of the important aspects of the gravitational counterpart.
eBook - ePubDielectrophoresis
Theory, Methodology and Biological Applications
- Ronald R. Pethig(Author)
- 2017(Publication Date)
- Wiley(Publisher)
vice versa. This is why Feynman knew he could stand stock still during his demonstration.Feynman's lecture concerned the action of the earth's gravitational field on an object having mass. An electrical force shares the same property as a gravitational force in being a reversible, conservative, force. The purpose of this chapter is to describe how the concepts of a conservative force and the work-energy theorem, widely used in the subject of mechanics, are also relevant to understanding an electrokinetic effect such as dielectrophoresis.4.2 Electrical Potential Energy
The concepts of work and potential energy described in Box 4.1 will now be applied to examples of the interaction of electric fields with charged bodies, commencing with the situations described in Chapter 2. In Figure 4.1 , a positively charged particle Q is located in a uniform electric field Ex . There are no components of the field acting along the y- and z-axes.Figure 4.1(a) When a positively charged particle Q moves in the direction of a uniform electric field Ex , the field does positive work on the particle and its potential energy U decreases. (b) If the particle moves in the opposite direction, against the field, the field does negative work and the particle's potential energy increases.Box 4.1 Work, Potential Energy and the Work-Energy Theorem
In the SI system the unit of work is the joule, with dimensions of newton-metre (1 J = 1 N.m). The unit of work is thus the product of the unit of force and the unit of distance. If a constant force F acts on body so that it moves a distance s in a straight line along the direction as the force, the magnitude of the work W done on the body by the force is given by:(4.1)For the general case, where the force is not constant and the body moves at an angle θ to it, the work done is calculated by summing up the product Fcosθ.ds for each incremental distance ds taken along the total displacement between points a and b
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
(The default assumption in the absence of other information is that the test charge is positive.) We briefly defined a field for gravity, but gravity is always attractive, whereas the electric force can be either attractive or repulsive. Therefore, although potential energy is perfectly adequate in a gravitational system, it is convenient to define a quantity that allows us to calculate the work on a charge independent of the magnitude of the charge. Calculating the work directly may be difficult, since W = F → · d → and the direction and magnitude of F → can be complex for multiple charges, for odd-shaped objects, and along arbitrary paths. But we do know that because F → = q E → , the work, and hence ΔU, is proportional to the test charge q. To have a physical quantity that is independent of test charge, we define electric potential V (or simply potential, since electric is understood) to be the potential energy per unit charge: Electric Potential The electric potential energy per unit charge is (7.4) V = U q . Since U is proportional to q, the dependence on q cancels. Thus, V does not depend on q. The change in potential energy ΔU is crucial, so we are concerned with the difference in potential or potential difference ΔV between two points, where Chapter 7 | Electric Potential 293 ΔV = V B − V A = ΔU q . Electric Potential Difference The electric potential difference between points A and B, V B − V A , is defined to be the change in potential energy of a charge q moved from A to B, divided by the charge. Units of potential difference are joules per coulomb, given the name volt (V) after Alessandro Volta. 1 V = 1 J/C The familiar term voltage is the common name for electric potential difference. Keep in mind that whenever a voltage is quoted, it is understood to be the potential difference between two points. For example, every battery has two terminals, and its voltage is the potential difference between them.
eBook - ePubElectromagnetism
Maxwell Equations, Wave Propagation and Emission
- Tamer Becherrawy(Author)
- 2013(Publication Date)
- Wiley-ISTE(Publisher)
macroscopic. These are the averaged values of the microscopic field and potential over finite space element and time intervals.Consider a small sphere S surrounding a particle (i) and containing no other charge (Figure 2.10b ). The total average field <E> in S is the vector sum <Ei >+ <E′> where Ei is the field of the particle (i) and E′ is the field of the other particles located outside S. As Ei is radial and it has a spherical symmetry, its average value in S is zero, while E’ is regular inside S. Thus the macroscopic field is regular. In the same way, we may show the regularity of the potential in the case of volume charge distribution and surface charge distribution.2.9. Electrostatic energy of a system of charges
The energy U of a system of particles without intrinsic structure is the sum of their kinetic energies and their interaction potential energy. The electrostatic interaction potential energy U E is the work required to bring the initially far away particles to their actual positions ri without acquiring kinetic energy. As the electrostatic forces are conservative, UE is a function of the relative positions of all the pairs of charged particles.Figure 2.11.Interaction potential energy: a) for a system of discrete charges, and b) for a continuous charge distributionConsider, for instance three charged particles qi (i = 1, 2, and 3) (Figure 2.11a ). To bring q1 from infinity to its position r1 in the absence of the other charges, no work is necessary. Then, to bring q2 from infinity to its position r2 in the presence of q1 , a force −F12 must be exerted and a work is required. Finally, to bring q3 from infinity to its position r3 , a force must be exerted and work is required. Thus, the total work necessary to assemble the three charges is[2.63]This result may be easily generalized to systems of several charges qi (i = 1, 2, N). Each pair of charges contributes a term Uij to the total potential energy. Thus, we may write UE
eBook - PDF- Michael Tammaro(Author)
- 2019(Publication Date)
- Wiley(Publisher)
| 513 Electrical energy is produced at power stations all over the world and transmitted to homes and businesses by high-voltage power lines. Transmitting electrical energy efficiently requires high voltage—also known as electric potential. Electric potential energy and elec- tric potential are the subjects of this chapter. The massive transmission tower pictured here is located in Japan and is owned by Tokyo Electric Power Company. It is rated as an ultra- high-voltage system, operating at 1100 kilovolts. Brian Guest/Shutterstock 513 Electric Potential 19 514 | Chapter 19 19.1 Solve problems dealing with electric potential and potential energy. 19.1.1 Apply the principle of conservation of energy to problems dealing with electric potential and electric potential energy. The concepts of work and energy were exploited in Chapter 6, where we predicted the out- comes of physical processes that could not be analyzed using only Newton’s laws (Chapter 4) and the equations of kinematics (Chapters 2 and 3). In particular, the principle of con- servation of mechanical energy provides a framework for dealing with complex processes in which the work done by nonconservative forces is zero. Here in Chapter 19, we extend the ideas of work and energy to the electric force and develop the ideas of electric potential energy and electric potential. The Conservative Nature of the Electric Force When the point of application of a (constant) force F moves through a displacement ∆r, the work done by that force is given by Equation 6.1.2, θ = ∆ ( ) W F r cos , where θ is the angle between the displacement and the force. For certain forces—called conservative forces—a potential energy can be defined. When a conservative force does work W c , the change in the potential energy U ∆ related to that force is given by Equation 6.4.1: W U c = −∆ (6.4.1) If the electric force is conservative, therefore, we can define an electric potential energy.
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