Physics
Electric Charge Field and Potential
The electric charge field is a region around an electric charge where another charge experiences a force. The electric potential is the amount of work needed to move a unit positive charge from infinity to a point in the electric field. Both concepts are fundamental in understanding the behavior of electric charges and are crucial in the study of electromagnetism.
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11 Key excerpts on "Electric Charge Field and Potential"
eBook - ePub- A. L. Stanford, J. M. Tanner(Authors)
- 2014(Publication Date)
- Academic Press(Publisher)
13Electric Potential
Publisher Summary
This chapter discusses electric potential. Electric fields are vector fields that have both magnitude and direction at every point at which the field is defined. The electrical properties of space can also be described by electric potential, which is, in some respects, a simpler and more practical concept than the electric field. Electric potential is simpler than electric fields because electric potential is a scalar quantity and, therefore, has no direction associated with it. Electric potential is more practical than the electric field because differences in potential, at least on conductors, are more readily measured directly. Electric potentials and electric fields in a given region are related to each other, and either can be used to describe the electrostatic properties of space. The gravitational potential energy of an object at a point is meaningful only in terms of the difference in potential energy between that point and the potential energy specified at some reference point. Electric potential should have characteristics similar to those of gravitational potential energy for electric potential to be equally useful.We have stressed that electric fields are a means of characterizing a physical property of space caused by the presence of electrostatic charge. Electric fields are vector fields that have both magnitude and direction at every point at which the field is defined. The electrical properties of space can also be described by electric potential, which is, in some respects, a simpler and more practical concept than the electric field. Electric potential is simpler than electric fields because electric potential is a scalar quantity and, therefore, has no direction associated with it. Electric potential is more practical than the electric field because differences in potential, at least on conductors, are more readily measured directly.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
Instead, particle 2 pushes by means of the electric field it has set up. Our goals in this chapter are to (1) define electric field, (2) discuss how to calculate it for various arrangements of charged particles and objects, and (3) dis- cuss how an electric field can affect a charged particle (as in making it move). The Electric Field A lot of different fields are used in science and engineering. For example, a tem- perature field for an auditorium is the distribution of temperatures we would find by measuring the temperature at many points within the auditorium. Similarly, we could define a pressure field in a swimming pool. Such fields are examples of scalar fields because temperature and pressure are scalar quantities, having only magnitudes and not directions. In contrast, an electric field is a vector field because it is responsible for conveying the information for a force, which involves both magnitude and direc- tion. This field consists of a distribution of electric field vectors E → , one for each point in the space around a charged object. In principle, we can define E → at some point near the charged object, such as point P in Fig. 22.1.2a, with this proce- dure: At P, we place a particle with a small positive charge q 0 , called a test charge because we use it to test the field. (We want the charge to be small so that it does not disturb the object’s charge distribution.) We then measure the electrostatic force F → that acts on the test charge. The electric field at that point is then E → = F → ___ q 0 (electric field). (22.1.1) Because the test charge is positive, the two vectors in Eq. 22.1.1 are in the same direction, so the direction of E → is the direction we measure for F → . The mag- nitude of E → at point P is F/q 0 . As shown in Fig. 22.1.2b, we always represent an electric field with an arrow with its tail anchored on the point where the measure- ment is made.
eBook - ePubElectromagnetics Explained
A Handbook for Wireless/ RF, EMC, and High-Speed Electronics
- Ron Schmitt(Author)
- 2002(Publication Date)
- Newnes(Publisher)
2 FUNDAMENTALS OF ELECTRIC FIELDSTHE ELECTRIC FORCE FIELD
To understand high-frequency and RF electronics, you must first have a good grasp of the fundamentals of electromagnetic fields. This chapter discusses the electric field and is the starting place for understanding electromagnetics. Electric fields are created by charges; that is, charges are the source of electric fields. Charges come in two types, positive (+) and negative (–). Like charges repel each other and opposites attract. In other words, charges produce a force that either pushes or pulls other charges away. Neutral objects are not affected. The force between two charges is proportional to the product of the two charges, and is called Coulomb’s law. Notice that the charges produce a force on each other without actually being in physical contact. It is a force that acts at a distance. To represent this “force at distance” that is created by charges, the concept of a force field is used. Figure 2.1 shows the electrical force fields that surround positive and negative charges.Figure 2.1 Field lines surrounding a negative and a positive charge. Dotted lines show lines of equal voltage.By convention, the electric field is always drawn from positive to negative. It follows that the force lines emanate from a positive charge and converge to a negative charge. Furthermore, the electric field is a normalized force, a force per charge. The normalization allows the field values to be specified independent of a second charge. In other words, the value of an electric field at any point in space specifies the force that would be felt if a unit of charge were to be placed there. (A unit charge has a value of 1 in the chosen system of units.)Electric field = Force field as “felt” by a unit chargeTo calculate the force felt by a charge with value, q, we just multiply the electric field by the charge,The magnitude of the electric field decreases as you move away from a charge, and increases as you get closer. To be specific, the magnitude of the electric field (and magnitude of the force) is proportional to the inverse of the distance squared. The electric field drops off rather quickly as the distance is increased. Mathematically this relation is expressed as
eBook - PDF- Paul Peter Urone, Roger Hinrichs(Authors)
- 2012(Publication Date)
- Openstax(Publisher)
• The electrostatic force between two subatomic particles is far greater than the gravitational force between the same two particles. 18.4 Electric Field: Concept of a Field Revisited • The electrostatic force field surrounding a charged object extends out into space in all directions. • The electrostatic force exerted by a point charge on a test charge at a distance r depends on the charge of both charges, as well as the distance between the two. • The electric field E is defined to be E = F q, where F is the Coulomb or electrostatic force exerted on a small positive test charge q . E has units of N/C. • The magnitude of the electric field E created by a point charge Q is 722 Chapter 18 | Electric Charge and Electric Field This OpenStax book is available for free at http://cnx.org/content/col11406/1.9 E = k | Q | r 2 . where r is the distance from Q . The electric field E is a vector and fields due to multiple charges add like vectors. 18.5 Electric Field Lines: Multiple Charges • Drawings of electric field lines are useful visual tools. The properties of electric field lines for any charge distribution are that: • Field lines must begin on positive charges and terminate on negative charges, or at infinity in the hypothetical case of isolated charges. • The number of field lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge. • The strength of the field is proportional to the closeness of the field lines—more precisely, it is proportional to the number of lines per unit area perpendicular to the lines. • The direction of the electric field is tangent to the field line at any point in space. • Field lines can never cross. 18.6 Electric Forces in Biology • Many molecules in living organisms, such as DNA, carry a charge. • An uneven distribution of the positive and negative charges within a polar molecule produces a dipole.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
541 CHAPTER 18 LEARNING OBJECTIVES After reading this module, you should be able to... 18.1 Define electric charge. 18.2 Describe the electric force between charged particles. 18.3 Distinguish between conductors and insulators. 18.4 Explain charging by contact and charging by induction. 18.5 Use Coulomb’s law to calculate the force on a point charge due to other point charges. 18.6 Calculate the net electric field due to a configuration of point charges. 18.7 Draw electric field lines. 18.8 Describe the electric field inside a conductor. 18.9 Use Gauss’ law to obtain the value of the electric field due to charge distributions. We have all experienced static electricity in our hair and on our clothes, and have been zapped on occasion when touching a doorknob after walking on carpet. These phenomena occur when electric charges, one of the fundamental building blocks of atoms, separate, and one type (either positive or negative) becomes more abundant than the other. As we will see in this chapter, like charges repel, which is why the toddler’s hair is standing on end. Rachel Hopper/Dreamstime.com *The definition of the coulomb depends on electric currents and magnetic fields, concepts that will be discussed later. Therefore, we postpone its definition until Section 21.7. Electric Forces and Electric Fields 18.1 The Origin of Electricity The electrical nature of matter is inherent in atomic structure. An atom consists of a small, relatively massive nucleus that contains particles called protons and neutrons. A proton has a mass of 1.673 × 10 −27 kg, and a neutron has a slightly greater mass of 1.675 × 10 −27 kg. Surround- ing the nucleus is a diffuse cloud of orbiting particles called electrons, as Figure 18.1 suggests. An electron has a mass of 9.11 × 10 −31 kg. Like mass, electric charge is an intrinsic property of protons and electrons, and only two types of charge have been discovered, positive and negative.
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.
- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
Two Cautions. (1) The (now very old) decision to call V a potential was unfortunate because the term is easily confused with potential energy. Yes, the two quantities are related (that is the point here) but they are very different and not interchangeable. (2) Electric potential is a scalar, not a vector. (When you come to the homework problems, you will rejoice on this point.) Language. A potential energy is a property of a system (or configuration) of objects, but sometimes we can get away with assigning it to a single object. For example, the gravitational potential energy of a baseball hit to outfield is actually a potential energy of the baseball–Earth system (because it is associated with the force between the baseball and Earth). However, because only the baseball notice- ably moves (its motion does not noticeably affect Earth), we might assign the gravi- tational potential energy to it alone. In a similar way, if a charged particle is placed in an electric field and has no noticeable effect on the field (or the charged object that sets up the field), we usually assign the electric potential energy to the particle alone. Units. The SI unit for potential that follows from Eq. 24.1.2 is the joule per coulomb. This combination occurs so often that a special unit, the volt (abbrevi- ated V), is used to represent it. Thus, 1 volt = 1 joule per coulomb. With two unit conversions, we can now switch the unit for electric field from newtons per coulomb to a more conventional unit: 1 N/C = ( 1 N __ C ) ( 1 V _____ 1 J / C ) ( 1 J _______ 1 N ⋅ m ) = 1 V / m. 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.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
Electric Potential Energy If a particle with charge q is placed at a point where the electric potential of a charged object is V, the electric potential energy U of the particle–object system is U = qV. (24-3) Review & Summary If the particle moves through a potential difference ΔV, the change in the electric potential energy is ΔU = q ΔV = q(V f – V i ). (24-4) Mechanical Energy If a particle moves through a change ΔV in electric potential without an applied force acting on it, applying the conservation of mechanical energy gives the change in kinetic energy as ΔK = –q ΔV. (24-9) If, instead, an applied force acts on the particle, doing work W app , the change in kinetic energy is ΔK = –q ΔV + W app . (24-11) In the special case when ΔK = 0, the work of an applied force 708 CHAPTER 24 ELECTRIC POTENTIAL 20 V 40 60 80 100 –140 V –120 –100 –10 V –30 –50 (1) (2) (3) Figure 24-25 Question 2. 1 Figure 24-24 shows eight par- ticles that form a square, with dis- tance d between adjacent particles. What is the net electric potential at point P at the center of the square if we take the electric potential to be zero at infinity? 2 Figure 24-25 shows three sets of cross sections of equipotential surfaces in uniform electric fields; all three cover the same size region of space. The electric potential is Questions Figure 24-24 Question 1. –4q +5q –q +q –5q +4q –2q –2q P d involves only the motion of the particle through a potential difference: W app = q ΔV (for K i = K f ). (24-12) Equipotential Surfaces The points on an equipotential sur- face all have the same electric potential. The work done on a test charge in moving it from one such surface to another is independent of the locations of the initial and final points on these surfaces and of the path that joins the points. The electric field E → is always directed perpendicularly to corresponding equipotential surfaces.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
If we choose V i = 0, we have, for the potential at a particular point, V = − ∫ f i E → · d s → . (24-19) In the special case of a uniform field of magnitude E, the potential change between two adjacent (parallel) equipotential lines separated by distance Δx is ΔV = –E Δx. (24-21) Potential Due to a Charged Particle The electric potential due to a single charged particle at a distance r from that particle is V = 1 4πε 0 q r , (24-26) where V has the same sign as q. The potential due to a collection of charged particles is V = ∑ n i =1 V i = 1 4πε 0 ∑ n i =1 q i r i . (24-27) Potential Due to an Electric Dipole At a distance r from an electric dipole with dipole moment magnitude p = qd, the electric potential of the dipole is V = 1 4πε 0 p cos θ r 2 (24-30) for r ⪢ d; the angle θ is defined in Fig. 24-13. Potential Due to a Continuous Charge Distribution For a continuous distribution of charge, Eq. 24-27 becomes V = 1 4πε 0 ∫ dq r , (24-32) in which the integral is taken over the entire distribution. Calculating E → from V The component of E → in any direction is the negative of the rate at which the potential changes with dis- tance in that direction: E s = − ∂V ∂s . (24-40) The x, y, and z components of E → may be found from E x = − ∂V ∂x ; E y = − ∂V ∂y ; E z = − ∂V ∂z . (24-41) When E → is uniform, Eq. 24-40 reduces to E = − ΔV Δs , (24-42) where s is perpendicular to the equipotential surfaces. Electric Potential Energy of a System of Charged Particles The electric potential energy of a system of charged particles is equal to the work needed to assemble the system with the particles initially at rest and infinitely distant from each other. For two particles at separation r, U = W = 1 4πε 0 q 1 q 2 r . (24-46) Potential of a Charged Conductor An excess charge placed on a conductor will, in the equilibrium state, be located entirely on the outer surface of the conductor.
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- P.F. Kelly(Author)
- 2014(Publication Date)
- CRC Press(Publisher)
E Electric Field and Potential Problems Useful Data Unless otherwise specified, here and throughout the other collections of problems we employ the following conventions. SI Times are measured in seconds, s , distances in metres, m , masses in kilograms, kg , forces in newtons, N , and angles in radians, rad . e The quantum of elementary charge is e ≃ 1 . 6 × 10 − 19 C . k Coulomb’s constant has the approximate value k ≃ 8 . 99 × 10 9 N · m 2 / C 2 . Here we shall use k = 9 × 10 9 for simplicity. ǫ 0 The permittivity of free space is ǫ 0 = (4 πk ) − 1 ≃ 8 . 85 × 10 − 12 C 2 /( N · m 2 ). m The electron mass is m e ≃ 9 . 1 × 10 − 31 kg . The proton mass is m p ≃ 1 . 67 × 10 − 27 kg . The atomic mass unit is 1 amu ≃ 1 . 66 × 10 − 27 kg . E.1 Two equal point-like charges, q = +1 C , are separated by a distance of 1 kilometre. Determine the Coulombic force acting between the two charges. Comment. E.2 Two point electric charges, q L = 3 μ C and q R = 12 μ C , lie along an axis in the xy -plane, at vector r L = ( − 4 , 0) and vector r R = (8 , 0). A third charge, q 0 = 2 μ C , is placed at the origin. Compute the electric force acting upon q 0 , produced by (a) q L and (b) q R . (c) Determine the net force acting on q 0 . (d) Discuss how the result for (c) would change if q 0 were displaced to (0 , 0 . 01). E.3 Two point-like electrons belonging to different atoms might be approximately one ˚ Angstrom [1 ˚ A = 10 − 10 m ] apart. (a) Estimate the magnitude of the Coulombic force that each electron experiences owing to the presence of the other. (b) Were it the case that this was the only force acting on the electrons, compute the magnitude of their respective accelerations. E.4 Three charged particles reside at fixed positions in a common plane. Charge q 0 = 2 μ C is at the origin, q 1 = 5 μ C has coordinates (3 , − 1), and q 2 = 10 μ C is at (8 , 6). Compute the Coulombic force exerted by (a) q 1 , (b) q 2 , and (c) both acting on q 0 .
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