Physics
Charged Particle in Uniform Electric Field
A charged particle in a uniform electric field experiences a force due to the presence of the field. The direction of the force depends on the charge of the particle and the direction of the field. The particle will accelerate in the direction of the force if it is positively charged, and in the opposite direction if it is negatively charged.
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9 Key excerpts on "Charged Particle in Uniform Electric Field"
- Raymond Serway, John Jewett(Authors)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
This problem can be solved with different approaches. We saw the same possibilities with mechanical problems. d q + + v = 0 S v S E S + + + + + - - - - - Figure 22.20 (Example 22.7) A positive point charge q in a uni- form electric field E S undergoes constant acceleration in the direc- tion of the field. Example 22.8 An Accelerated Electron An electron enters the region of a uniform electric field as shown in Figure 22.21, with v i 5 3.00 3 10 6 m/s and E 5 200 N/C. The horizontal length of the plates is , 5 0.100 m. (A) Find the acceleration of the electron while it is in the electric field. Copyright 2019 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 22.6 Motion of a Charged Particle in a Uniform Electric Field 607 22.8 c o n t i n u e d S O L U T I O N Conceptualize This example differs from the preceding one because the velocity of the charged particle is initially perpendicular to the elec- tric field lines. (In Example 22.7, the velocity of the charged particle is always parallel to the electric field lines.) As a result, the electron in this example follows a curved path as shown in Figure 22.21. The motion of the electron is the same as that of a massive particle projected horizon- tally in a gravitational field near the surface of the Earth. Categorize The electron is a particle in a field (electric). Because the electric field is uniform, a constant electric force is exerted on the electron. To find the acceleration of the electron, we can model it as a particle under a net force.
eBook - PDF- Donald Dunn(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
C H A P T E R 5 Nonuniform Motion of Charged Particles in Prescribed Electric and Magnetic Fields Two great universal phenomena which must be understood in order to understand electronics are the motions o f particles— that is, very small bodies— and the motion o f waves . . . . The particles with which electronics deals are chiefly electrons. In order to understand the motion o f electrons or ions through the emptiness o f a vacuum tube, we must have some understanding o f the laws o f motion, laws which govern not only the motion o f electrons and o f ions in vacuum tubes but all motions in the world about us and the motions o f heavenly bodies as well: the motion o f baseballs and automobiles, the motions o f satellites and planets in their orbits , and the motion o f the stars in their courses . To one familiar with the laws o f motion, they come to seem simple and obvious. Certainly they are not obvious, for they eluded thoughtful and intelligent men for many centuries. Indeed, recently, during a trip by air, the man in the next seat next to mine marveled that when he dropped a pencil in the plane it did not fall behind on its way to the floor . I explained to him that in the seventeenth century Newton stated that a body continues at rest or in uniform motion in a straight line unless it is acted on by a force, and that this explained the behavior o f the dropped pencil. J. R. Pierce, “ Electrons, Waves, and Messages.” Doubleday, Garden City, New York, 1956. Reprinted by permission. 137 138 5. NONUNIFORM MOTION OF PARTICLES 5.0 Introduction In this chapter we picture a region of space within which the values of the electric and magnetic fields are given. We use the Lorentz force equation to calculate the motion of a single point charge within this region, given the initial conditions for the position and velocity of the charge.
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 - PDFMaxwell's Equations and Their Consequences
Elementary Electromagnetic Theory
- B. H. Chirgwin, C. Plumpton, C. W. Kilmister(Authors)
- 2013(Publication Date)
- Pergamon(Publisher)
CHAPTER 14 THE MOTION OF CHARGED PARTICLES 14.1. Introduction The motion of electrically charged particles in electromagnetic and gravitational fields is of interest in various studies of astronomical and engineering problems. During the past five decades research into the motion of charged particles in the terrestrial magnetic and gravitational fields has greatly improved our understanding of the structure and extent of the terrestrial magnetic field. In electronics, devices such as the magnetron were designed after theoretical studies similar to those illustrated in the examples of this chapter; in thermonuclear research, studies of magnetic bottles, wells and traps are of prime importance. However, much care must be taken when attempts are made to generalize the results for a single particle to the case of an ionized gas, which consists of a multitude of charged particles, in a magnetic field, since the interactions between charged particles can modify or completely change the calculated (and observed) results concerning a single particle. In fact the essential feature of the motion of a charged particle in a magnetic field is the tendency of the particle to spiral around the magnetic field lines. This is regarded as the counterpart of the magnetohydrodynamic (or ionized-gas) phenomenon in which a highly (electrically) conducting material can flow freely along the lines of magnetic force but motion of the material perpendicular to the magnetic field carries the magnetic field lines with the material. [This result is similar to the classical hydrodynamic result that vorticity lines are frozen into a perfect fluid.] In this chapter, we first give an account of the non-relativistic motion of a charged particle in uniform crossed electric and magnetic fields. This is followed by a brief account of the flow of charged particles when space charge density is taken into account. Finally relativistic corrections are 569
eBook - ePub- A. L. Stanford, J. M. Tanner(Authors)
- 2014(Publication Date)
- Academic Press(Publisher)
11Electric Charge and Electric Fields
Publisher Summary
This chapter begins our study of electric and magnetic phenomena, collectively called electromagnetism . Electromagnetic forces, like gravitational forces, are fundamental interactions that occur between particles. Just as mass is that property of matter that engenders gravitational attraction, electric charge is a property of certain fundamental particles, like electrons and protons, that causes electromagnetic interaction. Our investigation of electrostatics , the analysis of interactions between charges at rest, is based on a force law for charges and on the concept of electric fields. The force law for charges, called Coulomb’s law, is the electrical analogue of the law of universal gravitation. The electric field is an abstract concept used to characterize how the presence of charge alters the properties of the space around that charge.11.1 Electric Charge and Coulomb’s Law
Electric charges exist in two forms, called positive charge and negative charge . The natural unit of charge is the positive charge of a proton or the negative charge of an electron. The SI unit of charge is the coulomb (C), which will be defined later in terms of electric current. This unusual definition is used because of the difficulty of making reproducible measurements on quantities of charge. For now, we will use as a measure of charge the experimentally obtained value for e , the magnitude of the charge of an electron or proton:e = 1.60 ×(11-1)10C− 19(11-1)Equivalently, a coulomb is the quantity of charge carried by 6.25 × 1018 electrons.An electron (or proton) bears the smallest unit of charge found in nature, so any quantity of charge q occurs as an integral number n of the basic charge e , or q = ne . Thus, as with any physical quantity made up of a number of “minimum parcels,” we say that electric charge is quantized; the least quantity that occurs, the quantum of charge, is the electronic charge e
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
C H A P T E R 2 2 Electric Fields 22-1 THE ELECTRIC FIELD Learning Objectives After reading this module, you should be able to . . . 22.01 Identify that at every point in the space surround- ing a charged particle, the particle sets up an electric field E → , which is a vector quantity and thus has both magnitude and direction. 22.02 Identify how an electric field E → can be used to explain how a charged particle can exert an electrostatic force F → on a second charged particle even though there is no contact between the particles. 22.03 Explain how a small positive test charge is used (in principle) to measure the electric field at any given point. 22.04 Explain electric field lines, including where they originate and terminate and what their spacing represents. Key Ideas ● A charged particle sets up an electric field (a vector quan- tity) in the surrounding space. If a second charged particle is located in that space, an electrostatic force acts on it due to the magnitude and direction of the field at its location. ● The electric field E → at any point is defined in terms of the electrostatic force F → that would be exerted on a positive test charge q 0 placed there: E → = F → q 0 . ● Electric field lines help us visualize the direction and magnitude of electric fields. The electric field vector at any point is tangent to the field line through that point. The density of field lines in that region is proportional to the magnitude of the electric field there. Thus, closer field lines represent a stronger field. ● Electric field lines originate on positive charges and terminate on negative charges. So, a field line extending from a positive charge must end on a negative charge. 544 What Is Physics? Figure 22-1 shows two positively charged particles. From the preceding chapter we know that an electrostatic force acts on particle 1 due to the presence of particle 2. We also know the force direction and, given some data, we can calculate the force magnitude.
- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
C H A P T E R 22 After reading this module, you should be able to . . . 22.1.1 Identify that at every point in the space surrounding a charged particle, the particle sets up an electric field E → , which is a vector quantity and thus has both magnitude and direction. 22.1.2 Identify how an electric field E → can be used to explain how a charged particle can exert an electrostatic force F → on a second charged particle even though there is no contact between the particles. 22.1.3 Explain how a small positive test charge is used (in principle) to measure the electric field at any given point. 22.1.4 Explain electric field lines, including where they originate and terminate and what their spacing represents. 22.1 THE ELECTRIC FIELD LEARNING OBJECTIVES 629 KEY IDEAS 1. A charged particle sets up an electric field (a vector quantity) in the sur- rounding space. If a second charged particle is located in that space, an elec- trostatic force acts on it due to the magnitude and direction of the field at its location. 2. The electric field E → at any point is defined in terms of the electrostatic force F → that would be exerted on a positive test charge q 0 placed there: E → = F → ___ q 0 . 3. Electric field lines help us visualize the direction and magnitude of elec- tric fields. The electric field vector at any point is tangent to the field line through that point. The density of field lines in that region is proportional to the magnitude of the electric field there. Thus, closer field lines represent a stronger field. 4. Electric field lines originate on positive charges and terminate on negative charges. So, a field line extending from a positive charge must end on a neg- ative charge. What Is Physics? Figure 22.1.1 shows two positively charged particles. From the preceding chap- ter we know that an electrostatic force acts on particle 1 due to the presence of particle 2. We also know the force direction and, given some data, we can calculate the force magnitude.
eBook - PDF- Edward Purcell(Author)
- 2011(Publication Date)
- Cambridge University Press(Publisher)
On the other hand, close to the moving charge itself, what hap- tPreviously we had the charge at rest in the unprimed frame, moving in the primed frame. Here we adopt xyz for the frame in which the charge is moving, to avoid clut- tering the subsequent discussion with primes. 185 186 CHAPTER FIVE y FIGURE 5.15 The electric field of a moving charge, shown for three instants of time; vi c = 'h. Time unit: 10- 10 sec pened in the remote past can't make any difference. The field must somehow change, as we consider regions farther and farther from the charge, at the given instant t = 2, from the field shown in the second diagram of Fig. 5.16 to the field of a charge at the origin. We can't deduce more than this without knowing how fast the news does travel. Suppose--just suppose--it travels as fast as it can without conflicting with the relativity postulates. Then if the period of acceleration is neglected, we should expect the field within the entire 6-cm-radius sphere, at t = 2, to be the field of a uniformly moving point charge. If that is so, the field of the electron which starts from rest, suddenly acquiring the speed u at t = 0, must look something like Fig. 5.17. There is a thin spherical shell (whose thickness in an actual case will depend on the duration of the interval required for acceleration) within which the transition from one type of field to the other takes place. This shell simply expands with speed c, its center remaining at x = 0. The arrowheads on the field lines indicate the direction of the field when the source is a negative charge, as we have been assuming. Figure 5.18 shows the field of an electron which had been mov- ing with uniform velocity until t = 0, at which time it reached x = ° where it was abruptly stopped. Now the news that it was stopped cannot reach, by time t, any point farther than ct from the origin.
eBook - PDF- Hermann Wollnik(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
2 General Relations for the Motion of Charged Particles in Electromagnetic Fields T o d e t e r m i n e t h e t r a j e c t o r i e s o f c h a r g e d p a r t i c l e s w i t h i n e l e c t r o m a g n e t i c fields, i t i s n e c e s s a r y t o k n o w t h e s p a t i a l d i s t r i b u t i o n o f t h e s e fields a s w e l l a s t h e p a r t i c l e s ' r i g i d i t y a g a i n s t e l e c t r o m a g n e t i c d e f l e c t i o n s . T h i s r i g i d i t y d e p e n d s o n t h e m a s s , c h a r g e , a n d v e l o c i t y o f t h e p a r t i c l e u n d e r i n v e s t i g a t i o n . 2.1 ENERGY, VELOCITY, A N D M A S S OF ACCELERATED PARTICLES A s s u m e a p a r t i c l e o f p o s i t i v e c h a r g e (ze) t o b e a t r e s t a t z e r o e l e c t r o s t a t i c p o t e n t i a l ( h e r e , e i s t h e c h a r g e o f a p r o t o n , a n d ζ i s a n i n t e g e r ) . U n d e r t h e a c t i o n o f a n e l e c t r o s t a t i c field, s u c h a p a r t i c l e o f r e s t m a s s m 0 w i l l m o v e t o a p o i n t o f p o t e n t i a l —V a n d t h e n h a v e t h e v e l o c i t y ν = | v | . S i n c e t h e t o t a l 2 7 28 2 Motion of Charged Particles in Electromagnetic Fields ^ « T i i . f i 3 S . (2.2b, 1 + 2 t j 1 + 2 t j For numerical calculations, it is advantageous to introduce dimensionless quantities m 0 , X, and ϋ with Κ = K MeV, m 0 = m 0 u, ν = ν m/ μ sec. Remember now that the energy equivalent m 0 c 2 of one mass unit* [w], is approximately 931.501 million electron voltst [MeV] so that the numerical value of η is found from Eq. (2.1c): η = X/1863.003m 0 . (2.3) Thus, m and ν are calculated from Eqs. (2.2a) and (2.2b) as m = m 0 (l + 2 V ), (2.4a) 13.891 ^ i l ± ^ . ( 2 . 4 b ) 1 -r-2 t 7 For relativistically slow particles [v « c or (K/m 0 ) « 931 M e V / u ] , we find η « 1 so that the Eqs. (2.4a) and (2.4b) simplify to m ~ m 0 , (2.4as) ϋ ~ 13.891332 V x / m o .
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