Physics
Electric Fields
Electric fields are regions of space around electrically charged particles where other charged particles experience a force. They are represented by vectors that indicate the direction and strength of the force experienced by a positive test charge placed in the field. The strength of an electric field is determined by the magnitude of the source charge and the distance from it.
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10 Key excerpts on "Electric Fields"
- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
630 CHAPTER 22 Electric Fields 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) discuss 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 mea- surement is made.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
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. 22-2a, 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) Because the test charge is positive, the two vectors in Eq. 22-1 are in the same direction, so the direction of E → is the direction we measure for F → . The magnitude of E → at point P is F/q 0 . As shown in Fig. 22-2b, we always represent an electric field with an arrow with its tail anchored on the point where the measurement is made.
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 - 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.
eBook - PDF- Ruth W. Chabay, Bruce A. Sherwood(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
A point charge does not exert a force on itself! In the next section we will see that mathematically this is reassuring, because at the location of a point charge its own electric field would be infinite (1/0 2 ). Physically, this makes sense too, since after all, the charge can’t start itself moving, nor is there any way to decide in what direction it should go. When we use the electric field concept with point charges we always talk about a charge q 1 (the source charge) making a field E 1 , and a different charge q 2 in a different place being affected by that field with a force F on q 2 = q 2 E 1 . The Physical Concept of “Field” The word “field” has a special meaning in mathematical physics. A field is a physical quantity that has a value at every location in space. Its value at every location can be a scalar or a vector. For example, the temperature in a room is a scalar field. At every location in the room, the temperature has a value, which we could write as T(x, y, z), or as T(x, y, z, t) if it were changing with time. The air flow in the room is a vector field. At every location in the room, air flows in a particular direction with a particular speed. Electric field is a vector field; at every location in space surrounding a charge the electric field has a magnitude and a direction. QUESTION Think of another example of a quantity that is a field. The field concept is also used with gravitation. Instead of saying that the Earth exerts a force on a falling object, we can say that the mass of the Earth creates a “gravitational field” surrounding the Earth, and any object near the Earth is acted upon by the gravitational field at that location (Figure 13.13). Gravitational field has units of newtons per kilogram. At a location near the Earth’s surface we can say that there is a gravitational field g pointing downward (that is, toward the center of the Earth) of magnitude g = 9.8 newtons per kilogram.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
Definition of the Electric Field The electric field E B that exists at a point is the electrostatic force F B experienced by a small test charge* q 0 placed at that point divided by the charge itself: E B 5 F B q 0 (18.2) The electric field is a vector, and its direction is the same as the direction of the force F B on a positive test charge. SI Unit of Electric Field: newton per coulomb (N/C) Equation 18.2 indicates that the unit for the electric field is that of force divided by charge, which is a newton/coulomb (N/C) in SI units. It is the surrounding charges that create an electric field at a given point. Any pos- itive or negative charge placed at the point interacts with the field and, as a result, experi- ences a force, as the next example indicates. *As long as the test charge is small enough that it does not disturb the surrounding charges, it may be either positive or negative. Compared to a positive test charge, a negative test charge of the same magnitude experiences a force of the same magnitude that points in the opposite direction. However, the same electric field is given by Equation 18.2, in which F B is replaced by 2 F B and q 0 is replaced by 2q 0 . EXAMPLE 7 | An Electric Field Leads to a Force In Figure 18.15 the charges on the two metal spheres and the ebonite rod create an electric field E B at the spot indicated. This field has a magnitude of 2.0 N/C and is directed as in the drawing. Determine the force on a charge placed at that spot, if the charge has a value of (a) q 0 5 118 3 10 28 C and (b) q 0 5 224 3 10 28 C. Reasoning The electric field at a given spot can exert a variety of forces, depending on the magnitude and sign of the charge placed there. The charge is assumed to be small enough that it does not alter the locations of the surrounding charges that create the field.
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)
Definition of the electric field The electric field E that exists at a point is the electrostatic force F experienced by a small test charge * q 0 placed at that point divided by the charge itself: E = F q 0 (18.2) The electric field is a vector, and its direction is the same as the direction of the force F on a positive test charge. SI unit of electric field: newton per coulomb (N/C) *As long as the test charge is small enough that it does not disturb the surrounding charges, it may be either positive or negative. Compared to a positive test charge, a negative test charge of the same magnitude experiences a force of the same magnitude that points in the opposite direction. However, the same electric field is given by equation 18.2, in which F is replaced by - F and q 0 is replaced by −q 0 . 488 Physics Equation 18.2 indicates that the unit for the electric field is that of force divided by charge, which is a newton/coulomb (N/C) in SI units. It is the surrounding charges that create an electric field at a given point. Any positive or negative charge placed at the point interacts with the field and, as a result, experiences a force, as the next example indicates. EXAMPLE 7 An electric field leads to a force In figure 18.16 the charges on the two metal spheres and the ebonite rod create an electric field E at the spot indicated. This field has a magnitude of 2.0 N/C and is directed as in the drawing. Determine the force on a charge placed at that spot, if the charge has a value of (a) q 0 = +18 × 10 −8 C and (b) q 0 = −24 × 10 −8 C. FIGURE 18.16 The electric field E that exists at a given spot can exert a variety of forces. The force exerted depends on the magnitude and sign of the charge placed at that spot. (a) The force on a positive charge points in the same direction as E, while (b) the force on a negative charge points opposite to E.
- David Halliday, Jearl Walker, Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons, Dipesh Bhattarai(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
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 . (22.1) The magnitude of E at point P is F/q 0 . As shown in figure 22.3, we always represent an electric field with an arrow with its tail anchored on the point where the measurement is made. This need of anchoring the tail at the measurement point may sound trivial, but drawing the vectors any other way often results in errors, especially during the anxiety of an exam. Also, another common error is to mix up the terms force and field because they both start with the letter f. Electric force is a push or pull. As in previous chapters, forces are real (you can feel them on a crowded bus, for example). Electric field, however, is an abstract property set up by a charged object. We can shift the test charge around to various other points, to measure the Electric Fields there, so that we can figure out the distribution of the electric field set up by the charged object. That field exists independent of the test charge. It is something that a charged object sets up in the surrounding space (even vacuum), independent of whether we happen to come along to measure it. For the next several modules, we determine the field around charged particles and various charged objects. First, however, let’s examine a way of visualising Electric Fields. Pdf_Folio:477 CHAPTER 22 The electric felds 477 Electric feld lines Look at the space in the room around you. Can you visualise a field of vectors throughout that space — vectors with different magnitudes and directions? As impossible as that seems, Michael Faraday, who introduced the idea of Electric Fields in the nineteenth century, found a way.
- Raymond Serway, John Jewett(Authors)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
Substitute numerical values: a y 5 2 s1.60 3 10 219 Cds200 NyCd 9.11 3 10 231 kg 5 23.51 3 10 13 m/s 2 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. 608 Chapter 22 Electric Fields Summary › Definitions The electric field E S at some point in space is defined as the electric force F S e that acts on a small positive test charge placed at that point divided by the magnitude q 0 of the test charge: E S ; F S e q 0 (22.7) › Concepts and Principles Electric charges have the following important properties: ● Charges of opposite sign attract one another, and charges of the same sign repel one another. ● The total charge in an isolated system is conserved. ● Charge is quantized. Conductors are materials in which electrons move freely. Insulators are materials in which electrons do not move freely. Coulomb’s law states that the electric force exerted by a point charge q 1 on a second point charge q 2 is F S 12 5 k e q 1 q 2 r 2 r ⁄ 12 (22.6) where r is the distance between the two charges and r ⁄ 12 is a unit vector directed from q 1 toward q 2 . The constant k e , which is called the Coulomb constant, has the value k e 5 8.988 3 10 9 N ? m 2 /C 2 . At a distance r from a point charge q, the electric field due to the charge is E S 5 k e q r 2 r ⁄ (22.9) where r ⁄ is a unit vector directed from the charge toward the point in question. The electric field is directed radially out- ward from a positive charge and radially inward toward a negative charge. The electric field due to a group of point charges can be obtained by using the superposition principle.
eBook - PDF- Edward Purcell(Author)
- 2011(Publication Date)
- Cambridge University Press(Publisher)
The y' component of the electrons' field will be exactly cancelled by the field of the ions. That E; is zero is guaranteed by Gauss's law, for the number of charges per unit length of wire is the same as it was in the lab frame. The wire is uncharged in both frames. E = 0 .t THE FIELDS OF MOVING CHARGES The force on our test charge, when transformed back into the lab frame, will be a force proportional to u in the x direction, which is the direction of v X B if B is a vector in the z direction, pointing at us out of the diagram. We could show that the magnitude of this velocity-dependent force is given here also by Eq. 24: F = 2quI/ rc 2 • The physics needed is all in Eq. 12, but the integration is somewhat laborious and will not be undertaken here. In this chapter we have seen how the fact of charge invariance implies forces between electric currents. That does not oblige us to look on one fact as the cause of the other. These are simply two aspects of electromagnetism whose relationship beautifully illustrates the more general law: Physics is the same in all inertial frames of reference. If we had to analyze every system of moving charges by trans- forming back and forth among various coordinate systems, our task would grow both tedious and confusing. There is a better way. The overall effect of one current on another, or of a current on a moving charge, can be described completely and concisely by introducing a new field, the magnetic field. ,. si n OJ = in (¢- a ) 199 FIGURE 5.23 A closer look at the geometry of Fig. 5.22b, showing that, for any pair of electrons equidistant from the test charge, the one on the right will have a larger value of sin 2 0'. Hence, according to Eq. 5.12, it will produce the stronger field at the test charge. r s in if o ¢ -I and () a I 200 CHAPTER FIVE PROBLEMS 5.1 A capacitor consists of two parallel rectangular plates with a vertical separation of 2 cm.
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