Physics
Electric Field Lines
Electric field lines are a visual representation of the electric field around a charged object. They show the direction and strength of the electric field at different points in space. The lines are drawn such that the electric field is tangent to the lines at any point, and the density of lines indicates the strength of the field.
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11 Key excerpts on "Electric Field Lines"
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
For each rod deduce the direction of the electric field at a point that is located directly above the midpoint of the rod. 18.7 | Electric Field Lines As we have seen, electric charges create an electric field in the space around them. It is useful to have a kind of “map” that gives the direction and strength of the field at various places. The great English physicist Michael Faraday (1791–1867) proposed an idea that provides such a “map”—the idea of Electric Field Lines. Since the electric field is the elec- tric force per unit charge, field lines are also called lines of force. To introduce the electric field line concept, Figure 18.22a shows a positive point charge 1q. At the locations numbered 1–8, a positive test charge would experience a repulsive force, as the arrows in the drawing indicate. Therefore, the electric field created by the charge 1q is directed radially outward. The Electric Field Lines are lines drawn to show this direction, as Figure 18.22b illustrates. They begin on the charge 1q and point radially outward. Figure 18.23 shows the field lines in the vicinity of a negative charge 2q. In this case they are directed radially inward because the force on a positive test charge is one of attraction, indicating that the electric field points inward. In general, Electric Field Lines are always directed away from positive charges and toward negative charges. The Electric Field Lines in Figures 18.22 and 18.23 are drawn in only two dimensions, as a matter of convenience. Field lines radiate from the charges in three dimensions, and an infinite number of lines could be drawn. However, for clarity only a small number are ever included in pictures. The number is chosen to be proportional to the magnitude of the charge; thus, five times as many lines would emerge from a 15q charge as from a 1q charge.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
For each rod deduce the direction of the electric field at a point that is located directly above the midpoint of the rod. 18.7 | Electric Field Lines As we have seen, electric charges create an electric field in the space around them. It is useful to have a kind of “map” that gives the direction and strength of the field at various places. The great English physicist Michael Faraday (1791–1867) proposed an idea that provides such a “map”—the idea of Electric Field Lines. Since the electric field is the elec- tric force per unit charge, field lines are also called lines of force. To introduce the electric field line concept, Figure 18.21a shows a positive point charge 1q. At the locations numbered 1–8, a positive test charge would experience a repulsive force, as the arrows in the drawing indicate. Therefore, the electric field created by the charge 1q is directed radially outward. The Electric Field Lines are lines drawn to show this direction, as Figure 18.21b illustrates. They begin on the charge 1q and point radially outward. Figure 18.22 shows the field lines in the vicinity of a negative charge 2q. In this case they are directed radially inward because the force on a positive test charge is one of attraction, indicating that the electric field points inward. In general, Electric Field Lines are always directed away from positive charges and toward negative charges. The Electric Field Lines in Figures 18.21 and 18.22 are drawn in only two dimensions, as a matter of convenience. Field lines radiate from the charges in three dimensions, and an infinite number of lines could be drawn. However, for clarity only a small number are ever included in pictures. The number is chosen to be proportional to the magnitude of the charge; thus, five times as many lines would emerge from a 15q charge as from a 1q charge.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
For each rod deduce the direction of the electric field at a point that is located directly above the midpoint of the rod. 18.7 Electric Field Lines As we have seen, electric charges create an electric field in the space around them. It is useful to have a kind of “map” that gives the direction and strength of the field at various places. The great English physicist Michael Faraday (1791–1867) proposed an idea that provides such a “map”— the idea of Electric Field Lines. Since the electric field is the electric force per unit charge, field lines are also called lines of force. To introduce the electric field line concept, Figure 18.22a shows a positive point charge +q. At the locations numbered 1–8, a positive test charge would experience a repulsive force, as the arrows in the drawing indicate. Therefore, the electric field created by the charge +q is directed radially outward. The Electric Field Lines are lines drawn to show this direction, as Figure 18.22b illustrates. They begin on the charge +q and point radially outward. Figure 18.23 shows the field lines in the vicinity of a negative charge ‒q. In this case they are directed radially inward because the force on a positive test charge is one of attraction, indicating that the electric field points inward. In general, Electric Field Lines are always directed away from positive charges and toward negative charges. The Electric Field Lines in Figures 18.22 and 18.23 are drawn in only two dimensions, as a matter of convenience. Field lines radiate from the charges in three dimensions, and an infinite CYU FIGURE 18.3 +q A B D C 506 CHAPTER 18 Electric Forces and Electric Fields number of lines could be drawn. However, for clarity only a small number are ever included in pictures. The number is chosen to be proportional to the magnitude of the charge; thus, five times as many lines would emerge from a +5q charge as from a +q charge.
- 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)
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. He envisioned lines, now called Electric Field Lines, in the space around any given charged particle or object. Figure 22.4 gives an example in which a sphere is uniformly covered with negative charge (the surface has uniform charge). If we place a positive test charge at any point near the sphere, we find that an electrostatic force pulls on it towards the centre of the sphere. Thus at every point around the sphere, an electric field vector points radially inward towards the sphere. We can represent this electric field with Electric Field Lines as shown in figure 22.5. FIGURE 22.4 The electrostatic force F acting on a positive test charge near a sphere of uniform negative charge. Positive test charge F + FIGURE 22.5 The electric feld vector E at the location of the test charge, and the electric feld lines in the space near the sphere. The feld lines extend towards the negatively charged sphere. (They originate on distant positive charges.) Electric Field Lines E - - - - - - - - At any point, such as the one shown, the direction of the field line through the point matches the direction of the electric vector at that point. The rules for drawing electric fields lines are as follows. 1. At any point, the electric field vector must be tangent to the electric field line through that point and in the same direction. (This is easy to see in our last figure where the lines are straight, but we’ll see some curved lines soon.) 2. The relative density of the lines represents the relative magnitude of the field there, with greater density for greater magnitude.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
18.7 Electric Field Lines 559 to show this direction, as Figure 18.22b illustrates. They begin on the charge +q and point radially outward. Figure 18.23 shows the field lines in the vicinity of a negative charge ‒q. In this case they are directed radially inward because the force on a positive test charge is one of attraction, indicating that the electric field points inward. In general, Electric Field Lines are always directed away from positive charges and toward negative charges. The Electric Field Lines in Figures 18.22 and 18.23 are drawn in only two dimen- sions, as a matter of convenience. Field lines radiate from the charges in three dimen- sions, and an infinite number of lines could be drawn. However, for clarity only a small number are ever included in pictures. The number is chosen to be proportional to the magnitude of the charge; thus, five times as many lines would emerge from a +5q charge as from a +q charge. The pattern of Electric Field Lines also provides information about the magnitude or strength of the field. Notice that in Figures 18.22 and 18.23, the lines are closer together near the charges, where the electric field is stronger. At distances far from the charges, where the electric field is weaker, the lines are more spread out. It is true in general that the electric field is stronger in regions where the field lines are closer together. In fact, no matter how many charges are present, the number of lines per unit area passing perpendicularly through a surface is proportional to the magnitude of the electric field. In regions where the Electric Field Lines are equally spaced, there is the same number of lines per unit area everywhere, and the electric field has the same strength at all points. For example, Figure 18.24 shows that the field lines between the plates of a parallel plate capacitor are parallel and equally spaced, except near the edges where they bulge outward.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
Electric Field Lines as in Fig. 22-3b. At any point, such as the one shown, the direc- tion of the field line through the point matches the direction of the electric vector at that point. The rules for drawing electric fields lines are these: (1) At any point, the elec- tric field vector must be tangent to the electric field line through that point and in the same direction. (This is easy to see in Fig. 22-3 where the lines are straight, but we’ll see some curved lines soon.) (2) In a plane perpendicular to the field lines, the relative density of the lines represents the relative magnitude of the field there, with greater density for greater magnitude. If the sphere in Fig. 22-3 were uniformly covered with positive charge, the electric field vectors at all points around it would be radially outward and thus so would the Electric Field Lines. So, we have the following rule: 632 CHAPTER 22 ELECTRIC FIELDS F E + + + + + + + + + + + + + + + + Positive test charge (a) (b) + + + + + + + + + + + + + + + + + + + + + + + (c) + + + Figure 22-4 (a) The force on a positive test charge near a very large, nonconducting sheet with uniform positive charge on one side. (b) The electric field vector E → at the test charge’s location, and the nearby Electric Field Lines, extending away from the sheet. (c) Side view. Figure 22-5 Field lines for two particles with equal positive charge. Doesn’t the pattern itself suggest that the particles repel each other? E + + Electric Field Lines extend away from positive charge (where they originate) and toward negative charge (where they terminate). 633 22-2 THE ELECTRIC FIELD DUE TO A CHARGED PARTICLE 22-2 THE ELECTRIC FIELD DUE TO A CHARGED PARTICLE Learning Objectives After reading this module, you should be able to . . . The Electric Field Due to a Point Charge To find the electric field due to a charged particle (often called a point charge), we place a positive test charge at any point near the particle, at distance r.
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
The concept of Electric Field Lines, and of electric field line diagrams, enables us to visualize the way in which the space is altered, allowing us to visualize the field. The purpose of this section is to enable you to create sketches of this geometry, so we will list the specific steps and rules involved in creating an accurate and useful sketch of an electric field. It is important to remember that electric fields are three-dimensional. Although in this book we include some pseudo-three- dimensional images, several of the diagrams that you’ll see (both here, and in subsequent chapters) will be two-dimensional projections, or cross-sections. Always keep in mind that in fact, you’re looking at a three-dimensional phenomenon. Our starting point is the physical fact that the electric field of the source charge causes a test charge in that field to experience a force. By definition, electric field vectors point in the same direction as the electric force that a (hypothetical) positive test charge would experience, if placed in the field (Figure 5.27) Figure 5.27 The electric field of a positive point charge. A large number of field vectors are shown. Like all vector arrows, the length of each vector is proportional to the magnitude of the field at each point. (a) Field in two dimensions; (b) field in three dimensions. We’ve plotted many field vectors in the figure, which are distributed uniformly around the source charge. Since the electric field is a vector, the arrows that we draw correspond at every point in space to both the magnitude and the direction of the field at that point. As always, the length of the arrow that we draw corresponds to the magnitude of the field vector at that point. For a point source charge, the length decreases by the square of the distance from the source charge. In addition, the Chapter 5 | Electric Charges and Fields 213
eBook - PDF- Michael Tammaro(Author)
- 2019(Publication Date)
- Wiley(Publisher)
These lines point away from the charge. The Electric Field Lines in Figure 18.4.1(c) point toward the charge because the charge is negative. Electric Field Lines can be used to depict the electric field in the vicinity of two or more charges. Before pursuing this, however, we state the general properties of Electric Field Lines as follows: Figure 18.4.1 (a) The electric field vectors surrounding an isolated positive point charge. Connecting the electric field vectors from part (a) produces Electric Field Lines, which (b) point away from the charge for a positive point charge and (c) point toward the charge for a negative point charge. + (a) + (b) - (c) Electric Field Lines ∙ Electric Field Lines begin on positive charges (or infinity) and end on negative charges (or infinity). ∙ The direction of the electric field at any point is tangent to an electric field line passing through that point. ∙ The number of field lines starting or ending on a charge is proportional to the magnitude of that charge. ∙ The magnitude of the electric field is greater where the lines are closely spaced, and weaker where the lines are more spread out. Using these four rules, the Electric Field Lines can be constructed for any configuration of charges. A simple configuration that has significant practical interest is illustrated in Figure 18.4.2(a). It consists of a pair of separated point charges of equal magnitude but opposite sign. This configuration is called an electric dipole. Figure 18.4.2(b) shows the Electric Field Lines of a pair of equal positive charges. For both configurations in Figure 18.4.2, the field lines are closely spaced near the charges (where the field is strong) and more widely spaced far from the charges (where the field is weaker). There are no lines near the midpoint of the line connecting the charges in Figure 18.4.2(b) because the electric field is zero at that point.
- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
(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. (This may sound trivial, but drawing the vectors any other way usually results in errors. 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. Electric field is an abstract property set up by a charged object.) From Eq. 22.1.1, we see that the SI unit for the electric field is the newton per coulomb (N/C). 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 parti- cles and various charged objects. First, however, let’s examine a way of visualiz- ing electric fields. Electric Field Lines Look at the space in the room around you. Can you visualize 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 19th century, found a way. He envisioned lines, now called Electric Field Lines, in the space around any given charged particle or object. Figure 22.1.3 gives an example in which a sphere is uniformly covered with negative charge. If we place a positive test charge at any point near the sphere (Fig. 22.1.3a), we find that an electrostatic force pulls on it toward the center of the sphere.
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)
As figure 18.21 shows, this device consists of two parallel metal plates, each with area A. A charge +q is spread uniformly over one plate, while a charge −q is spread uniformly over the other plate. In the region between the plates and away from the edges, the electric field points from the positive plate towards the negative plate and is perpendicular to both. It can be shown (see example 15 in section 18.9) that this electric field has a magnitude of Parallel plate capacitor E = q 0 A = 0 (18.4) where 0 is the permittivity of free space. In this expression the Greek symbol sigma () denotes the charge per unit area ( = q/A) and is sometimes called the charge density. Except in the region near the edges, the field has the same value at all places between the plates. The field does not depend on the distance from the charges, in distinct contrast to the field created by an isolated point charge. 18.7 Electric Field Lines LEARNING OBJECTIVE 18.7 Draw Electric Field Lines. As we have seen, electric charges create an electric field in the space around them. It is useful to have a kind of ‘map’ that gives the direction and strength of the field at various places. The great English physicist Michael Faraday (1791–1867) proposed an idea that provides such a ‘map’ — the idea of Electric Field Lines. Since the electric field is the electric force per unit charge, field lines are also called lines of force. To introduce the electric field line concept, figure 18.22a shows a positive point charge +q. At the locations numbered 1–8, a positive test charge would experience a repulsive force, as the arrows in the drawing indicate. Therefore, the electric field created by the charge +q is directed radially outwards. The Electric Field Lines are lines drawn to show this direction, as figure 18.22b illustrates. They begin on the charge +q and point radially outwards. Figure 18.23 shows the field lines in the vicinity of a negative charge −q.
eBook - PDF- David Halliday, Robert Resnick, Kenneth S. Krane(Authors)
- 2019(Publication Date)
- Wiley(Publisher)
which shows a nonuniform field, the electric field has dif- ferent directions at points P 1 and P 2 , in each case tangent to the electric field line passing through that point. For the Electric Field Lines to have this property, they must also be drawn so that The Electric Field Lines start on positive charges and end on negative charges. For example, Fig. 26-10 represents the field lines for an iso- lated positive point charge (or a small sphere of positive charge). The lines point radially outward, so that at any point P the field is radial. The field lines begin on the posi- tive charge and extend to infinity, since there are no nega- tive charges in this region. If the charge were negative, the field lines would point in the opposite direction (radially in- ward). One final property of Electric Field Lines is that The magnitude of the electric field at any point is pro- portional to the number of field lines per unit cross-sec- tional area perpendicular to the lines. In other words, the more densely packed the field lines are near any point, the stronger is the field at that point. Figure 26-9b, for example, suggests that the magnitude of the field is larger at the bottom of the drawing (near point P 1 ) than it is at the top of the drawing (near point P 2 ). In Fig. 26-9a, on the other hand, the spacing of the field lines is the same at all points, suggesting that the field has the same magni- tude everywhere. For a point charge (Fig. 26-10), the field lines are close together near the charge and further apart away from the charge, which indicates that the field grows weaker as the distance from the charge increases. The uniform field near a large sheet of positive charge is shown in Fig. 26-11. The direction of the field is perpendic- ular to the sheet.
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