Unformatted text preview: ELECTRIC FIELDS AND POTENTIAL
Objectives • Describe how to measure the strength of an electric field at different points. (33.1) • Describe how electric fields are represented by vectors and by electric field lines. (33.2) • Describe how objects can be completely shielded from electric fields. (33.3) • Explain why a charged object in an electric field is considered to have electrical potential energy. (33.4) • Distinguish between electrical potential energy and electric potential. (33.5) • Describe how electrical energy can be stored. (33.6) • Describe the operation of a Van de Graaff generator. (33.7) 33
T ELECTRIC FIELDS AND POTENTIAL
An electric field is a storehouse of energy. THE BIG IDEA discover!
MATERIALS cell phone, aluminum foil EXPECTED OUTCOME Students will find that they have to encase most, if not all, of the cell phone in foil in order to block an incoming call. ANALYZE AND CONCLUDE he space around a strong magnet is different from how it would be if the magnet were not there. Put a paper clip in the space and you’ll see the paper clip move. The space around the sun is different from how it would be if the sun were not there. The sun’s gravitational influence affects the motions of the planets around it. Similarly, the space around a concentration of electric charge is different from how it would be if the charge were not there. If you walk by the charged dome of an electrostatic machine—a Van de Graaff generator, for example—you can sense the charge. Hair on your body stands out—just a tiny bit if you’re more than a meter away, and more if you’re closer. The space that surrounds each of these things—the magnet, the sun, and the electric charge—is altered. The space is said to contain a force field. discover!
What Is Electric Shielding?
1. Wrap a cellular phone completely in aluminum foil. 2. Make a call to the wrapped phone. 3. Unwrap the cell phone, and now cover only part of it with foil. Make a call to the partly wrapped cell phone. 4. Repeat Step 3 a few more times, covering different parts of the phone. 1. See Expected Outcome. 2. Answers may include metal containers or wire mesh. 3. Electric shielding involves blocking an object from outside electrical activity. Electric shielding works because when the charge on a conductor is not moving, the electric field inside the conductor is zero. Analyze and Conclude
1. Observing What effect did completely wrapping the phone have on reception? Did wrapping only part of the phone block the incoming signal? If so, which part of the phone needed to be covered in order to block the signal? 2. Predicting What other materials do you think could be used to shield a cellular phone? 3. Making Generalizations What is electric shielding, and why does it work? 664 664 33.1 Electric Fields 33.1 Electric Fields
The force field that surrounds a mass is a gravitational field. If you throw a ball into the air, it follows a curved path. Earlier chapters showed that it curves because there is an interaction between the ball and Earth—between their centers of gravity, to be exact. Their centers of gravity are quite far apart, so this is “action at a distance.” The idea that things not in contact could exert forces on one another bothered Isaac Newton and many others. The concept of a force field explains how Earth can exert a force on things without touching them, like a tossed ball. The ball is in contact with the field all the time. The ball curves because it interacts with Earth’s gravitational field. You can think of distant space probes as interacting with gravitational fields rather than with the masses of Earth and other astronomical bodies that are responsible for the fields. Just as the space around Earth and every other mass is filled with a gravitational field, the space around every electric charge is filled with an electric field. An electric field is a force field that surrounds an electric charge or group of charges. In Figure 33.2, a gravitational force holds a satellite in orbit about a planet, and an electrical force holds an electron in orbit about a proton. In both cases there is no contact between the objects, and the forces are “acting at a distance.” In terms of the field concept, the satellite and electron interact with the force fields of the planet and the proton and are everywhere in contact with these fields. Just as in the gravitational case, the force that one electric charge exerts on another can be described as the interaction between one charge and the electric field set up by the other. Key Term electric field Teaching Tip Introduce electric fields by mentioning (or showing) a Van de Graaff generator. Describe the altered space around it when it is charged. This space is an electric field. Teaching Tip Compare gravitational and electric fields. Both are regions that are altered, by mass for the gravitational field, and by charge for the electric field. Teaching Tip The easiest fields for students to visualize are magnetic fields because of the familiar iron filing patterns (Figures 36.4 and 36.5.) Explain that fields are called “force fields” because forces are exerted on bodies in their vicinity, but a better term would be “energy field” because energy is stored in a field. In the case of an electric field, any charges in the vicinity are energized. We speak about the PE that electrically charged bodies have in a field—or more often, the PE compared to the amount of charge—electric potential. Explain that the field energy, and correspondingly the electric potential, is greater nearer the charged dome and weaker with increased distance, thus following the inverse-square law. Teaching Tip Point out that measuring instruments sometimes alter that which is being measured. A cold thermometer placed in a warm liquid absorbs heat from the liquid, thereby altering the temperature of the liquid. Similarly, placing a test charge in an electric field changes the nature of the field. The test charges used to measure electric fields are small so as to minimize such changes. FIGURE 33.1
You can sense the force field that surrounds a charged Van de Graaff generator. The force on a charged particle gives electric field strength E. In equation form, E F/q. FIGURE 33.2
The satellite and the electron both experience forces; they are both in force fields. An electric field has both magnitude and direction. The magnitude (strength) of an electric field can be measured by its effect on charges located in the field. Imagine a small positive “test charge” that is placed in an electric field. Where the force is greatest on the test charge, the field is strongest. Where the force on the test charge is weak, the field is small.33.1
665 CHAPTER 33 ELECTRIC FIELDS AND POTENTIAL 665 Demonstration
Hold a fluorescent lamp tube in the field of a charged Van de Graaff generator to show that it lights up when one end of the tube is closer to the dome than the other end. The direction of an electric field at any point, by convention, is the direction of the electrical force on a small positive test charge placed at that point. Thus, if the charge that sets up the field is positive, the field points away from that charge. If the charge that sets up the field is negative, the field points toward that charge. (Be sure to distinguish between the hypothetical small test charge and the charge that sets up the field.) CHECK
The electric field is stronger near the dome, and weaker farther away. Charges nearer the dome experience more force, which means more work is done when they are moved in the stronger parts of the field. Thus, each charge in the stronger field has more energy. The energy per charge is what we call potential. Show that when the two ends of the fluorescent tube are equidistant from the charged dome, light emission ceases. ...... CONCEPT How are the magnitude and direction of an electric field determined? FIGURE 33.3 a. In a vector representation
of an electric field, the length of the vectors indicates the magnitude of the field. b. In a lines-of-force representation, the distance between field lines indicates magnitudes. 33.2 Electric Field Lines
Since an electric field has both magnitude and direction, it is a vector quantity and can be represented by vectors. The negatively charged particle in Figure 33.3a is surrounded by vectors that point toward the particle. (If the particle were positively charged, the vectors would point away from the particle. The vectors always point in the direction of the force that would act on a positive test charge.) The magnitude of the field is indicated by the length of the vectors. The electric field is greater where the vectors are long than it is where the vectors are short. To represent a complete electric field by vectors, you would have to show a vector at every point in the space around the charge. Such a diagram would be totally unreadable! A more useful way to describe an electric field is shown in Figure 33.3b. You can use electric field lines (also called lines of force) to represent an electric field. Where the lines are farther apart, the field is weaker. For an isolated charge, the lines extend to infinity, while for two or more opposite charges, the lines emanate from a positive charge and terminate on a negative charge. Some electric field configurations are shown in Figure 33.4. The photographs in Figure 33.5 show bits of thread that are suspended in an oil bath surrounding charged conductors. The ends of the bits of thread line up end-to-end with the electric field lines. In Figures 33.5a and 33.5b, we see the field lines are characteristic of a single pair of point charges. a The magnitude of an CHECK electric field can be measured by its effect on charges located in the field. The direction of the field at any point is the direction of the electrical force on a positive test charge placed at that point.
CONCEPT ...... b
FIGURE 33.4 a. The field lines around
a single positive charge extend to infinity. b. For a pair of equal but opposite charges, the field lines emanate from the positive charge and terminate on the negative charge. c. Field lines are evenly spaced between two oppositely charged capacitor plates. Teaching Resources • Reading and Study Workbook • PresentationEXPRESS • Interactive Textbook a b c 666 666 33.2 Electric Field
Bits of fine thread suspended in an oil bath surrounding charged conductors line up end to end along the direction of the field. The photos illustrate field patterns for a. equal and opposite charges; b. equal like charges; c. oppositely charged plates; and d. oppositely charged cylinder and plate. Lines
Teaching Tip Describe the vector nature of a force field and describe the lines of force as shown in Figure 33.5. Ask If a tiny test charge were dropped in the oil bath shown in Figure 33.5, in what direction would it move? Along the same directions as the bits of thread—away from the conductor of same sign of charge and toward the conductor of opposite sign of charge. Teaching Tidbit Sharks and related species of fish are equipped with specialized receptors in their snouts that sense extremely weak electric fields generated by other creatures in seawater. a b c d The oppositely charged parallel plates in Figure 33.5c produce nearly parallel field lines between the plates. Except near the ends, the field between the plates has a constant strength. Notice that in Figure 33.5d, there is no electric field inside the charged cylinder. The conductor shields the space from the field outside. CHECK How can you represent an electric field? CONCEPT think! Teaching Resources • Reading and Study Workbook A beam of electrons is produced at one end of a glass tube and lights up a phosphor screen at the other end. When the beam is straight, it produces a spot in the middle of the screen. If the beam passes through the electric field of a pair of oppositely charged plates, it is deflected upward as shown. If the charges on the plates are reversed, in what direction will the beam deflect? Answer: 33.2 • Concept-Development Practice Book 33-1 • Problem-Solving Exercises in Physics 16-2 • Transparencies 78, 79 • PresentationEXPRESS • Interactive Textbook ...... CONCEPT ...... You can use electric CHECK field lines (also called lines of force) to represent an electric field. Where the lines are farther apart, the field is weaker. CHAPTER 33 ELECTRIC FIELDS AND POTENTIAL 667 667 33.3 Electric
Teaching Tip Call attention to Figure 33.5d showing that the threads have no directional properties inside the charged cylinder. This shows that the electric field is shielded by the metal. The dramatic photo of the car being struck by lightning (Figure 33.6) also illustrates that the electric field inside a conductor is normally zero, regardless of what is happening outside. Teaching Tip After discussing Figure 33.7, go a step further and consider the test charge off center, twice as far from region A as region B, as shown. 33.3 Electric Shielding
The dramatic photo in Figure 33.6 shows a car being struck by lightning. Yet, the occupant inside the car is completely safe. This is because the electrons that shower down upon the car are mutually repelled and spread over the outer metal surface, finally discharging when additional sparks jump from the car’s body to the ground. The configuration of electrons on the car’s surface at any moment is such that the electric fields inside the car practically cancel to zero. This is true of any charged conductor. If the charge on a conductor is not moving, the electric field inside the conductor is exactly zero.
Charged Conductors The absence of electric field within a conductor holding static charge does not arise from the inability of an electric field to penetrate metals. It comes about because free electrons within the conductor can “settle down” and stop moving only when the electric field is zero. So the charges arrange themselves to ensure a zero field with the material. Consider the charged metal sphere shown in Figure 33.7. Because of mutual repulsion, the electrons spread as far apart from one another as possible. They distribute themselves uniformly over the surface of the sphere. A positive test charge located exactly in the middle of the sphere would feel no force. The electrons on the left side of the sphere would tend to pull the test charge to the left, but the electrons on the right side of the sphere would tend to pull the test charge to the right equally hard. The net force on the test charge would be zero. Thus, the electric field is also zero. Interestingly enough, complete cancellation will occur anywhere inside the sphere. If the conductor is not spherical, then the charge distribution will not be uniform. The remarkable thing is this: The exact charge distribution over the surface is such that the electric field everywhere inside the conductor is zero. Look at it this way: If there were an electric field inside a conductor, then free electrons inside the conductor would be set in motion. How far would they move? Until equilibrium is established, which is to say, when the positions of all the electrons produce a zero field inside the conductor. FIGURE 33.6
Electrons from the lightning bolt mutually repel and spread over the outer metal surface. The overall electric field inside the car practically cancels to zero. The dotted lines represent a sample cone of action, subtending both A and B. Region A has twice the diameter, four times the area, and four times the charge of region B. Four times the charge at twice the distance will have one fourth the effect. The greater charge is balanced by the correspondingly greater distance. This will be the case for all points inside the conductor. And the conductor need not be a sphere, as shown by the shapes in Figure 33.8. FIGURE 33.7
The forces on a test charge located inside a charged hollow sphere cancel to zero. Teaching Resources • Reading and Study Workbook • PresentationEXPRESS • Interactive Textbook FIGURE 33.8
Static charges are distributed on the surface of all conductors in such a way that the electric field inside the conductors is zero. 668 668 How to Shield an Electric Field There is no way to shield gravity, because gravity only attracts. There are no repelling parts of gravity to offset attracting parts. Shielding electric fields, however, is quite simple. Surround yourself or whatever you wish to shield with a conducting surface. Put this surface in an electric field of whatever field strength. The free charges in the conducting surface will arrange themselves on the surface of the conductor in a way such that all field contributions inside cancel one another. That’s why certain electronic components are encased in metal boxes, and why certain cables have a metal covering—to shield them from all outside electrical activity.
CONCEPT CHECK How can you describe the electric field within a conductor holding static charge? ...... FIGURE 33.9
The metal-lined cover shields the internal electrical components from external electric fields. Similarly, a metal cover shields the coaxial cable. Teaching Tip Another point to consider: If the field inside a conductor were not zero, then free charges inside would move, but the movement would not continue forever. The charges would finally move to positions of equilibrium. In these positions their effects on one another would be mutually balanced. There would be complete cancellation of fields everywhere inside the conductor. This is what happens—not gradually, but suddenly. Teaching Tip Revisit the Discover! activity at the beginning of the chapter, but with a twist: Use a small portable radio instead of a cell phone, and a metal screen enclosure instead of aluminum foil. Using a metal screen or meshwork demonstrates that shielding still may occur even with small gaps in the conductor. The foil and screen are examples of Faraday cages. Named after physicist Michael Faraday, a Faraday cage is an enclosure or mesh made from conducting material. If the charge on a conductor is not moving, the electric field inside the conductor is exactly zero.
It is said that a gravitational field, unlike an electric field, cannot be shielded. But the gravitational field at the center of Earth cancels to zero. Isn’t this evidence that a gravitational field can be shielded? Answer: 33.3 33.4 Electrical Potential Energy
Recall the relationship between work and potential energy. Work is done when a force moves something in the direction of the force. An object has potential energy by virtue of its location, say in a force field. For example, if you lift an object, you apply a force equal to its weight. When you raise it through some distance, you are doing work on the object. You are also increasing its gravitational potential energy. The greater the distance it is raised, the greater is the increase in its gravitational potential energy. Doing work increases its gravitational potential energy, as shown in Figure 33.10a. CHECK 33.4 Electrical
Key Term electrical potential energy Teaching Tip Briefly review the relationship between work and potential energy (Chapter 9). Explain that, just as doing work on an object increases the object’s gravitational potential energy, the work required to push a charged particle against the electric field of a charged object increases the particle’s electrical potential energy. FIGURE 33.10 a. Work is done to lift the
mass against the gravitational field of Earth. In an elevated position, the mass has gravitational potential energy. When released, this energy is transferred to the piling below. b. Similar energy transfer occurs for electric charges. ...... CHAPTER 33 ELECTRIC FIELDS AND POTENTIAL 669 669 The electrical potential energy of a charged particle is increased when work is done to push it against the electric field of something else that is charged.
CONCEPT CHECK ...... ...
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- Spring '10
- Electrostatics, Electrical Potential Energy, Electric charge, electrical energy, Van de Graaff