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Chapter 19: Electric Forces and Electric Fields 1. Three objects are brought close to one another, two at a time. When objects A and B are brought together, they repel. When objects B and C are brought together, they also repel. Which of the following statements are true? (a) Objects A and C possess charges of the same sign. (b) Objects A and C possess charges of opposite sign. (c) All three objects possess charges of the same sign. (d) One of the objects is neutral. (e) We need to perform additional experiments to determine the signs of the charges. Answer: (a), (c), and (e). The experiment shows that objects A and B have charges of the same sign, as do objects B and C. Therefore, all three objects have charges of the same sign. We cannot determine from this information, however, whether the charges are positive or negative. 2. Three objects are brought close to one another, two at a time. When objects A and B are brought together, they attract. When objects B and C are brought together, they repel. From this experiment, what can we conclude? (a) Objects A and C possess charges of the same sign. (b) Objects A and C possess charges of opposite sign. (c) All three of the objects possess charges of the same sign. (d) One of the objects is neutral. (e) We need to perform additional experiments to determine information about the charges on the objects. Answer: (e). In the first experiment, objects A and B may have charges with opposite signs or one of the objects may be neutral. The second experiment shows that objects B and C have charges with opposite signs, so object B must be charged. We still do not know if object A is charged or neutral, however. 3. (i) Object A has a charge of +2 μC, and object B has a charge of +6 μC. Which of the following statements is true about the electric forces on the objects? (a) FAB = −3FBA (b) FAB = −FBA (c) 3FAB = −FBA (d) FAB = 3FBA (e) FAB = FBA (f) 3FAB = FBA (ii) Which of the following statements is true about the electric forces on the objects? (a) FAB 3FBA (b) FAB FBA (c) 3FAB FBA (d) FAB 3FBA (e) FAB FBA (f) 3FAB FBA Answer: (i), (e). From Newton’s third law, the electric force exerted by object B on object A is equal in magnitude to the force exerted by object A on object B. (ii), (b). From Newton’s third law, the electric force exerted by object B on object A is equal in magnitude to the force exerted by object A on object B and in the opposite direction. 4. A test charge of +3 μC is at a point P where an external electric field is directed to the right and has a magnitude of 4 × 106 N/C. If the test charge is replaced with another charge of −3 μC, the external electric field at P (a) is unaffected, (b) reverses direction, or (c) changes in a way that cannot be determined. Answer: (a). There is no effect on the electric field if we assume that the source charge producing the field is not disturbed by our actions. Remember that the electric field is created by source charge(s) (unseen in this case), not the test charge(s). 5. Rank the magnitudes of the electric field at points A, B, and C in Figure 19.18a, largest magnitude first. Figure 19.18a The electric field lines for two positive point charges. Answer: A, B, and C. The field is greatest at point A because that is where the field lines are closest together. The absence of lines near point C indicates that the electric field there is zero. 6. For a gaussian surface through which the net flux is zero, the following four statements could be true. Which of the statements must be true? (a) No charges are inside the surface. (b) The net charge inside the surface is zero. (c) The electric field is zero everywhere on the surface. (d) The number of electric field lines entering the surface equals the number leaving the surface. Answer: (b) and (d). Statement (a) is not necessarily true because an equal number of positive and negative charges could be present inside the surface. Statement (c) is not necessarily true as can be seen from Figure 19.30 because a nonzero electric field exists everywhere on the surface, but the charge is not enclosed within the surface. Thus, the net flux is zero. Figure 19.30 A point charge located outside a closed surface. The number of lines entering the surface equals the number leaving the surface. 7. Consider the charge distribution shown in Active Figure 19.31. (i) What are the charges contributing to the total electric flux through surface S ’? (a) q1 only (b) q4 only (c) q2 and q3 (d) all four charges (e) none of the charges (ii) What are the charges contributing to the total electric field at a chosen point on the surface S ’? (a) q1 only (b) q4 only (c) q2 and q3 (d) all four charges (e) none of the charges Active Figure 19.31 The net electric flux through any closed surface depends only on the charge inside that surface. The net flux through surface S is ql/ε0, the net flux through surface S ’ is (q2 + q3)/ε0, and the net flux through surface S ’’ is zero. Charge q4 does not contribute to the flux through any surface because it is outside all surfaces. Answer: (i), (c). The charges q1 and q4 are outside the surface and contribute zero net flux through S ’. (ii), (d). We don’t need the surfaces to realize that any given point in space will experience an electric field due to all local source charges.