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©1997 by Eric Mazur Published by Pearson Prentice Hall Upper Saddle River, NJ 07458 ISBN No portion of the file may be distributed, transmitted in any form, or included in other documents without express written permission from the publisher.

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Electrostatics

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**1. both positive and negative charges move freely. **

A positively charged object is placed close to a conducting object attached to an insulating glass pedestal (a). After the opposite side of the conductor is grounded for a short time interval (b), the conductor becomes negatively charged (c). Based on this information, we can conclude that within the conductor 1. both positive and negative charges move freely. 2. only negative charges move freely. 3. only positive charges move freely. 4. We can’t really conclude anything. Answer: 4.The same result is achieved regardless of whether the charge carriers are positive or negative.

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**1. 1 and 3 carry charges of opposite sign. **

Three pithballs are suspended from thin threads. Various objects are then rubbed against other objects (nylon against silk, glass against polyester, etc.) and each of the pithballs is charged by touching them with one of these objects. It is found that pithballs 1 and 2 repel each other and that pithballs 2 and 3 repel each other. From this we can conclude that 1. 1 and 3 carry charges of opposite sign. 2. 1 and 3 carry charges of equal sign. 3. all three carry the charges of the same sign. 4. one of the objects carries no charge. 5. we need to do more experiments to determine the sign of the charges. Answer: 3. Charges of equal sign repel, so 1 and 2 carry charges of equal sign and so, too, do 2 and 3.

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**1. 1 and 3 carry charges of opposite sign. **

Three pithballs are suspended from thin threads. Various objects are then rubbed against other objects (nylon against silk, glass against polyester, etc.) and each of the pithballs is charged by touching them with one of these objects. It is found that pithballs 1 and 2 attract each other and that pithballs 2 and 3 repel each other. From this we can conclude that 1. 1 and 3 carry charges of opposite sign. 2. 1 and 3 carry charges of equal sign. 3. all three carry the charges of the same sign. 4. one of the objects carries no charge. 5. we need to do more experiments to determine the sign of the charges. Answer: 5. Charges of opposite sign attract, charges of equal sign repel, and any type of charge attracts a neutral object. So 1 and 2 either carry charges of opposite sign or one of the two is neutral and the other charged. Since 2 and 3 repel, however, we know that 2 and 3 carry charges of equal sign. So there are two possibilities: 2 and 3 carry charges of equal sign and (i) 1 is neutral, or (ii) 1 carries a charge of the opposite sign to that of 2 and 3.

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**1. Yes, we must move the particles farther apart. **

A hydrogen atom is composed of a nucleus containing a single proton, about which a single electron orbits. The electric force between the two particles is 2.3 x 1039 greater than the gravitational force! If we can adjust the distance between the two particles, can we find a separation at which the electric and gravitational forces are equal? 1. Yes, we must move the particles farther apart. 2. Yes, we must move the particles closer together. 3. No, at any distance Answer: 3. Both the electric and gravitational forces vary as the inverse square of the separation between two bodies. Thus, the forces cannot be equal at any distance.

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Two uniformly charged spheres are firmly fastened to and electrically insulated from frictionless pucks on an air table. The charge on sphere 2 is three times the charge on sphere 1. Which force diagram correctly shows the magnitude and direction of the electrostatic forces: Answer: 5. The magnitude of the electrostatic force exerted by 2 on 1 is equal to the magnitude of the electrostatic force exerted by 1 on 2. If the charges are of the same sign, the forces are repulsive; if the charges are of opposite sign, the forces are attractive.

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**6. some other combination 7. None of the above.**

Consider the four field patterns shown. Assuming there are no charges in the regions shown, which of the patterns represent(s) a possible electrostatic field: 1. (a) 2. (b) 3. (b) and (d) 4. (a) and (c) 5. (b) and (c) 6. some other combination 7. None of the above. Answer: 2. Pattern (a) can be eliminated because field lines cannot simultaneously emanate from and converge at a single point; (c) can be eliminated because there are no charges in the region, and so there are no sources of field lines; (d) can be eliminated because electrostatic field lines do not close on themselves.

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**6. some other combination 7. none of the above**

An electrically neutral dipole is placed in an external field. In which situation(s) is the net force on the dipole zero? 1. (a) 2. (c) 3. (b) and (d) 4. (a) and (c) 5. (c) and (d) 6. some other combination 7. none of the above Answer: 5. An electric dipole in a uniform electric field experiences zero net force, and the field is uniform in (c) and (d). Notice that there is a net torque in case (d).

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**2. 2s /eo between, ±s /eo outside. 3. zero both between and outside. **

The electric charge per unit area is +s for plate 1 and –s for plate 2.The magnitude of the electric field associated with plate 1 is s/eo, and the electric field lines for this plate are as shown. When the two are placed parallel to one another, the magnitude of the electric field is 1. 2s /eo between, 0 outside. 2. 2s /eo between, ±s /eo outside. 3. zero both between and outside. 4. ±s /eo both between and outside. 5. none of the above. Answer: 1.The magnitude of the electric field for plate 2 is also σ /2Aεo, but the field lines for this plate are directed toward the plate. Using the principle of superposition in the regions between and outside the plates gives answer 1.

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A cylindrical piece of insulating material is placed in an external electric field, as shown. The net electric flux passing through the surface of the cylinder is 1. positive. 2. negative. 3. zero. Answer: 3. Because each field line entering the surface also leaves the surface, there is no net flux through it.

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Two test charges are brought separately into the vicinity of a charge +Q. First, test charge +q is brought to point A a distance r from +Q. Next, +q is removed and a test charge +2q is brought to point B a distance 2r from +Q. Compared with the electrostatic potential of the charge at A, that of the charge at B is 1. greater. 2. smaller. 3. the same. Answer: 2.The electrostatic potential at A is Q/r, whereas at point B it is Q/2r. The magnitudes of the charges q and 2q at A and B do not enter into the expression for the electrostatic potential.

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Two test charges are brought separately into the vicinity of a charge +Q. First, test charge +q is brought to a point a distance r from +Q. Then this charge is removed and test charge –q is brought to the same point. The electrostatic potential energy of which test charge is greater: 1. +q 2. –q 3. It is the same for both. Answer: 1.The electrostatic potential energy of a test charge depends on both its position and its charge. For the +q charge, the electrostatic potential energy equals Qq/r, whereas for the –q charge it equals –Qq/r.

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An electron is pushed into an electric field where it acquires a 1-V electrical potential. Suppose instead that two electrons are pushed the same distance into the same electric field. The electrical potential of the two electrons is V. V. 3. 1 V. 4. 2 V. 5. 4 V. Answer: 3.The electrostatic potential of a charged particle in an electric field depends only on the position of the particle, not on its charge.

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**3. largest somewhere between center and surface. **

A solid spherical conductor is given a net nonzero charge. The electrostatic potential of the conductor is 1. largest at the center. 2. largest on the surface. 3. largest somewhere between center and surface. 4. constant throughout the volume. Answer: 4. By definition, the electric field inside a conductor is zero.The electric field is the gradient of the electrostatic potential. Thus, the electrostatic potential inside a conductor must be constant and, by continuity, must be equal to its value on the surface.

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**3. They have the same potential.**

Consider two isolated spherical conductors each having net charge Q. The spheres have radii a and b, where b > a. Which sphere has the higher potential? 1. the sphere of radius a 2. the sphere of radius b 3. They have the same potential. Answer: 1. The electrostatic potential for a conducting sphere varies inversely as the sphere radius.

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