Physics Solutions Manual Chapter 40 Tipler
Chapter 21 The Electric Field I: Discrete Charge Distributions Conceptual Problems 1. Objects are composed of atoms which are composed of charged particles (protons and electrons); however, we rarely observe the effects of the electrostatic force. Explain why we do not observe these effects.
Determine the Concept The net charge on large objects is always very close to zero. Hence the most obvious force is the gravitational force. 2. A carbon atom can become a carbon ion if it has one or more of its electrons removed during a process called ionization. What is the net charge on a carbon atom that has had two of its electrons removed? (a) +e, (b) – e, (c) +2e, (d) –2e Determine the Concept If two electrons are removed from a carbon atom, it will have a net positive charge of +2e. (c ) is correct.
3. You do a simple demonstration for your high school physics teacher in which you claim to disprove Coulomb’s law. You first run a rubber comb through your dry hair, then use it to attract tiny neutral pieces of paper on the desk. You then say ″Coulomb’s law states that for there to be electrostatic forces of attraction between two objects, both objects need to be charged. However, the paper was not charged.
So according to Coulomb’s law, there should be no electrostatic forces of attraction between them, yet there clearly was.″ You rest your case. (a) What is wrong with your assumptions? (b) Does attraction between the paper and the comb require that the net charge on the comb be negative?
Determine the Concept (a) Coulomb’s law is only valid for point particles. The paper bits cannot be modeled as point particles because the paper bits become polarized. (b) No, the attraction does not depend on the sign of the charge on the comb. The induced charge on the paper that is closest to the comb is always opposite in sign to of the charge on the comb, and thus the net force on the paper is always attractive.
4. You have a positively charged insulating rod and two metal spheres on insulating stands. Give step-by-step directions of how the rod, without actually touching either sphere, can be used to give one of the spheres (a) a negative charge, and (b) a positive charge. 1997 1998 Chapter 21 Determine the Concept (a) Connect the metal sphere to ground; bring the insulating rod near the metal sphere and disconnect the sphere from ground; then remove the insulating rod. The sphere will be negatively charged. (b) Bring the insulating rod in contact with the metal sphere; some of the positive charge on the rod will be transferred to the metal sphere.
5. (a) Two point particles that have charges of +4q and –3q are separated by distance d. Use field lines to draw a visualization of the electric field in the neighborhood of this system. (b) Draw the field lines at distances much greater than d from the charges. Determine the Concept (a) We can use the rules for drawing electric field lines to draw the electric field lines for this system. Two field lines have been assigned to each charge q.
(b) At distances much greater than the separation distance between the two charges, the system of two charged bodies will ″look like″ a single charge of +q and the field pattern will be that due to a point charge of +q. Eight field lines have been assigned to the single charge. (a) (b) + 4q − 3q +q 6. A metal sphere is positively charged. Is it possible for the sphere to electrically attract another positively charged ball? Explain your answer. Determine the Concept Yes.
Because a metal sphere is a conductor, the proximity of a positively charged ball (not necessarily a conductor), will induce a redistribution of charges on the metal sphere with the surface nearer the positively charged ball becoming negatively charged. Because the negative charges on the metal sphere are closer to the positively charged ball than are the positive charges on the metal sphere, the net force will be attractive. The Electric Field I: Discrete Charge Distributions 7. A simple demonstration of electrostatic attraction can be done simply by dangling a small ball of crumpled aluminum foil on a string and bringing a charged rod near the ball.
The ball initially will be attracted to the rod, but once they touch, the ball will be strongly repelled from it. Explain these observations. 1999 Determine the Concept Assume that the rod has a negative charge. When the charged rod is brought near the aluminum foil, it induces a redistribution of charges with the side nearer the rod becoming positively charged, and so it swings toward the rod. When it touches the rod, some of the negative charge is transferred to the foil, which, as a result, acquires a net negative charge and is now repelled by the rod. 8.
Two positive point charges that are equal in magnitude are fixed in place, one at x = 0.00 m and the other at x = 1.00 m, on the x axis. A third positive point charge is placed at an equilibrium position. (a) Where is this equilibrium position? (b) Is the equilibrium position stable if the third particle is constrained to move parallel with the x axis? (c) What about if it is constrained to move parallel with the y axis? Determine the Concept (a) A third positive charge can be placed midway between the fixed positive charges. This is the only location.
The position identified in (a) is one of stable equilibrium. It is stable in the x-direction because regardless of whether you displace the third positive charge to the right or to the left, the net force acting on it is back toward the midpoint between the two fixed charges. (c) If the third positive charge is displaced in the y direction, the net force acting on it will be away from its equilibrium position.
Hence the position midway between the fixed positive charges is one of unstable equilibrium in the y direction. 9. Two neutral conducting spheres are in contact and are supported on a large wooden table by insulated stands. A positively charged rod is brought up close to the surface of one of the spheres on the side opposite its point of contact with the other sphere. (a) Describe the induced charges on the two conducting spheres, and sketch the charge distributions on them.
(b) The two spheres are separated and then the charged rod is removed. The spheres are then separated far apart.
Sketch the charge distributions on the separated spheres. Determine the Concept Because the spheres are conductors, there are free electrons on them that will reposition themselves when the positively charged rod is brought nearby. 2000 Chapter 21 (a) On the sphere near the positively charged rod, the induced charge is negative and near the rod. On the other sphere, the net charge is positive and on the side far from the rod. This is shown in the diagram. (b) When the spheres are separated and far apart and the rod has been removed, the induced charges are distributed uniformly over each sphere. The charge distributions are shown in the diagram.
+ + + + + − − − − + + + + − + − − + − + + + + − − 10. Three point charges, +q, +Q, and –Q, are placed at the corners of an equilateral triangle as shown in Figure 21-33. No other charged objects are nearby. (a) What is the direction of the net force on charge +q due to the other two charges? (b) What is the total electric force on the system of three charges? Determine the Concept The forces acting on point charge +q are shown in the diagram.
The force acting on point charge +q due to point charge −Q is along the line joining them and directed toward −Q. The force acting on point charge +q due to point charge +Q is along the line joining them and directed away from point charge +Q.
R F+Q +q r F−Q 1 +Q 2 −Q (a) Because point charges +Q and −Q are equal in magnitude, the forces due to these charges are equal and their sum (the net force on charge +q) will be to the right. Note that the vertical components of these forces add up to zero. (b) Because no other charged objects are nearby, the forces acting on this system of three point charges are internal forces and the net force acting on the system is zero.
11. A positively charged particle is free to move in a region with an r electric field E.
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Which statements must be true? (a) r The particle is accelerating in the direction perpendicular to E. The Electric Field I: Discrete Charge Distributions (b) ( c) (d) ( e) (f) r The particle is accelerating in the directionrof E. The particle is moving in the direction of E. The particle could be momentarily at rest.
R The force on the particle is opposite the directionrof E. The particle is moving opposite the direction of E. 2001 Determine the Concept r (a) False. The only force acting on the particle is in the direction of E.
Therelectrical force experienced by the particle is, by definition, in the direction of E. We don’t know whether the particle is moving or momentarily at rest.
R All we know is that the net force acting on it is in the direction of E. (d) Possibly, Whether the particle is ever at rest depends on how it was initially placed in the electric field. On whether its initial velocity was r r That is, it depends zero, in the direction of E, or opposite E. By definition, the electric force acting on a positively charged particle in an electric field is in the direction of the field. All we know for sure is that the electric force and, hence, the r acceleration of the particle, is in the direction of E. The particle could be moving in the direction of the field, in the direction opposite the field, or it could be momentarily at rest.
We do know that, if it is at any time at rest, it will not stay at rest. 12. Four charges are fixed in place at the corners of a square as shown in Figure 21-34. No other charges are nearby.
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Which of the following statements is true? (a) (b) ( c) r E r is zero at the midpoints of all four sides of the square. E r is zero at the center of the square. E is zero midway between the top two charges and midway between the bottom two charges. R Determine the Concept E is zero wherever the net force acting on a test charge is zero.
A test charge placed at these locations will experience a net force. 2002 Chapter 21 (b) True. At the center of the square the two positive charges alone produce a net electric field of zero, and the two negative charges alone also produce a net electric field of zero. Thus, the net force acting on a test charge at the midpoint of the square is zero. A test charge placed at any of these locations will experience a net force. 13. SSM Two point particles that have charges of +q and –3q are separated by distance d.
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(a) Use field lines to sketch the electric field in the neighborhood of this system. (b) Draw the field lines at distances much greater than d from the charges. Determine the Concept (a) We can use the rules for drawing electric field lines to draw the electric field lines for this system. In the field-line sketch we’ve assigned 2 field lines to each charge q. (b) At distances much greater than the separation distance between the two charges, the system of two charged bodies will ″look like″ a single charge of −2q and the field pattern will be that due to a point charge of −2q.
Four field lines have been assigned to each charge −q. (a) (b) − 2q 14. Three equal positive point charges (each charge +q) are fixed at the vertices of an equilateral triangle with sides of length a. The origin is at the midpoint of one side the triangle, the center of the triangle on the x axis at x = x1 and the vertex opposite the origin is on the x axis at x = x2. (a) Express x1 and x2 in terms of a. (b) Write an expression for the electric field on the x axis a distance x from the origin on the interval 0 ≤ x.