1. Figure 23.1 (a) A negatively charged rubber rod suspended by a thread is attracted
to a positively charged glass rod. (b) A negatively charged rubber rod is repelled by
another negatively charged rubber rod.

2. Figure 23.4 Charging a metallic object by induction (that is, the two objects never touch each other). (a) A neutral metallic sphere, with equal numbers of positive and negative charges. (b) The electrons on the neutral sphere are redistributed when a charged rubber rod is placed near the sphere. (c) When the sphere is grounded, some of its electrons leave through the ground wire. (d) When the ground connection is removed, the sphere has excess positive charge that is nonuniformly distributed. (e) When the rod is removed, the remaining electrons redistribute uniformly and there is a net uniform distribution of positive charge on the sphere.

3. Figure 23.5 (a) The charged object on the left induces a charge distribution on the surface of an insulator due to realignment of charges in the molecules.

5. Figure 23.7 Two point charges separated by a distance r exert a force on each other that is given by Coulomb’s law. The force F21 exerted by q2 on q1 is equal in magnitude and opposite in direction to the force F12 exerted by q1 on q2. (a) When the charges are of the same sign, the force is repulsive. (b) When the charges are of opposite signs, the force is attractive.

6. Figure 23. 8 (Example 23. 2) The force exerted by q1 on q3 is F13
Figure 23.8 (Example 23.2) The force exerted by q1 on q3 is F13. The force exerted by q2 on q3 is F23. The resultant force F3 exerted on q3 is the vector sum F13 F23.

7. Figure 23.9 (Example 23.3) Three point charges are placed along the x axis. If the resultant force acting on q3 is zero, then the force F13 exerted by q1 on q3 must be equal in magnitude and opposite in direction to the force F23 exerted by q2 on q3.

8. Figure (Example 23.4) (a) Two identical spheres, each carrying the same charge q, suspended in equilibrium. (b) The
free-body diagram for the sphere on the left.

9. Figure A small positive test charge q0 placed near an object carrying a much larger positive charge Q experiences an electric field E directed as shown.

11. Figure (Example 23.5) The total electric field E at P equals the vector sum E1 + E2, where E1 is the field due to the positive charge q 1 and E2 is the field due to the negative charge q2.

12. Figure The electric field at P due to a continuous charge distribution is the vector sum of the fields E due to all the elements q of he charge distribution.

13. Figure (Example 23.7) The electric field at P due to a uniformly charged rod lying along the x axis. The magnitude of the field at P due to the segment of charge dq is kedq/x 2 . The total field at P is the vector sum over all segments of the rod.

14. Figure 23. 18 (Example 23. 8) A uniformly charged ring of radius a
Figure (Example 23.8) A uniformly charged ring of radius a. (a) The field at P on the x axis due to an element of charge dq. (b) The total electric field at P is along the x axis. The perpendicular component of the field at P due to segment 1 is canceled by the perpendicular component due to segment 2.

15. Figure 23. 19 (Example 23. 9) A uniformly charged disk of radius R
Figure (Example 23.9) A uniformly charged disk of radius R. The electric field at an axial point P is directed along the central axis, perpendicular to the plane of the disk.

16. Figure 23. 21 The electric field lines for a point charge
Figure The electric field lines for a point charge. (a) For a positive point charge, the lines are directed radially outward. (b) For a negative point charge, the lines are directed radially inward. Note that the figures show only those field lines that lie in the
plane of the page. (c) The dark areas are small pieces of thread suspended in oil, which align with the electric field produced by a small charged conductor at the center.

17. Figure 23. 21 The electric field lines for a point charge
Figure The electric field lines for a point charge. (c) The dark areas are small pieces of thread suspended in oil, which align with the electric field produced by a small charged conductor at the center.

18. Figure (a) The electric field lines for two point charges of equal magnitude and opposite sign (an electric dipole). The number of lines leaving the positive charge equals the number terminating at the negative charge. (b) The dark lines are small
pieces of thread suspended in oil, which align with the electric field of a dipole.

19. Figure (b) The dark lines are small pieces of thread suspended in oil, which align with the electric field of a dipole.

20. Figure (a) The electric field lines for two positive point charges. (The locations A, B, and C are discussed in Quick Quiz 23.7.)

21. Figure (b) Pieces of thread suspended in oil, which align with the electric field created by two equal-magnitude positive charges. Courtesy of Harold M. Waage, Princeton University

22. Figure (Example 23.10) A positive point charge q in a uniform electric field E undergoes constant acceleration in the direction of the field.

23. E
(x, y)
Figure An electron is projected horizontally into a uniform electric field produced by two charged plates. The electron undergoes a downward acceleration (opposite E), and its motion is parabolic while it is between the plates.

24. Figure 24.1 Field lines representing a uniform electric field penetrating a plane of area A perpendicular to the field. The electric flux E hrough this area is equal to EA.

25. Figure 24.2 Field lines representing a uniform electric field penetrating an area A’ that is at an angle  to the field. Because the number of lines that go through the area A is the same as the number that go through A, the flux through A is equal to the flux through A and is given by E= EAcos .

26. Figure 24. 3 A small element of surface area Ai
Figure 24.3 A small element of surface area Ai. The electric field makes an angle i with he vector Ai, defined as being normal to the surface element, and the flux through the element is equal to Ei Ai cos i .

27. Figure 24.5 (Example 24.2) A closed surface in the shape of a cube in a uniform electric field oriented parallel to the x axis. Side 4 is the bottom of the cube, and side 1 is opposite side 2.

28. and from Equation 24.4 we find that the net flux through the gaussian surface is
E EdA E dA E dA
Figure 24.6 A spherical gaussian surface of radius r surrounding a point charge q. When the charge is at the center of the sphere, the electric field is everywhere normal to the surface and constant in magnitude.

29. Figure 24. 7 Closed surfaces of various shapes surrounding a charge q
Figure 24.7 Closed surfaces of various shapes surrounding a charge q. The net electric flux is the same through all surfaces.

30. Figure 24. 8 A point charge located outside a closed surface
Figure 24.8 A point charge located outside a closed surface. The number of lines entering the surface equals the number leaving the surface.

31. Figure 24. 16 A conducting slab in an external electric field E
Figure A conducting slab in an external electric field E. The charges induced on the two surfaces of the slab produce an electric field that opposes the external field, giving a resultant field of zero inside the slab.

32. Figure 24. 17 A conductor of arbitrary shape
Figure A conductor of arbitrary shape. The broken line represents a gaussian surface just inside the surface of the conductor.

33. Figure A gaussian surface in the shape of a small cylinder is used to calculate the electric field just outside a charged conductor. The flux through the gaussian surface is EA. Remember that E is zero inside the conductor.