1. Figure 25.2 (a) When the electric field E is directed downward, point B is at a lower electric potential than point A. When a positive test charge moves from point A to point B, the charge–field system loses electric potential energy. (b) When an object of mass m moves downward in the direction of the gravitational field g, the object–field system loses gravitational potential energy.

2. Figure 25.3 A uniform electric field directed along the positive x axis. Point B is at a lower electric potential than point A. Points B and C are at the same electric potential.

3. Active Figure (a) If two point charges are separated by a distance r12, the potential energy of the pair of charges is given by keq1q2/r 12 . (b) If charge q1 is removed, a potential keq2/r 12 exists at point P due to charge q 2 .

4. Figure Equipotential surfaces (the dashed blue lines are intersections of these surfaces with the page) and electric field lines (red- rown lines) for (a) a uniform electric field produced by an infinite sheet of charge In all cases,the equipotential surfaces are perpendicular to the electric field lines at every point.

5. Figure Equipotential surfaces (the dashed blue lines are intersections of these surfaces with the page) and electric field lines (red- rown lines) for (b) a point charge In all cases,the equipotential surfaces are perpendicular to the electric field lines at every point.

6. Figure Equipotential surfaces (the dashed blue lines are intersections of these surfaces with the page) and electric field lines (red- rown lines) for (c) an electric dipole. In all cases,the equipotential surfaces are perpendicular to the electric field lines at every point.

7. Figure The electric potential at the point P due to a continuous charge distribution can be calculated by dividing the charge distribution into elements of charge dq and summing the electric potential contributions over all elements.

8. Figure (a) The excess charge on a conducting sphere of radius R is uniformly distributed on its surface. (b) Electric potential versus distance r from the center of the charged conducting sphere. (c) Electric field magnitude versus distance r from the center of the charged conducting sphere.

9. Figure A conductor in electrostatic equilibrium containing a cavity. The electric field in the cavity is zero, regardless of the charge on the conductor.

11. Figure 26. 1 A capacitor consists of two conductors
Figure 26.1 A capacitor consists of two conductors. When the capacitor is charged, the conductors carry charges of equal magnitude and opposite sign.

12. Figure 26.2 A parallel-plate capacitor consists of two parallel con-ducting plates, each of area A, separated by a distance d. When the capacitor is charged by connecting the plates to the terminals of a battery, the plates carry equal amounts of charge. One plate carries positive charge, and the other carries negative charge.

13. Figure 26.3 (a) The electric field between the plates of a parallel-plate capacitor is uniform near the center but nonuniform near the edges.

14. Active Figure 26.4 (a) A circuit consisting of a capacitor, a battery, and a switch. (b) When the switch is closed, the battery establishes an electric field in the wire that causes electrons to move from the left plate into the wire and into the right plate from the wire. As a result, a separation of charge exists on the plates, which represents an increase in electric potential energy of the system of the circuit. This energy in the system has been transformed from chemical energy in the battery.

15. Figure 26. 8 Circuit symbols for capacitors, batteries, and switches
Figure 26.8 Circuit symbols for capacitors, batteries, and switches. Note that capacitors are in blue and batteries and switches are in red.

16. Active Figure 26.9 (a) A parallel combination of two capacitors in an electric circuit in which the potential difference across the battery terminals is V. (b) The circuit diagram for the parallel combination. (c) The equivalent capacitance is Ceq C1=C2.

17. Active Figure 26. 10 (a) A series combination of two capacitors
Active Figure (a) A series combination of two capacitors. The charges on the two capacitors are the same. (b) The circuit diagram for the series combination. (c) The equivalent capacitance can be calculated from the relationship 1 /Ceq =1 /C 1+ 1/ C 2 .

18. Figure A charged capacitor (a) before and (b) after insertion of a dielectric between the plates. The charge on the plates remains unchanged, but the potential difference decreases from V0 to V= V0/k . Thus, the capacitance increases from C0 to C0.

19. Figure A charged capacitor (a) before and (b) after insertion of a dielectric between the plates. The charge on the plates remains unchanged, but the potential difference decreases from V0 to V= V0/k . Thus, the capacitance increases from C0 to C0.

20. Figure A charged capacitor (a) before and (b) after insertion of a dielectric between the plates. The charge on the plates remains unchanged, but the potential difference decreases from V0 to V= V0/k . Thus, the capacitance increases from C0 to C0.

22. Figure 26. 17 Three commercial capacitor designs
Figure Three commercial capacitor designs. (a) A tubular capacitor, whose plates are separated by paper and then rolled into a cylinder. (b) A high-voltage capacitor consisting of many parallel plates separated by insulating oil. (c) An electrolytic capacitor.