University Physics Volume 2

# Chapter 8

8.1

$1.1 × 10 −3 m 1.1 × 10 −3 m$

8.3

3.59 cm, 17.98 cm

8.4

a. 25.0 pF; b. 9.2

8.5

a. $C=0.86pF,Q1=10pC,Q2=3.4pC,Q3=6.8pCC=0.86pF,Q1=10pC,Q2=3.4pC,Q3=6.8pC$;
b. $C=2.3pF,Q1=12pC,Q2=Q3=16pCC=2.3pF,Q1=12pC,Q2=Q3=16pC$;
c. $C=2.3pF,Q1=9.0pC,Q2=18pC,Q3=12pC,Q4=15pCC=2.3pF,Q1=9.0pC,Q2=18pC,Q3=12pC,Q4=15pC$

8.6

a.$4.0×10−13J4.0×10−13J$; b. 9 times

8.7

a. 3.0; b. $C=3.0C0C=3.0C0$

8.9

a. $C0=20pFC0=20pF$, $C=42pFC=42pF$; b. $Q0=0.8nCQ0=0.8nC$, $Q=1.7nCQ=1.7nC$; c. $V0=V=40VV0=V=40V$; d. $U0=16nJU0=16nJ$, $U=34nJU=34nJ$

## Conceptual Questions

1.

no; yes

3.

false

5.

no

7.

$3.0 μ F , 0.33 μ F 3.0 μ F , 0.33 μ F$

9.

11.

Dielectric strength is a critical value of an electrical field above which an insulator starts to conduct; a dielectric constant is the ratio of the electrical field in vacuum to the net electrical field in a material.

13.

Water is a good solvent.

15.

When energy of thermal motion is large (high temperature), an electrical field must be large too in order to keep electric dipoles aligned with it.

17.

## Problems

19.

21.6 mC

21.

1.55 V

23.

25.0 nF

25.

$1.1 × 10 −3 m 2 1.1 × 10 −3 m 2$

27.

500 µC

29.

1:16

31.

a. 1.07 nC; b. 267 V, 133 V

33.

$0.29 μ F 0.29 μ F$

34.

500 capacitors; connected in parallel

35.

$3.08μF3.08μF$ (series) and $13.0μF13.0μF$ (parallel)

37.

$11.4 μ F 11.4 μ F$

39.

0.89 mC; 1.78 mC; 444 V

41.

$7.5 μ J 7.5 μ J$

43.

a. 405 J; b. 90.0 mC

45.

1.17 J

47.

a. $4.43×10−9F4.43×10−9F$; b. 0.453 V; c. $4.53×10−10J4.53×10−10J$; d. no

49.

0.7 mJ

51.

a. 7.1 pF; b. 42 pF

53.

a. before 3.00 V; after 0.600 V; b. before 1500 V/m; after 300 V/m

55.

a. 3.91; b. 22.8 V

57.

a. 37 nC; b. 0.4 MV/m; c. 19 nC

59.

a. $4.4μF4.4μF$; b. $4.0×10-5C4.0×10-5C$

61.

$0.0135 m 2 0.0135 m 2$

63.

$0.185 μ J 0.185 μ J$

65.

a. 0.277 nF; b. 27.7 nC; c. 50 kV/m

67.

a. 0.065 F; b. 23,000 C; c. 4.0 GJ

69.

a. $75.6μC75.6μC$; b. 10.8 V

71.

a. 0.13 J; b. no, because of resistive heating in connecting wires that is always present, but the circuit schematic does not indicate resistors

73.

a. $−3.00μF−3.00μF$; b. You cannot have a negative $C2C2$ capacitance. c. The assumption that they were hooked up in parallel, rather than in series, is incorrect. A parallel connection always produces a greater capacitance, while here a smaller capacitance was assumed. This could only happen if the capacitors are connected in series.

75.

a. 14.2 kV; b. The voltage is unreasonably large, more than 100 times the breakdown voltage of nylon. c. The assumed charge is unreasonably large and cannot be stored in a capacitor of these dimensions.

## Challenge Problems

77.

a. 89.6 pF; b. 6.09 kV/m; c. 4.47 kV/m; d. no

79.

a. 421 J; b. 53.9 mF

81.

$C=ε0A/(d1+d2)C=ε0A/(d1+d2)$

83.

proof