Homework #5 203-1-1721 Physics 2 for students of Mechanical Engineering
Part A
*Note that in all questions the symbol p (such as in pC or pF) represents pico=10 -12
.
, the symbol n represents nano=10 -9 , and the symbol represents micro = 10 -6
2. The two metal objects in Fig. 30-21 below have net charges of +73 pC and -73 pC, and this results in a 19.2-V potential difference between them. (a) What is the capacitance of the system? (b) If the charges are changed to +210 pC and -210 pC, what does the capacitance become? (c) What does the potential difference become?
6. Two sheets of aluminum foil have a separation of 1.20 mm, a capacitance of 9.70 pF, and are charged to 13.0 V. (a) Calculate the plate area. (b) The separation is now decreased by 0.10 mm with the charge held constant. Find the new capacitance. (c)
By how much does the potential difference change?
10. In Fig. 30-23 below, find the equivalent capacitance of the combination. Assume that C
1
= 10.3 F, C
2
= 4.80 F, and C
3
= 3.90 F.
13. A 6.0- F capacitor is connected in series with a 4.0- F capacitor; a potential difference of 200 V is applied across the pair. (a) Calculate the equivalent capacitance. (b) What is the charge on each capacitor? (c) What is the potential difference across each capacitor?
23. A parallel-plate, air-filled capacitor having area 42.0 cm 2 and spacing of 1.30 mm is charged to a potential difference of 625 V. Find (a) the capacitance, (b) the magnitude of the charge on each plate, (c) the stored energy, (d) the electric field between the plates, and (e) the energy density between the plates.

29. An air-filled, parallel-plate capacitor has a capacitance of 1.32 pF. The separation of the plates is doubled and wax is inserted between them. The new capacitance is
2.57 pF. Find the dielectric constant of the wax.
37. A slab of copper of thickness b is thrust into a parallel plate capacitor as shown in
Fig. 30-27. (a) What is the capacitance after the slab is inserted? (b) If a charge q is maintained on the plates, find the ratio of the stored energy before to that after the slab is inserted. (c) How much work is done on the slab as it is inserted? Is the slab pulled in or do you need to push it in the gap?
Part B
3. Figure 30-29 below shows two capacitors in series, the rigid center section of length
( b being movable vertically. Show that the equivalent capacitance of the series combination is independent of the position of the center section and is given by C = o
A )/( a b ).
5. In Fig. 30-31 below, capacitors C
1
= 1.16 F and C
2
= 3.22 F are each charged to a potential difference V = 96.6 V but with opposite polarity, so that points a and c are on the side of the respective positive plates of C
1
and C
2
, and points b and d are on the side of the respective negative plates. Swithces S1 and S2 are now closed. (a)
What is the potential difference between points e and f ? (b) What the charge on C
(c) What is the charge on C
2
?
1
?

18. A parallel-plate capacitor is filled with two dielectrics as in Fig. 30-37. Show that the capacitance is given by C = ( o
A /2 d )( e1
+ e2
). Check this formula for all limiting cases of the values of the two dielectric constants e1
and e2
.
19. A parallel plate capacitor is filled with two dielectrics as in Fig. 30-38. Show that the capacitance is given by C = (2 o
A / d )[( e1 e2
)/( e1
+ e2
)]. Check this formula for all limiting cases of the values of the two dielectric constants e1
and e2
.
25. Figure 30-12 below shows a dielectric slab of thickness b and dielectric constant placed between the plates of a parallel plate capacitor of plate area A and separation d . A potential difference V o
is applied with no dielectric present. The battery is then disconnected and the dielectric slab inserted. Assume that A = 100 cm 2 , d = 1.0 cm, b = 0.50 cm, = 7.0, and V o
= 100 V. (a) Calculate the capacitance C o
before the slab is inserted. (b) Calculate the free charge q . (c) Calculate the electric field in the gap between the plate and the dielectric slab. (d) Calculate the electric field in the dielectric slab. (e) Calculate the potential difference between the plates after the dielectric slab is inserted. (f) Calculate the capacitance with the slab inserted. (g) If the dielectric slab filled the entire gap between the plates, what would be the capacitance?

Examples of dielectric constants e
for various materials:

P30-25