The chocolate crumb mystery. This story

Figure 25-18 shows plots of charge versus potential difference for three parallel-plate capacitors that have the plate areas and separations given in the table. Which plot goes with which capacitor?

What is Ceq of three capacitors, each of capacitance C, if they are connected to a battery (a) in series with one another and (b) in parallel? (c) In which arrangement is there more charge on the equivalent capacitance?

(a) In Fig. 25-19a, are capacitors 1 and 3 in series? (b) In the same figure, are capacitors 1 and 2 in parallel? (c) Rank the equivalent capacitances of the four circuits shown in Fig. 25-19, greatest first.

Figure 25-20 shows three circuits, each consisting of a switch and two capacitors, initially charged as indicated (top plate positive). After the switches have been closed, in which circuit (if any) will the charge on the left -hand capacitor (a) increase, (b) decrease, and (c) remain the same?

Initially, a single capacitance C1 is wired to a battery. Then capacitance C2 is added in parallel. Are (a) the potential difference across C1 and (b) the charge ql on C1 now more than, less than, or the same as previously? (c) Is the equivalent capacitance Cl2 of C1 and C2 more than, less than, or equal to Cj ? (d) Is the charge stored on C1 and C2 together more than, less than, or equal to the charge stored previously on C1?

Repeat Question 5 for C2 added in series rather than in parallel.

For each circuit in Fig. 25-21, are the capacitors connected in series, in parallel, or in neither mode?

Figure 25-22 shows an open switch, a battery of potential difference V, a current-measuring meter A, and three identical uncharged capacitors of capacitance C. When the switch is closed and the circuit reaches equilibrium, what are (a) Fig.25-22 Question 8. the potential difference across each capacitor and (b) the charge on the left plate of each capacitor? (c) During charging, what net charge passes through the meter?

A parallel-plate capacitor is connected to a battery of electric potential difference V. If the plate separation is decreased, do the following quantities increase, decrease, or remain the same: (a) the capacitor's capacitance, (b) the potential difference across the capacitor, (c) the charge on the capacitor, (d) the energy stored by the capacitor, (e) the magnitude of the electric field between the plates, and (f) the energy density of that electric field?

When a dielectric slab is inserted between the plates of one of the two identical capacitors in Fig. 25-23, do the following properties of that capacitor increase, decrease, or remain the same: (a) capacitance, (b) charge, (c) potential difference, and (d) potential energy? (e) How about the same properties of the other capacitor?

You are to connect capacitances C1 and C2, with Cj > C2, to a battery, first individually, then in series, and then in parallel. Rank those arrangements according to the amount of charge stored, greatest first.

Two parallel-plate capacitors, 6.0 ,uF each, are connected in parallel to a 10 V battery. One of Fig. 25-29 Problems 11, the capacitors is then squeezed so that its plate separation is 50.0% of 17, and 38. its initial value. Because of the squeezing, (a) how much additional charge is transferred to the capacitors by the battery and (b) what is the increase in the total charge stored on the capacitors?

A 100 pF capacitor is charged to a potential difference of 50 V, and the charging battery is disconnected. The capacitor is then connected in parallel with a second (initially uncharged) capacitor. If the potential difference across the first capacitor drops to 35 V, what is the capacitance of this second capacitor?

In Fig. 25-30, the battery has a potential difference of V = 10.0 V and the five capacitors each have a capacitance of 10.0 ,uFo What is the charge on (a) capacitor 1 and (b) ca- Fig. 25-30 Problem 14. pacitor2?

In Fig. 25-31, a 20.0 V battery is connected across capacitors of capacitances Cj = C6 = 3.00,uF and C3 = Cs = 2.00C2 = 2.00C4 = 4.00,uF. What are (a) the equivalent capacitance Ceq of the capacitors and (b) the charge stored by Ceq? What PROBLEMS 677 are (c) Vj and (d) qj of capacitor 1, (e) V2 and (f) q2 of capacitor 2, and (g) V3 and (h) q3 of capacitor 3?

Plot 1 in Fig. 25-32a gives the charge q that can be stored on capacitor 1 versus the electric potential V set up across it. The vertical scale is set by qs = 16.0 ,uC, and the horizontal scale is set by Vs = 2.0 V. Plots 2 and 3 are similar plots for capacitors 2 and 3, respectively. Figure 25-32b shows a circuit with those three capacitors and a 6.0 V battery. What is the charge stored on capacitor 2 in that circuit?

In Fig. 25-29, a potential difference of V = 100.0 V is applied across a capacitor arrangement with capacitances Cj = 10.0 ,uF, C2 = 5.00 ,uF, and C3 = 4.00,uF. If capacitor 3 undergoes electrical breakdown so that it becomes equivalent to conducting wire, what is the increase in (a) the charge on capacitor 1 and (b) the potential difference across capacitor 1 ?

Figure 25-33 shows a circuit section of four air-filled capacitors that is connected to a larger circuit. The graph below the section shows the electric potential V(x) as a function of position x along the lower part of the section, through capacitor 4. Similarly, the graph above the section shows the electric potential V(x) as a function of position x along the upper part of the section, through capacitors 1, 2, and 3. Capacitor 3 has a capacitance of 0.80 JLF. What are the capacitances of (a) capacitor 1 and (b) capacitor 2?

In Fig. 25-34, the battery has potential difference V = 9.0 V, C2 = 3.0 JLF, C4 = 4.0 JLF, and all the capacitors are initially uncharged. When switch S is closed, a total charge of 12 JLC passes through point a and a total charge of 8.0 JLC passes through point b. What are (a) CI and (b) C3?

Figure 25-35 shows a variable "air gap" capacitor for manual tuning. Alternate plates are connected together; one group of plates is fixed in position, and the other group is capable of rotation. Consider a capacitor of n = 8 plates of alternating polarity, each plate having area A = 1.25 cm2 and Fig. 25-35 Problem 20. separated from adjacent plates by distance d = 3.40 mm. What is the maximum capacitance of the device?

In Fig. 25-36, the capacitances are CI = 1.0 JLF and C2 = 3.0 JLF, and both capacitors are charged to a potential difference of V = 100 V but with opposite polarity as shown. Switches SI and S2 are now closed. (a) What is now the potential difference between points a and b? What now is the charge on Fig. 25-36 Problem 21. capacitor (b) 1 and (c) 2?

In Fig. 25-37, V = 10 V, CI = 10 JLF, and C2 = C3 = 20 JLF. Switch S is first thrown to the left side until capacitor 1 reaches equilibrium. Then the switch is thrown to the right. When equilibrium is again reached, how much charge is on capacitor I?

The capacitors in Fig. 25-38 are initially uncharged. The capacitances are CI = 4.0 JLF, C2 = 8.0 JLF, and C3 = 12 JLF, and the battery's potential difference is V = 12 V. When switch S Fig. 25-37 Problem 22. is closed, how many electrons travel through (a) point a, (b) point b, (c) Fig.25-38 Problem 23. point c, and (d) point d? In the figure, do the electrons travel up or down through (e) point b and (f) point c?

Figure 25-39 represents two air-filled cylindrical capacitors connected in series across a battery with potential V = 10 V. Capacitor 1 has an inner plate radius of 5.0 mm, an outer plate radius of 1.5 cm, and a length of 5.0 cm. Capacitor 2 has an inner plate radius of 2.5 mm, an outer plate radius of 1.0 cm, 1 ; .~J and a length of 9.0 cm. The outer plate of ca- .' .. ... '.1.,'.'. CI pacitor 2 is a conducting organic membrane V T that can be stretched, and the capacitor can _ ~'J:: C2 be inflated to increase the plate separation. I....-___ ..J If the outer plate radius is increased to 2.5 cm by inflation, (a) how many electrons move through point P and (b) do they move toward or away from the battery?

In Fig. 25-40, two parallel-plate capacitors (with air between the plates) are connected to a battery. Capacitor 1 has a plate area of 1.5 cm2 and an electric field (between its plates) of magnitude 2000 Vim. Capacitor 2 has a plate area of 0.70 cm2 and 1 T Fig. 25-39 Problem 24. C 1,,1" J" Fig. 25-40 Problem 25. an electric field of magnitude 1500 Vim. What is the total charge on the two capacitors?

Capacitor 3 in Fig. 25-41a is a variable capacitor (its capacitance C3 can be varied). Figure 25-41b gives the electric potential VI across capacitor 1 versus C3 The horizontal scale is set by C3s = 12.0 JLF. Electric potential VI approaches an asymptote of 10 V as C3 ----> 00. What are (a) the electric potential V across the battery, (b) Cj,and (c) C2?

Figure 25-42 shows a 12.0 V battery and four uncharged capacitors of capacitances CI = 1.00 JLF, C2 = 2.00 JLF, C3 = 3.00 JLF, and C4 = 4.00 JLF. If only switch S] is closed, what is the charge on (a) capacitor 1, (b) capacitor 2, ( c) capacitor 3, and (d) capacitor 4? If both switches are closed, what is the charge on (e) capacitor 1, (f) capacitor 2, (g) capacitor 3, and (h) capacitor 4?

Figure 25-43 displays a 12.0 V battery and 3 uncharged capacitors of capacitances C1 = 4.00 JLF, C2 = 6.00 JLF, and C3 = 3.00 JLF. The switch is thrown to the left side until capacitor 1 is fully charged. Then B Fig. 25-42 Problem 27. Fig 25 43 Problem 28. the switch is thrown to the right. .- What is the final charge on (a) capacitor 1, (b) capacitor 2, and (c) capacitor3?

What capacitance is required to store an energy of 10 kW h at a potential difference of 1000 V?

How much energy is stored in 1.00 m3 of air due to the "fair weather" electric field of magnitude 150 Vim?

A 2.0 p,F capacitor and a 4.0 p,F capacitor are connected in parallel across a 300 V potential difference. Calculate the total energy stored in the capacitors

A parallel-plate air-filled capacitor having area 40 cm2 and plate spacing 1.0 mm is charged to a potential difference of 600 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.

A charged isolated metal sphere of diameter 10 cm has a potential of 8000 V relative to V = 0 at infinity. Calculate the energy density in the electric field near the surface of the sphere.

In Fig. 25-28, a potential difference V = 100 V is applied across a capacitor arrangement with capacitances C, = 10.0 p,F, C2 = 5.00 p,F, and C3 = 4.00 p,F. What are (a) charge q3, (b) potential difference V3, and (c) stored energy V3 for capacitor 3, (d) q" (e) V" and (f) V, for capacitor 1, and (g) qb (h) Vb and (i) V2 for capacitor 2?

Assume that a stationary electron is a point of charge. What is the energy density it of its electric field at radial distances (a) r = 1.00 mm, (b) r = 1.00 p,m, (c) r = 1.00 nm, and (d) r = 1.00 pm? (e) What is II in the limit as r ~ O?

As a safety engineer, you must evaluate the practice of storing flammable conducting liquids in nonconducting containers. The company supplying a certain liquid has been using a squat, cylindri- Venting port ---- -+ - - - - + + + + + ++ cal plastic container of radius r = Fig. 25-44 Problem 36. 0.20 m and filling it to height h = 10 cm, which is not the container's full interior height (Fig. 25-44). Your investigation reveals that during handling at the company, the exterior surface of the container commonly acquires a negative charge density of magnitude 2.0 p,C/m2 (approximately uniform). Because the liquid is a conducting material, the charge on the container induces charge separation within the liquid. (a) How much negative charge is induced in the center of the liquid's bulk? (b) Assume the capacitance of the central portion of the liquid relative to ground is 35 pF. What is the potential energy associated with the negative charge in that effective capacitor? (c) If a spark occurs between the ground and the central portion of the liquid (through the venting port), the potential energy can be fed into the spark. The minimum spark energy needed to ignite the liquid is 10 mJ. In this situation, can a spark ignite the liquid?

The parallel plates in a capacitor, with a plate area of 8.50 cm2 and an air-filled separation of 3.00 mm, are charged by a 6.00 V battery. They are then disconnected from the battery and pulled apart (without discharge) to a separation of 8.00 mm. Neglecting fringing, find (a) the potential difference between the plates, (b) the initial stored energy, (c) the final stored energy, and (d) the work required to separate the plates.

In Fig. 25-29, a potential difference V = 100 V is applied across a capacitor arrangement with capacitances C, = 10.0 p,F, PROS LEMS 679 C2 = 5.00 p,F, and C3 = 15.0 p,F. What are (a) charge q3, (b) potential difference V3, and (c) stored energy V3 for capacitor 3, (d) q" (e) V" and (f) V, for capacitor 1, and (g) q2, (h) V2, and (i) V2 for capacitor 2?

In Fig. 25-45, C, = 10.0 p,F, C2 = 20.0 p,F, and C3 = 25.0 p,F. If no capacitor can with- ----1! ! ! I I stand a potential difference of A~ 1---1 1---1 :---.B more than 100 V without fail- C, C2 C3 ure, what are (a) the magnitude Fig.25-45 Problem 39. of the maximum potential difference that can exist between points A and Band (b) the maximum energy that can be stored in the three-capacitor arrangement?

An air-filled parallel-plate capacitor has a capacitance of 1.3 pF. The separation of the plates is doubled, and wax is inserted between them. The new capacitance is 2.6 pF. Find the dielectric constant of the wax.

A coaxial cable used in a transmission line has an inner radius of 0.10 mm and an outer radius of 0.60 mm. Calculate the capacitance per meter for the cable. Assume that the space between the conductors is filled with polystyrene.

A parallel-plate air-filled capacitor has a capacitance of 50 pF. (a) If each of its plates has an area of 0.35 m2, what is the separation? (b) If the region between the plates is now filled with material having K = 5.6, what is the capacitance?

Given a 7.4 pF air-filled capacitor, you are asked to convert it to a capacitor that can store up to 7.4 p,J with a maximum potential difference of 652 V. Which dielectric in Table 25-1 should you use to fill the gap in the capacitor if you do not allow for a margin of error?

You are asked to construct a capacitor having a capacitance near 1 nF and a breakdown potential in excess of 10 000 V. You think of using the sides of a tall Pyrex drinking glass as a dielectric, lining the inside and outside curved surfaces with aluminum foil to act as the plates. The glass is 15 cm tall with an inner radius of 3.6 cm and an outer radius of 3.8 cm. What are the (a) capacitance and (b) breakdown potential of this capacitor?

A certain parallel-plate capacitor is filled with a dielectric for which I( = 5.5. The area of each plate is 0.034 m2, and the plates are separated by 2.0 mm. The capacitor will fail (short out and burn up) if the electric field between the plates exceeds 200 kN/C. What is the maximum energy that can be stored in the capacitor?

In Fig. 25-46, how much charge is stored on the parallel-plate capacitors by the 12.0 V battery? One is filled with air, and the other is filled with a dielectric for which I( = 3.00; both capacitors have a plate area of 5.00 X 10-3 m2 and a plate separation of 2.00 mm.

A certain substance has a dielectric constant of 2.8 and a dielectric strength of 18 MV/m. If it is used as the dielectric material in a parallel-plate capacitor, what minimum area should the plates of the capacitor have to obtain a capacitance of 7.0 X 10-2 p,F and to ensure that the capacitor will be able to withstand a potential difference of 4.0 k V?

Figure 25-47 shows a parallel-plate capacitor with a plate area A = 5.56 cm2 and separation d = 5.56 mm. The left half of the gap is filled with material of dielectric constant Kj = 7.00; the right half is filled with material of dielectric constant K2 = 12.0. What is the capacitance?

Figure 25-48 shows a parallel-plate capacitor with a plate area A = 7.89 cm2 and plate separation d = 4.62 mm. The top half of the gap is filled with material of dielectric constant Kj = 11.0; the bottom half is filled with material of dielectric constant K2 = 12.0. What is the capacitance?

Figure 25-49 shows a parallel-plate capacitor of plate area A = 10.5 cm2 and plate separation 2d = 7.12 mm. The left half of the gap is filled with material of dielectric constant Kj = 21.0; the top of the right half is filled with material of dielectric constant K2 = 42.0; the Fig. 25-48 Problem 49. d bottom of the right half is filled with Fig. 25-49 Problem 50. material of dielectric constant K3 = 58.0. What is the capacitance?

A parallel-plate capacitor has a capacitance of 100 pF, a plate area of 100 cm2, and a mica dielectric (K = 5.4) completely filling the space between the plates. At 50 V potential difference, calculate (a) the electric field magnitude E in the mica, (b) the magnitude of the free charge on the plates, and (c) the magnitude of the induced surface charge on the mica.

For the arrangement of Fig. 25-17, suppose that the battery remains connected while the dielectric slab is being introduced. Calculate (a) the capacitance, (b) the charge on the capacitor plates, (c) the electric field in the gap, and (d) the electric field in the slab, after the slab is in place.

A parallel-plate capacitor has plates of area 0.12 m2 and a separation of 1.2 cm. A battery charges the plates to a potential difference of 120 V and is then disconnected. A dielectric slab of thickness 4.0 mm and dielectric constant 4.8 is then placed symmetrically between the plates. (a) What is the capacitance before the slab is inserted? (b) What is the capacitance with the slab in place? What is the free charge q (c) before and (d) after the slab is inserted? What is the magnitude of the electric field (e) in the space between the plates and dielectric and (f) in the dielectric itself? (g) With the slab in place, what is the potential difference across the plates? (h) How much external work is involved in inserting the slab?

Two parallel plates of area 100 cm2 are given charges of equal magnitudes 8.9 X 10-7 C but opposite signs. The electric field within the dielectric material filling the space between the plates is 1.4 X 106 Vim. (a) Calculate the dielectric constant of the material. (b) Determine the magnitude of the charge induced on each dielectric surface.

The space between two concentric conducting spherical shells of radii b = 1.70 cm and a = 1.20 cm is filled with a substance of dielectric constant K = 23.5. A potential difference V = 73.0 V is applied across the inner and outer shells. Determine (a) the capacitance of the device, (b) the free charge q on the inner shell, and (c) the charge q' induced along the surface of the inner shell.

In Fig. 25-50, the battery potential difference V is 10.0 V and each of the seven capacitors has capacitance 10.0 JLF. What is the charge on (a) capacitor 1 and (b) capacitor 2?

In Fig. 25-51, V = 9.0 V, C1 = C2 = 30 JLF, and C3 = C4 = 15 JLF. What is the charge on capacitor 4?

The capacitances of the four capacitors shown in Fig. 25-52 are given in terms of a certain quantity C. (a) If C = 50 JLF, what is the equivalent capacitance between points A and B? (Hint: ki] ~ '.::C, - + "'N,' V Fig. 25-50 Problem 56. Fig. 25-51 Problem 57. First imagine that a battery is connected between those two points; then reduce the circuit to an equivalent capacitance.) (b) Repeat for points A and D.

In Fig. 25-53, V = 12 V, C1 = C4 = 2.0 JLF, C2 = 4.0 JLF, and C3 = 1.0 JLF. What is the charge on capacitor 4?

The chocolate crumb mystery. This story begins with Problem 60 in Chapter 23. As part of the investigation of the biscuit factory explosion, the electric potentials of the workers were measured as they emptied sacks of chocolate crumb powder into the loading bin, stirring up a cloud of the powFig. 25-53 Problem 59. der around themselves. Each worker had an electric potential of about 7.0 kV relative to the ground, which was taken as zero potential. (a) Assuming that each worker was effectively a capacitor with a typical capacitance of 200 pF, find the energy stored in that effective capacitor. If a single spark between the worker and any conducting object connected to the ground neutralized the worker, that energy would be transferred to the spark. According to measurements, a spark that could ignite a cloud of chocolate crumb powder, and thus set off an explosion, had to have an energy of at least 150 mJ. (b) Could a spark from a worker have set off an explosion in the cloud of powder in the loading bin? (The story continues with Problem 60 in Chapter 26.)

Figure 25-54 shows capacitor 1 (Cj = 8.00 JLF), capacitor 2 (C2 = 6.00 JLF), and capacitor 3 (C3 = 8.00 JLF) connected to a 12.0 V battery. When switch S is closed so as to connect uncharged capacitor 4 (C4 = 6.00 ttF), (a) how much charge passes through point P from the battery and (b) how much charge shows up on capacitor 4? (c) Explain the discrepancy in those two results.

Tho air-filled, parallel-plate capacitors are to be connected to a 10 V battery, first individually, then in series, and then in parallel. In those arrangements, the energy stored in the capacitors turns out to be, listed least to greatest: 75 p.J, 100 p.J, 300 p.J, and 400 p.J. Of the two capacitors, what is the (a) smaller and (b) greater capacitance?

Tho parallel-plate capacitors, 6.0 ttF each, are connected in series to a 10 V battery. One of the capacitors is then squeezed so that its plate separation is halved. Because of the squeezing, (a) how much additional charge is transferred to the capacitors by the battery and (b) what is the increase in the total charge stored on the capacitors (the charge on the positive plate of one capacitor plus the charge on the positive plate of the other capacitor)?

In Fig. 25-55, V = 12 V, C, = Cs = C6 = 6.0 ttF, and Cz = C3 = C4 = 4.0 ttF. What are (a) the net charge stored on the capacitors and (b) the charge on capacitor 4?

In Fig. 25-56, the parallel- Fig. 25-55 Problem 64. plate capacitor of plate area 2.00 X lO-z mZ is filled with two dielectric slabs, 1 each with thickness 2.00 mm. One slab has dielectric constant 3.00, and the other, T V 4.00. How much charge does the 7.00 V battery store on the capacitor?

A cylindrical capacitor has radii a and b as in Fig. 25-6. Show that half the stored electric potential energy lies within a cylinder whose radius is r = YfiE.

A capacitor of capacitance C, = 6.00 ttF is connected in series with a capacitor of capacitance Cz = 4.00 ttF, and a potential difference of 200 V is applied across the pair. (a) Calculate the equivalent capacitance. What are (b) charge q, and (c) potential difference V, on capacitor 1 and (d) qz and (e) Vz on capacitor 2?

Repeat Problem 67 for the same two capacitors but with them now connected in parallel.

A certain capacitor is charged to a potential difference V. If you wish to increase its stored energy by 10%, by what percentage should you increase V?

A slab of copper of thickness b = 2.00 mm is thrust into a parallel-plate capacitor of plate area A = 2.40 cm2 and plate separation d = 5.00 mm, as shown in Fig. 25-57; the slab is exactly halfway between the plates. (a) What is the capacitance after the slab is introduced? (b) If a charge q = 3.40 ttC is maintained on the plates, what is 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? (d) Is the slab sucked in or must it be pushed in?

Repeat Problem 70, assuming that a potential difference V = 85.0 V, rather than the charge, is held constant.

A potential difference of 300 V is applied to a series connection of two capacitors of capacitances C, = 2.00 ttF and C2 = 8.00 ttF. What are (a) charge q, and (b) potential difference V, on capacitor 1 and (c) qz and (d) Vz on capacitor 2? The charged capacitors are then disconnected from each other and from the battery. Then the capacitors are reconnected with plates of the same signs wired together (the battery is not used). What now are (e) q" (f) V" (g) qz, and (h) V2? Suppose, instead, the capacitors charged in part (a) are reconnected with plates of opposite signs wired together. What now are (i) q" (D V" (k) qz, and (1) V2?

Figure 25-58 shows a four-capacitor arrangement that is connected to a larger circuit at points A and B. The capacitances are C, = 10 ttF and C2 = C3 = C4 = 20 ttF. The charge on capacitor 1 is 30 ttc. What is the magnitude of the potential difference VA - VB?

You have two plates of copper, a sheet of mica (thickness = 0.10 mm, K = 5.4), a sheet of glass (thickness = 2.0 mm, K = 7.0), and a slab of paraffin (thickness = 1.0 cm, K = 2.0). To make a parallel-plate capacitor with the largest C, which sheet should you place between the copper plates?

A capacitor of unknown capacitance C is charged to 100 V and connected across an initially uncharged 60 ttF capacitor. If the final potential difference across the 60 ttF capacitor is 40 V, what is C?

A 10 V battery is connected to a series of n capacitors, each of capacitance 2.0 ttF. If the total stored energy is 25 p.J, what is n?

a~~:;~5-;:d t~o ~r~a~~~~ ~,J,,__ cJ~_~ 1 nected in parallel across a 600 V bat- 'Bl'---' '-~I :1' Ttery. Each plate has area 80.0 cmz; . IL-. ___ ....I.L.-__ ---J_ the plate separations are 3.00 mm. Fig.25-59 Problem 77. Capacitor A is filled with air; capacitor B is filled with a dielectric of dielectric constant I( = 2.60. Find the magnitude of the electric field within (a) the dielectric of capacitor Band (b) the air of capacitor A. What are the free charge densities (1" on the higher-potential plate of (c) capacitor A and (d) capacitor B? (e) What is the induced charge density (1"' on the top surface of the dielectric?

You have many 2.0 ttF capacitors, each capable of withstanding 200 V without undergoing electrical breakdown (in which they conduct charge instead of storing it). How would you assemble a combination having an equivalent capacitance of (a) 0.40 ttF and (b) 1.2 ttF, each combination capable of withstanding 1000 V?