Deck 26: Charge Separation and Storage

Question 1

The charge on the square plates of a parallel-plate capacitor is Q.The potential across the plates is maintained with constant voltage by a battery as they are pulled apart to twice their original separation,which is small compared to the dimensions of the plates.The amount of charge on the plates is now equal to

A) 4Q.
B) 2Q.
C) Q.
D) Q/2.
E) Q/4.

Answer 1

Q/2.

Question 2

A metal cylinder of radius 2.0 mm is concentric with another metal cylinder of radius 5.0 mm.If the space between the cylinders is filled with air and the length of the cylinders is 50 cm,what is the capacitance of this arrangement? (k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

A) 33 pF
B) 60 pF
C) 22 pF
D) 30 pF
E) 11 pF

Answer 2

30 pF

Question 3

A cylindrical capacitor is made of two thin-walled concentric cylinders.The inner cylinder has radius r₁ = 4.0 mm,and the outer one a radius r₂ = 8.0 mm.The common length of the cylinders is L = 150 m. What is the potential energy stored in this capacitor when a potential difference 4.0 V is applied between the inner and outer cylinder? (k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

A) 9.6 × 10^-8 J
B) 1.3 × 10^-8 J
C) 6.3 × 10^-8 J
D) 0.34 × 10^-8 J
E) 4.6 × 10^-8 J

Answer 3

9.6 × 10^-8 J

Question 4

An air-filled capacitor is formed from two long conducting cylindrical shells that are coaxial and have radii of 48 mm and 84 mm.The electric potential of the inner conductor with respect to the outer conductor is -400 V.(k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)The energy stored in a 1.0-m length of this capacitor is closest to

A) 8.0 μJ.
B) 5.7 μJ.
C) 11 μJ.
D) 16 μJ.
E) 22 μJ.

Question 5

An ideal air-filled parallel-plate capacitor has round plates and carries a fixed amount of equal but opposite charge on its plates.All the geometric parameters of the capacitor (plate diameter and plate separation)are now DOUBLED.If the original capacitance was C₀,what is the new capacitance?

A) 4C₀
B) 2C₀
C) C₀
D) C₀/2
E) C₀/4

Question 6

A 1.0 m long piece of coaxial cable has a wire with a radius of 1.1 mm and a concentric conductor with inner radius 1.3 mm.The area between the cable and the conductor is filled with a dielectric.If the voltage drop across the capacitor is 6000 V when the line charge density is 8.8 μC/m,find the value of the dielectric constant.(k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

A) 4.4
B) 4.8
C) 5.3
D) 5.7

Question 7

Two thin-walled concentric conducting spheres of radii 5.0 cm and 10 cm have a potential difference of 100 V between them.(k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)
(a)What is the capacitance of this combination?
(b)What is the charge carried by each sphere?

Question 8

The electric field between square the plates of a parallel-plate capacitor has magnitude E.The potential across the plates is maintained with constant voltage by a battery as they are pulled apart to twice their original separation,which is small compared to the dimensions of the plates.The magnitude of the electric field between the plates is now equal to

A) 4E.
B) 2E.
C) E.
D) E/2.
E) E/4.

Question 9

An ideal air-filled parallel-plate capacitor has round plates and carries a fixed amount of equal but opposite charge on its plates.All the geometric parameters of the capacitor (plate diameter and plate separation)are now DOUBLED.If the original energy density between the plates was u₀,what is the new energy density?

A) 16u₀
B) 4u₀
C) u₀
D) u₀/4
E) u₀/16

Question 10

An ideal parallel-plate capacitor consists of a set of two parallel plates of area A separated by a very small distance d.When this capacitor is connected to a battery that maintains a constant potential difference between the plates,the energy stored in the capacitor is U₀.If the separation between the plates is doubled,how much energy is stored in the capacitor?

A) 4U₀
B) 2U₀
C) U₀
D) U₀/2
E) U₀/4

Question 11

Equal but opposite charges Q are placed on the square plates of an air-filled parallel-plate capacitor.The plates are then pulled apart to twice their original separation,which is small compared to the dimensions of the plates.Which of the following statements about this capacitor are true? (There may be more than one correct choice.)

A) The energy stored in the capacitor has doubled.
B) The energy density in the capacitor has increased.
C) The electric field between the plates has increased.
D) The potential difference across the plates has doubled.
E) The capacitance has doubled.

Question 12

A parallel-plate capacitor has plates of area 0.40 m² and plate separation of 0.20 mm.The capacitor is connected across a 9.0-V potential source.(ε₀ = 8.85 × 10^-12 C²/N • m²)
(a)What is the magnitude of the electric field between the plates?
(b)What is the capacitance of the capacitor?
(c)What is the magnitude of the charge on each plate of the capacitor?

Question 13

The capacitance per unit length of a very long coaxial cable,made of two concentric cylinders,is
50 pF/m.What is the radius of the outer cylinder if the radius of the inner one is 1.0 mm?
(k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

A) 3.0 mm
B) 2.0 mm
C) 4.0 mm
D) 1.0 mm
E) 0.50 mm

Question 14

A charged capacitor stores energy U.Without connecting this capacitor to anything,dielectric having dielectric constant K is now inserted between the plates of the capacitor,completely filling the space between them.How much energy does the capacitor now store?

A) 2KU
B) KU
C) U
D)
E)

Question 15

An isolated air-filled parallel-plate capacitor that is no longer connected to anything has been charged up to Q = 2.9 nC.The separation between the plates initially is 1.20 mm,and for this separation the capacitance is 31 pF.Calculate the work that must be done to pull the plates apart until their separation becomes 5.30 mm,if the charge on the plates remains constant.(ε₀ = 8.85 × 10^-12 C²/N • m²)

Question 16

An ideal parallel-plate capacitor consists of a set of two parallel plates of area A separated by a very small distance d.When the capacitor plates carry charges +Q and -Q,the capacitor stores energy U₀.If the separation between the plates is doubled,how much electrical energy is stored in the capacitor?

A) 4U₀
B) 2U₀
C) U₀
D) U₀/2
E) U₀/4

Question 17

An air-filled parallel-plate capacitor is connected to a battery and allowed to charge up.Now a slab of dielectric material is placed between the plates of the capacitor while the capacitor is still connected to the battery.After this is done,we find that

A) the energy stored in the capacitor had decreased.
B) the voltage across the capacitor had increased.
C) the charge on the capacitor had increased.
D) the charge on the capacitor had not changed.
E) None of these choices are true.

Question 18

Each plate of a parallel-plate air-filled capacitor has an area of 0.0020 m²,and the separation of the plates is 0.020 mm.An electric field of 3.9 × 10⁶ V/m is present between the plates.What is the surface charge density on the plates? (ε₀ = 8.85 × 10^-12 C²/N • m²)

A) 35 µC/m²
B) 73 µC/m²
C) 17 µC/m²
D) 52 µC/m²
E) 87 µC/m²

Question 19

An air-filled capacitor is formed from two long conducting cylindrical shells that are coaxial and have radii of 13 mm and 85 mm.The electric potential of the inner conductor with respect to the outer conductor is -600 V.(k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)The maximum energy density of the capacitor is closest to

A) 2.7 × 10^-3 J/m³.
B) 1.3 × 10^-3 J/m³.
C) 6.7 × 10^-4 J/m³.
D) 3.4 × 10^-3 J/m³.
E) 1.7 × 10^-4 J/m³.

Question 20

An ideal air-filled parallel-plate capacitor has round plates and carries a fixed amount of equal but opposite charge on its plates.All the geometric parameters of the capacitor (plate diameter and plate separation)are now DOUBLED.If the original energy stored in the capacitor was U₀,how much energy does it now store?

A) 4U₀
B) 2U₀
C) U₀
D) U₀/2
E) U₀/4

Question 21

Two square air-filled parallel plates that are initially uncharged are separated by 1.2 mm,and each of them has an area of 190 mm².How much charge must be transferred from one plate to the other if 1.1 nJ of energy are to be stored in the plates? (ε₀₀ = 8.85 × 10^-12 C²/N • m²)

A) 56 pC
B) 39 pC
C) 78 pC
D) 3.5 µC

Question 22

A parallel-plate capacitor has a capacitance of 10 mF and charged with a 20-V power supply.The power supply is then removed and a dielectric material of dielectric constant 4.0 is used to fill the space between the plates.How much energy is now stored by the capacitor?

A) 250 mJ
B) 125 mJ
C) 500 mJ
D) 62.5 mJ
E) 1200 mJ

Question 23

A 6.00-μF parallel-plate capacitor has charges of ±40.0 μC on its plates.How much potential energy is stored in this capacitor?

A) 103 μJ
B) 113 μJ
C) 123 μJ
D) 133 μJ
E) 143 μJ

Question 24

A parallel-plate capacitor with plate separation of 1.0 cm has square plates,each with an area of
6)0 × 10^-2 m².What is the capacitance of this capacitor if a dielectric material with a dielectric constant of 2.4 is placed between the plates,completely filling them? (ε₀ = 8.85 × 10^-12 C²/N • m²)

A) 15 × 10^-12 F
B) 15 × 10^-14 F
C) 64 × 10^-14 F
D) 1.3 × 10^-12 F
E) 1.3 × 10^-10 F

Question 25

A parallel-plate capacitor,with air between the plates,is connected across a voltage source.This source establishes a potential difference between the plates by placing charge of magnitude 4.15 × 10^-6 _C on each plate.The space between the plates is then filled with a dielectric material,with a dielectric constant of 7.74.What must the magnitude of the charge on each capacitor plate now be,to produce the same potential difference between the plates as before?

Question 26

A parallel-plate capacitor has a capacitance of 10 mF and is charged with a 20-V power supply.The power supply is then removed and a dielectric material of dielectric constant 4.0 is used to fill the space between the plates.What is the voltage now across the capacitor?

A) 80 V
B) 20 V
C) 10 V
D) 5.0 V
E) 2.5 V

Question 27

Each plate of an air-filled parallel-plate air capacitor has an area of 0.0040 m²,and the separation of the plates is 0.080 mm.An electric field of 5.3 × 10⁶ V/m is present between the plates.What is the energy density between the plates? (ε₀ = 8.85 × 10^-12 C²/N • m²)

A) 124 J/m³
B) 84 J/m³
C) 170 J/m³
D) 210 J/m³
E) 250 J/m³

Question 28

A charge of 2.00 μC flows onto the plates of a capacitor when it is connected to a 12.0-V potential source. What is the minimum amount of work that must be done in charging this capacitor?

A) 6.00 µJ
B) 24.0 µJ
C) 12.0 µJ
D) 144 µJ
E) 576 µJ

Question 29

A 15-μF air-filled capacitor is connected to a 50-V voltage source and becomes fully charged. The voltage source is then removed and a slab of dielectric that completely fills the space between the plates is inserted. The dielectric has a dielectric constant of 5.0.
(a)What is the capacitance of the capacitor after the slab has been inserted?
(b)What is the potential difference across the plates of the capacitor after the slab has been inserted?

Question 30

An air-filled capacitor stores a potential energy of 6.00 mJ due to its charge.It is accidentally filled with water in such a way as not to discharge its plates.How much energy does it continue to store after it is filled? (The dielectric constant for water is 78 and for air it is 1.0006.)

A) 0.077 mJ
B) 468 mJ
C) 0.040 mJ
D) 6.00 mJ

Question 31

A parallel-plate capacitor consists of two parallel,square plates that have dimensions 1.0 cm by 1.0 cm.If the plates are separated by 1.0 mm,and the space between them is filled with teflon,what is the capacitance of this capacitor? (The dielectric constant for teflon is 2.1,and ε₀ = 8.85 × 10^-12 C²/N • m².)

A) 1.9 pF
B) 0.44 pF
C) 2.1 pF
D) 0.89 pF

Question 32

A 6.0-μF air-filled capacitor is connected across a 100-V voltage source. After the source fully charges the capacitor,the capacitor is immersed in transformer oil (of dielectric constant 4.5). How much ADDITIONAL charge flows from the voltage source,which remained connected during the process?

A) 1.2 mC
B) 1.5 mC
C) 1.7 mC
D) 2.1 mC
E) 2.5 mC

Question 33

A 1.0 μF capacitor has a potential difference of 6.0 V applied across its plates.If the potential difference across its plates is increased to 8.0 V,how much ADDITIONAL energy does the capacitor store?

A) 14 μJ
B) 28 μJ
C) 2.0 μJ
D) 4.0 μJ