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Exam 29: Potential and Field

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Question 1

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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?

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(a) 11 pF ...

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Question 2

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A 1.0-μF and a 2.0-μF capacitor are connected in series across a 3.0-V voltage source. (a) What is the charge on the 1.0-μF capacitor? (b) What is the voltage across the 2.0-μF capacitor?

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(a) 2.0 µC...

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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)

In a certain region, the electric potential due to a charge distribution is given by the equation V(x,y) = 2xy - x² - y, where x and y are measured in meters and V is in volts. At which point is the electric field equal to zero?

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 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 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)

Three capacitors are arranged as shown in the figure. C₁ has a capacitance of 5.0 pF, C₂ has a capacitance of 10.0 pF, and C₃ has a capacitance of 15.0 pF. Find the voltage drop across the entire arrangement if the voltage drop across C₂ is 311 V.

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 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?

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 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 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 x 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?

The network shown in the figure is assembled with uncharged capacitors X, Y, and Z, with , and And open switches, S₁ and S₂. A potential difference V_ab = +120 V is applied between points a and b. After the network is assembled, switch S₁ is closed for a long time, but switch S₂ is kept open. Then switch S₁ is opened and switch S₂ is closed. What is the final voltage across capacitor X?

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?

If the electric potential in a region is given by V(x) = 6/x², the x component of the electric field in that region is

When two or more capacitors are connected in series across a potential difference

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?

In the circuit shown in the figure, the capacitors are initially uncharged. The switch is first thrown to position A and kept there for a long time. It is then thrown to position B. Let the charges on the capacitors be Q₁, Q₂, and Q₃ and the potential differences across them be V₁, V₂, and V₃. Which of the following conditions must be true with the switch in position B?

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?