Exam 26: Potential and Field

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.)

Two capacitors, C₁ and C₂, are connected in series across a source of potential difference. With the potential source still connected, a dielectric is now inserted between the plates of capacitor C₁. What happens to the charge on capacitor C₂?

The graph in the figure shows the variation of the electric potential V(x) (in arbitrary units) as a function of the position x (also in arbitrary units). Which of the choices below correctly describes the orientation of the x-component of the electric field along the x-axis?

The capacitive network shown in the figure is assembled with initially uncharged capacitors. A potential difference, V_ab = +100V, is applied across the network. The switch S in the network is kept open. Assume that all the capacitances shown are accurate to two significant figures. What is potential difference V_cd across the open switch S?

A conducting sphere contains positive charge distributed uniformly over its surface. Which statements about the potential due to this sphere are true? All potentials are measured relative to infinity. (There may be more than one correct choice.)

The capacitive network shown in the figure is assembled with initially uncharged capacitors. A potential difference, V_ab = +100V, is applied across the network. The switch S in the network is kept open. Assume that all the capacitances shown are accurate to two significant figures. What is the total energy stored in the seven capacitors?

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?

Three capacitors, with capacitances = 4.0 μF, = 3.0 μF, and = 2.0 μF, are connected to a 12 -V voltage source, as shown in the figure. What is the charge on capacitor ?

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?

Three capacitors, of capacitance 5.00 μF, 10.0 μF, and 50.0 μF, are connected in series across a 12.0-V voltage source. (a) How much charge is stored in the 5.00-μF capacitor? (b) What is the potential difference across the 10.0-μF capacitor?

The graph in the figure shows the variation of the electric potential V (measured in volts) as a function of the radial direction r (measured in meters). For which range or value of r is the magnitude of the electric field the largest?

A metallic sphere of radius 5 cm is charged such that the potential of its surface is 100 V (relative to infinity). Which of the following plots correctly shows the potential as a function of distance from the center of the sphere?

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

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?

The potential as a function of position x is shown in the graph in the figure. Which statement about the electric field is true?

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?

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

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 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)