Question 1

In a certain region, the electric potential due to a charge distribution is given by the equation V(x,y,z) = 3x2y2 + yz3 - 2z3x, where x, y, and z are measured in meters and V is in volts. Calculate the magnitude of the electric field vector at the position (x,y,z) = (1.0, 1.0, 1.0).

Accepted Answer

A)  4.3 V/m 
B)  2.0 V/m 
C)  -8.1 V/m 
D)  8.6 V/m 
E)  74 V/m

Question 2

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 x 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)

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

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?

Accepted Answer

A)  The charge on C2 increases. 
B)  The charge on C2 decreases. 
C)  The charge on C2 remains the same.

Question 5

A conducting sphere of radius R carries an excess positive charge and is very far from any other charges. Which one of the following graphs best illustrates the potential (relative to infinity) produced by this sphere as a function of the distance r from the center of the sphere?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 6

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?

Accepted Answer

A)  from r = 0 m to r = 3 m 
B)  from r = 3 m to r = 4 m 
C)  from r = 4 m to r = 6 m 
D)  at r = 3 m 
E)  at r = 4 m

Question 7

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

Accepted Answer

A)  the potential difference across each capacitor is the same. 
B)  each capacitor carries the same amount of charge. 
C)  the equivalent capacitance of the combination is less than the capacitance of any of the capacitors. 
D)  All of the above choices are correct. 
E)  None of the above choices are correct.

Question 8

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?

Accepted Answer

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

Question 9

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

Accepted Answer

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 10

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

Accepted Answer

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

Question 11

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?

Accepted Answer

A)  16u0 
B)  4u0 
C)  u0 
D)  u0/4 
E)  u0/16

Question 12

The four identical capacitors in the circuit shown in the figure are initially uncharged. Let the charges on the capacitors be Q1, Q2, Q3, and Q4 and the potential differences across them be V1, V2, V3, and V4. The switch is thrown first to position A and kept there for a long time. It is then thrown to position B. Which of the following conditions is true with the switch in position B?

Accepted Answer

A)  V1 = V2 = V3 = V4 
B)  V1 = V0 
C)  V1 + V2 + V3 + V4 = V0 
D)  Q1 = 3 Q2 
E)  Q1 = Q2

Question 13

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.)

Accepted Answer

A)  The potential is lowest, but not zero, at the center of the sphere. 
B)  The potential at the center of the sphere is zero. 
C)  The potential at the center of the sphere is the same as the potential at the surface. 
D)  The potential at the surface is higher than the potential at the center. 
E)  The potential at the center is the same as the potential at infinity.

Question 14

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 initially open but is then closed. Assume that all the capacitances shown are accurate to two significant figures. What is the equivalent capacitance between ab (a) with the switch S open? (b) with the switch S closed?

Accepted Answer

The answer of The capacitive network shown in the figure...

Question 15

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?

Accepted Answer

The answer of Three capacitors, of capacitance 5.00 μF, 10.0...

Question 16

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?

Accepted Answer

The answer of A 15-μF air-filled capacitor is connected to...

Question 17

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?

Accepted Answer

A)  4U0 
B)  2U0 
C)  U0 
D)  U0/2 
E)  U0/4

Question 18

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?

Accepted Answer

A)  plot W 
B)  plot X 
C)  plot Y 
D)  plot Z

Question 19

The capacitive network shown in the figure is assembled with initially uncharged capacitors. A potential difference, Vab = +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 Vcd across the open switch S?

Accepted Answer

A)  0 V 
B)  40 V 
C)  50 V 
D)  60 V 
E)  70 V

Question 20

The capacitors in the network shown in the figure all have a capacitance of 5.0 µF. What is the equivalent capacitance, Cab, of this capacitor network?

Accepted Answer

A)  20 µF 
B)  3.0 µF 
C)  10 µF 
D)  5.0 µF 
E)  1.0 µF

Exam 29: Potential and Field

In a certain region, the electric potential due to a charge distribution is given by the equation V(x,y,z) = 3x²^y² + yz³ - 2z³^x, where x, y, and z are measured in meters and V is in volts. Calculate the magnitude of the electric field vector at the position (x,y,z) = (1.0, 1.0, 1.0) .

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 x 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)

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?

A conducting sphere of radius R carries an excess positive charge and is very far from any other charges. Which one of the following graphs best illustrates the potential (relative to infinity) produced by this sphere as a function of the distance r from the center of the sphere?

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?

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

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?

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 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.)

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?

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?

The capacitors in the network shown in the figure all have a capacitance of 5.0 µF. What is the equivalent capacitance, C_ab, of this capacitor network?

Exam 29: Potential and Field

In a certain region, the electric potential due to a charge distribution is given by the equation V(x,y,z) = 3x2y2 + yz3 - 2z3x, where x, y, and z are measured in meters and V is in volts. Calculate the magnitude of the electric field vector at the position (x,y,z) = (1.0, 1.0, 1.0) .

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 x 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)

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?

A conducting sphere of radius R carries an excess positive charge and is very far from any other charges. Which one of the following graphs best illustrates the potential (relative to infinity) produced by this sphere as a function of the distance r from the center of the sphere?

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?

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

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?

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 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.)

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?

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?

The capacitors in the network shown in the figure all have a capacitance of 5.0 µF. What is the equivalent capacitance, Cab, of this capacitor network?

In a certain region, the electric potential due to a charge distribution is given by the equation V(x,y,z) = 3x²^y² + yz³ - 2z³^x, where x, y, and z are measured in meters and V is in volts. Calculate the magnitude of the electric field vector at the position (x,y,z) = (1.0, 1.0, 1.0) .

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 x 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)

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 capacitors in the network shown in the figure all have a capacitance of 5.0 µF. What is the equivalent capacitance, C_ab, of this capacitor network?