Deck 23: Electric Potential

Question 1

Use the following to answer the next question:
Which of the points shown in the diagram are at the same potential?

A)2 and 5
B)2,3,and 5
C)1 and 4
D)1 and 5
E)2 and 4

Answer 1

1 and 4

Question 2

A uniform electric field exists between two parallel plates separated by 1.2 cm.The intensity of the field is 23 kN/C.What is the potential difference between the plates?

A)7.5 MV
B)3.0 MV
C)15 kV
D)0.30 kV
E)None of these is correct.

Answer 2

0.30 kV

Question 3

The electric field in a region is given by where the units are in V/m.What is the potential from the origin to (x,y)= (2,2)m?

A) V
B) V
C) V
D)- 6 V
E)none of the above

Answer 3

V

Question 4

When 2.0 C of charge moves at constant speed along a path between two points differing in potential by 6.0 V,the amount of work done is

A)2 J
B)3 J
C)6 J
D)12 J
E)24 J

Question 5

The electric field in a region is given by where Q is the charge.What is the potential between r = a to r = b?

A)
B)
C)
D)
E)none of the above

Question 6

The voltage between the cathode and the screen of a television set is 22 kV.If we assume a speed of zero for an electron as it leaves the cathode,what is its speed just before it hits the screen?

A)8.8 × 10⁷ m/s
B)2.8 × 10⁶ m/s
C)6.2 × 10⁷ m/s
D)7.7 × 10¹⁵ m/s
E)5.3 × 10⁷ m/s

Question 7

Two parallel horizontal plates are spaced 0.60 cm apart in air.You introduce an oil droplet of mass 7.4 × 10^-17 kg between the plates.If the droplet carries five electronic charges and if there were no air buoyancy,you could hold the droplet motionless between the plates if you kept the potential difference between them at

A)5.4 V
B)27 V
C)3.0 V
D)0.54 V
E)0.27 kV

Question 8

Two parallel horizontal plates are spaced 0.40 cm apart in air.You introduce an oil droplet of mass 4.9 × 10^-17 kg between the plates.If the droplet carries two electronic charges and if there were no air buoyancy,you could hold the droplet motionless between the plates if you kept the potential difference between them at

A)60 V
B)12 V
C)3.0 V
D)0.12 kV
E)6.0 V

Question 9

The electric field in a region is given by where the units are in V/m.What is the potential from the origin to (x,y)= (2,0)m?

A)8 V
B)-8 V
C)-16/3 V
D)-24/3 V
E)11 V

Question 10

When 5.0 C of charge moves at constant speed along a path between two points differing in potential by 12 V,the amount of work done is

A)2.4 J
B)0.42 J
C)5.0 J
D)12 J
E)60 J

Question 11

The concept of difference in electric potential is most closely associated with

A)the mechanical force on an electron.
B)the number of atoms in one gram-atom.
C)the charge on one electron.
D)the resistance of a certain specified column of mercury.
E)the work per unit quantity of electricity.

Question 12

Two parallel metal plates 5.0 cm apart have a potential difference between them of 75 V.The electric force on a positive charge of 3.2 × 10^-19 C at a point midway between the plates is approximately

A)4.8 × 10^-18 N
B)2.4 × 10^-17 N
C)1.6 × 10^-18 N
D)4.8 × 10^-16 N
E)9.6 × 10^-17 N

Question 13

The voltage between the cathode and the screen of a computer monitor is 12 kV.If we assume a speed of zero for an electron as it leaves the cathode,what is its speed just before it hits the screen?

A)8.8 × 10⁷ m/s
B)6.5 × 10⁷ m/s
C)4.2 × 10¹⁵ m/s
D)7.7 × 10¹⁵ m/s
E)5.3 × 10⁷ m/s

Question 14

The electron volt is a unit of

A)capacitance
B)charge
C)energy
D)momentum
E)potential

Question 15

A charge of 2.0 mC is located in a uniform electric field of intensity 4.0 × 10⁵ N/C.How much work is required to move this charge 20 cm along a path making an angle of 60° with the electric field?

A)0.14 J
B)0.34 J
C)80 mJ
D)14 J
E)8.0 J

Question 16

A lithium nucleus with a charge of 3(1.6 × 10^-19)C and a mass of 7(1.67 × 10^-27)kg,and an alpha particle with a charge of 2(1.6 × 10^-19)C and a mass of 4(1.67 × 10^-27)kg,are at rest.They could be accelerated to the same kinetic energy by

A)accelerating them through the same electrical potential difference.
B)accelerating the alpha particle through V volts and the lithium nucleus through 2V/3 volts.
C)accelerating the alpha particle through V volts and the lithium nucleus through 7V/4 volts.
D)accelerating the alpha particle through V volts and the lithium nucleus through 7V/6 volts.
E)none of these procedures

Question 17

Two parallel metal plates 0.35 cm apart have a potential difference between them of 175 V.The electric force on a positive charge of 6.4 × 10^-19 C at a point midway between the plates is approximately

A)4.8 × 10^-18 N
B)2.4 × 10^-17 N
C)1.6 × 10^-18 N
D)4.8 × 10^-16 N
E)3.2 × 10^-14 N

Question 18

A charge of 5.0 mC is located in a uniform electric field of intensity 3.5 × 10⁵ N/C.How much work is required to move this charge 50 cm along a path making an angle of 33° with the electric field?

A)0.27 J
B)0.16 J
C)0.54 J
D)0.73 J
E)7.3 mJ

Question 19

Correct units for electric potential are

A)N/C
B)V/m
C)N/kg
D)J/C
E)C/N

Question 20

A uniform electric field exists between two parallel plates separated by 2.0 cm.The intensity of the field is 15 kN/C.What is the potential difference between the plates?

A)0.75 MV
B)30 kV
C)15 kV
D)0.30 kV
E)54 kV

Question 21

An electric dipole that has a positive charge of 4.80 × 10^-19 C is separated from a negative charge of the same magnitude by 6.40 × 10^-10 m.The magnitude of the electric field at the midpoint of the dipole is

A)zero
B)27.0 N/C
C)4.22 × 10¹⁰ N/C
D)8.44 × 10¹⁰ N/C
E)12.3 × 10¹⁰ N/C

Question 22

Use the following to answer the next question:
Which point in the electric field in the diagram is at the highest potential?

A)1
B)2
C)3
D)4
E)5

Question 23

A proton (charge = e,mass = 1.67  10^-27 kg)with initial kinetic energy 3 MeV is fired head-on towards a fixed stationary uranium nucleus (charge 92e,mass = 3.95  10^-25 kg).Calculate how close to the uranium the proton gets before it comes to rest.(Assume the uranium nucleus does not move.)

A)2.75  10⁵ m
B)4.40  10^-8 m
C)4.40  10^-14 m
D)2.10  10^-7 m
E)none of the above

Question 24

Two charges Q₁ (= +6 C)and Q₂ (= -2 C)are brought from infinity to positions on the x-axis of x = -4 cm and x = +4 cm,respectively.Is it possible to bring a third charge Q₃ (= +3 C)from infinity to a point on the x-axis between the charges where the potential is zero,and if so,where would this position be?

A)it is not possible
B)x = 0 cm
C)x = +2 cm
D)x = +6 cm
E)x = +1.5 cm

Question 25

Use the following figure to answer the next problem: The electric field versus distance for a charge is plotted above.Use the reference point

The potential for r < 1 m is

A)4000 V
B)2000 V
C)1000 V
D)zero
E)cannot be determined precisely

Question 26

Use the following figure to answer the next problem:
ABC is a straight line with AB = BC = 0.60 nm.BP is perpendicular to ABC and BP = 0.80 nm.Charges of +3.2 × 10^-19 C are placed at A and C,and a charge of -3.2 × 10^-19 C is placed at B.The electric potential at P is

A)2.2 V
B)9.4 V
C)29 V
D)0.43 nV
E)0.16 kV

Question 27

Use the following figure to answer the next problem: Two equal positive charges are placed x m apart.The equipotential lines are at 100 V interval.
The potential at a point due to a unit positive charge is found to be V.If the distance between the charge and the point is tripled,the potential becomes

A)V/3
B)3V
C)V/9
D)9V
E)1/V²

Question 28

Use the following figure to answer the next problem:
ABC is a straight line with AB = BC = 0.60 nm.BP is perpendicular to ABC and BP = 0.80 nm.Charges of +3.2 × 10^-19 C are placed at A and B.The electric potential at P is approximately

A)2.9 V
B)3.6 V
C)6.5 V
D)9.3 V
E)1.5 V

Question 29

Use the following figure to answer the next problem: Two equal positive charges are placed x m apart.The equipotential lines are at 100 V interval.
The electrical potential 2.5 cm from a point charge of Q₁ = +4.5  10^-9 C and 2.0 cm from a second charge Q₂ is 3.2 kV.Find Q₂.

A)2.7  10^-9 C
B)4.4  10^-9 C
C)1.1  10^-8 C
D)3.5  10^-9 C
E)5.5  10^-9 C

Question 30

Use the following figure to answer the next problem: Two equal positive charges are placed x m apart.The equipotential lines are at 100 V interval.
The electrical potential 2.0 cm from a point charge of Q₁ = +6.5  10^-9 C and 3.5 cm from a second charge Q₂ is 1.2 kV.Find Q₂.

A)-6.7  10^-9 C
B)-3.8  10^-9 C
C)-1.0  10^-9 C
D)3.8  10^-9 C
E)1.0  10^-9 C

Question 31

Use the following to answer the next question:
Which point in the electric field in the diagram is at the lowest potential?

A)1
B)2
C)3
D)4
E)5

Question 32

Use the following figure to answer the next problem:
ABC is a straight line with AB = BC = 0.60 nm.BP is perpendicular to ABC and BP = 0.80 nm.Charges of +3.2 × 10^-19 C are placed at A and C,and a charge of -3.2 × 10^-19 C is placed at B.The magnitude of the electric field at P is approximately

A)1.7 × 10⁷ N/C
B)10 × 10⁷ N/C
C)4.5 × 10⁷ N/C
D)2.3 × 10⁷ N/C
E)zero

Question 33

Use the following figure to answer the next problem: Two equal positive charges are placed x m apart.The equipotential lines are at 100 V interval.
The work required to move a third charge,q = e,from the 100 V line to b is

A)100 eV
B)100 eV
C)200 eV
D)200 eV
E)zero

Question 34

Use the following figure to answer the next problem:
ABC is a straight line with AB = BC = 0.60 nm.BP is perpendicular to ABC and BP = 0.80 nm.Charges of +3.2 × 10^-19 C are placed at A and B.The magnitude of the electric field at P is

A)9.1 × 10⁹ N/C
B)6.8 × 10⁹ N/C
C)1.2 × 10¹⁰ N/C
D)2.6 × 10¹⁰ N/C
E)3.3 × 10¹⁰ N/C

Question 35

An electric dipole that has a positive charge of 4.8 × 10^-19 C is separated from a negative charge of the same magnitude by 6.4 × 10^-10 m.The electric potential at a point 9.2 × 10^-10 m from each of the two charges is

A)9.4 V
B)zero
C)4.2 V
D)5.1 × 10⁹ V
E)1.7 V

Question 36

Two charges Q₁ (= +6 C)and Q₂ (= -2 C)are brought from infinity to positions on the x-axis of x = -4 cm and x = +4 cm,respectively.How much work was done in bringing the charges together?

A)-1.80  10⁶ J
B)-9.00  10⁵ J
C)-16.9 J
D)-1.35 J
E)none of the above

Question 37

Use the following figure to answer the next problem: The electric field versus distance for a charge is plotted above.Use the reference point

The work required to move a charge,q = e from infinity to r = 2 m is

A)4000 eV
B)2000 eV
C)1000 eV
D) 4000 eV
E)zero

Question 38

The electric potential in a region of space is given by The electric field in this region is

A)50 V
B)50 V
C)50 V
D)0
E)50 V

Question 39

Use the following figure to answer the next problem: Two equal positive charges are placed x m apart.The equipotential lines are at 100 V interval.
The potential for line c is

A)100 V
B)100 V
C)200 V
D)200 V
E)zero

Question 40

The electric potential in a region of space is given by The electric field in this region is

A)50 V
B)(15 V/m)x
C)(50 V/m + 15 V/m)
D)(15 V/m)
E)-(15 V/m)

Question 41

A conducting sphere of radius r₁ = 10 cm and charge q₁ = 2 C is placed far apart from a second conducting sphere of radius r₂ = 30 cm and charge q₂ = 3 C.The two spheres are then connected by a thin conducting wire.What is the charge on the first sphere after the two spheres are connected by the wire?

A)2 C
B)2.5 C
C)3 C
D)1.25 C
E)none of the above

Question 42

A conducting sphere of radius r₁ = 10 cm and charge q₁ = 2 C is placed far apart from a second conducting sphere of radius r₂ = 30 cm and charge q₂ = 3 C.The two spheres are then connected by a thin conducting wire.What is the potential on the surface of the first sphere after the two spheres are connected by the wire? Use the reference V = 0 for r at infinity.

A)1.12  10⁵ V
B)1.80  10⁵ V
C)2.25  10⁵ V
D)2.70  10⁵ V
E)none of the above

Question 43

Use the following figure to answer the next problem:
A ring of radius 5 cm is the yz plane with its center at the origin.The ring carries a uniform charge of 10 nC.A small particle of mass m = 10 mg and charge q₀ = 5 nC is placed at x = 12 cm and released.The speed of the particle when it is a great distance from the ring is

A)1.36 cm/s
B)1.94 cm/s
C)2.63 cm/s
D)3.43 cm/s
E)None of these is correct.

Question 44

The dielectric strength of the atmosphere is of the order of

A)1 V/m
B)10² V/m
C)10⁴ V/m
D)10⁶ V/m
E)10⁸ V/m

Question 45

The electric potential is known to be a function of x only; i.e.,v = V(x).The electric field at a position x₁ is given by

A)V(x₁)
B)
C)
D)
E)

Question 46

The electric potential in a region of space is given by V = 2xy + 3y² in units of V.The electric field,in V/m,in this region is

A)
B)
C)
D)
E)none of the above

Question 47

Use the following figure to answer the next problem:
A ring of radius 5 cm is in the yz plane with its center at the origin.The ring carries a uniform charge of 10 nC.The electric potential at x = 12 cm is approximately

A)217 V
B)543 V
C)692 V
D)809 V
E)963 V

Question 48

The electric potential in a region of space is given by The x-component of the electric field in this region is

A)(10 V/m)
B)-(10 V/m)
C)(20 V/m)
D)-(20 V/m)
E)-(30 V/m)

Question 49

The metal sphere at the top of a small Van de Graaf generator has a radius of 10 cm.How much charge can be accumulated on this sphere before dielectric breakdown of the air around it occurs? (The dielectric strength of air is 3.0 MV/m.)

A)67 µC
B)33 µC
C)13 µC
D)6.7 µC
E)3.3 µC

Question 50

Use the following figure to answer the next problem:
A disk of radius 10 cm has a uniform charge density of 20 nC/cm².The electric potential at a distance x = 20 cm on its axis is

A)189 kV
B)267 kV
C)302 kV
D)356 kV
E)421 kV

Question 51

Which of the following statements regarding potential is true?

A)The units of potential are N/C.
B)Potential is a vector quantity.
C)Equipotential surfaces are at right angles to lines of force.
D)Potential differences can be measured directly with a ballistic galvanometer.
E)Equipotential surfaces for an isolated point charge are cubes concentric with the charge.

Question 52

The metal sphere at the top of a small Van de Graaf generator has a radius of 8.0 cm.How much charge can be accumulated on this sphere before dielectric breakdown of the air around it occurs? (The dielectric strength of air is 3.0 MV/m.)

A)2.1 µC
B)3.3 µC
C)1.3 nC
D)6.7 µC
E)4.2 µC

Question 53

A charge of 100 nC resides on the surface of a spherical shell of radius 20 cm.The electric potential at a distance of 15 cm from the center of the spherical shell is

A)18 V
B)180 V
C)1800 V
D)18,000 V
E)None of these is correct.

Question 54

Which of the following statements is true?

A)The gradient of the potential must be larger at a place where the electric field is stronger.
B)The gradient of the potential must be smaller at a place where the electric field is stronger.
C)The potential must be larger at a place where the electric field is stronger.
D)The potential must be smaller at a place where the electric field is stronger.
E)Local electric field strength is proportional to the local electrical potential.

Question 55

The potential of a spherical shell carrying 6.0 C of charge is 540 kV.What is the radius of the shell?

A)1.0  10¹ m
B)1.0  10² m
C)3.2  10^-1 m
D)1.0  10^-1 m
E)none of the above

Question 56

Use the following figure to answer the next problem:
A disk of radius 10 cm has a uniform charge density of 20 nC/cm².A small particle of mass m = 10 mg and charge q₀ = 5 nC is placed at x = 20 cm and released.The speed of the particle when it is a great distance from the disk is

A)14.2 cm/s
B)22.5 cm/s
C)42.9 cm/s
D)51.8 cm/s
E)66.1 cm/s

Question 57

The charge density of an infinite line of charge is  = 100 nC/m.If zero of potential is chosen to be at a point having a perpendicular distance of 1 m from the line,the electric potential at a perpendicular distance of 50 cm from this line is

A)1.25 kV
B)2.34 kV
C)0
D)-1.25 kV
E)-2.34 kV

Question 58

Use the following figure to answer the next problem:
The electric potential at the surface of an infinite plane of charge is 100 V.If the charge density of the charge on the infinite plane is s  = 1 nC/m²,the electric potential at a distance of 1 m from the infinite plane is

A)22.3 V
B)43.5 V
C)50.0 V
D)65.7 V
E)83.4 V

Question 59

The electric potential in a region of space is given by The y-component of the electric field in this region is

A)(10 V/m)
B)-(10 V/m)
C)-(20 V/m)
D)(20 V/m)
E)-(30 V/m)

Question 60

The electric potential in a region of space is given by The z-component of the electric field in this region is

A)-(30 V/m)
B)-(10 V/m)
C)(20 V/m)
D)-(20 V/m)
E)(30 V/m)

Question 61

The potential on the surface of a solid conducting sphere of radius r = 20 cm is 100 V.The potential at r = 10 cm is

A)100 V
B)50 V
C)25 V
D)zero
E)cannot be determined

Question 62

Dielectric breakdown occurs in the air at an electric field strength of E_max = 3.0  10⁶ V/m.If the maximum charge that can be placed on a spherical conductor is 2.0  10^-3 C before breakdown,calculate the diameter of the sphere.

A)6.0 m
B)4.9 m
C)1.2 m
D)2.5 m
E)3.0 m

Question 63

Use the following figure to answer the next problem.
The electrostatic potential energy of the system of point charges q₁ = 1 µC,q₂ = 2 µC,and q₃ = 3 µC at the corners of the equilateral triangle whose side s = 30 cm is

A)1.10 J
B)0.990 J
C)0.631 J
D)0.330 J
E)0.123 J

Question 64

Use the following figure to answer the next problem.
Four point charges q₁ = -1 C,q₂ = 2 C,q₃ = 3 C,and q₄ = 4 C are located at the corners of a square whose side s = 1 m.The electrostatic potential energy of this system of charges is

A)0.140 J
B)0.176 J
C)0.286 J
D)0.337 J
E)0.492 J

Question 65

Use the following figure to answer the next problem.
Four point charges q₁ = 1 µC,q₂ = 2 µC,q₃ = 3 µC,and q₄ = 4 µC are located at the corners of a square whose side s = 1 m.The electrostatic potential energy of this system of charges is

A)0.167 J
B)0.176 J
C)0.286 J
D)0.337 J
E)0.492 J

Question 66

What is the approximate radius of an equipotential spherical surface of 100 V about a point charge of +45 nC if the potential at an infinite distance from the surface is zero?

A)1.0 m
B)2.1 m
C)3.0 m
D)4.5 m
E)4.0 m

Question 67

A solid spherical conductor of radius 20 cm has a charge Q = 25 nC on it.A second,initially uncharged,spherical conductor of radius 12 cm is moved toward the first until they touch and is then moved far away from it.How much charge is there on the second sphere after the two spheres have been separated?

A)15 nC
B)9.4 nC
C)25 nC
D)3.9 nC
E)2.1 nC

Question 68

A solid conducting sphere of radius r_a is placed concentrically inside a conducting spherical shell of inner radius r_b1 and outer radius r_b2.The inner sphere carries a charge Q while the outer sphere does not carry any net charge.The potential for r  r_a is

A)
B)
C)
D)
E)zero

Question 69

When a small,positively charged metal ball comes in contact with the interior of a positively charged metal shell,

A)the charge on the ball becomes negative.
B)the amount of positive charge on the ball increases.
C)the positive charge on the shell decreases.
D)the charge on the shell and the ball reach the same value.
E)the ball loses all of its excess charge.

Question 70

An electric charge q is placed on an isolated metal sphere of radius r₁.If an uncharged sphere of radius r₂ (with r₂ > r₁)is then connected to the first sphere,the spheres will have equal

A)and like charges on their surfaces.
B)electric fields.
C)potentials.
D)capacitances.
E)but opposite charges on their surfaces.

Question 71

Use the following figure to answer the next problem.
The electrostatic potential energy of the system of point charges q₁ = 1 µC,q₂ = -2 µC,and q₃ = 3 µC at the corners of the equilateral triangle whose side s = 40 cm is

A)1.10 J
B)0.990 J
C)-0.631 J
D)0.330 J
E)-0.113 J

Question 72

The electrostatic potential energy of two protons separated by 2.6  10^-15 m is approximately

A)zero
B)4.7  10^-34 J
C)4.3  10^-24 J
D)3.8  10^-14 J
E)8.9  10^-14 J

Question 73

A solid spherical conductor of radius 15 cm has a charge Q = 6.5 nC on it.A second,initially uncharged,spherical conductor of radius 10 cm is moved toward the first until they touch and is then moved far away from it.How much charge is there on the second sphere after the two spheres have been separated?

A)2.6 nC
B)2.2 nC
C)3.2 nC
D)3.9 nC
E)4.3 nC

Question 74

A solid conducting sphere of radius r_a is placed concentrically inside a conducting spherical shell of inner radius r_b1 and outer radius r_b2.The inner sphere carries a charge Q while the outer sphere does not carry any net charge.The potential for r_b1  r  r_b2 is

A)
B)
C)
D)
E)zero

Question 75

What is the approximate radius of an equipotential spherical surface of 30 V about a point charge of +15 nC if the potential at an infinite distance from the surface is zero?

A)1.0 m
B)2.1 m
C)3.0 m
D)4.5 m
E)6.8 m

Question 76

Two protons in a nucleus of ²³⁸U are 6.0  10^-15 m apart.The electrostatic potential energy of the pair is approximately

A)zero
B)4.7  10^-34 J
C)4.3  10^-24 J
D)3.8  10^-14 J
E)2.4  10⁴ J

Question 77

A positive point charge of 10^-4 C is located 3 m from another positive point charge of 10^-5 C.Their mutual electric potential energy is

A)3 J
B)2 J
C)1 J
D)zero
E)-1 J

Question 78

Use the following figure to answer the next problem.
The electrostatic potential energy of the system of point charges q₁ = -1 µC,q₂ = 2 µC,and q₃ = 3 µC at the corners of the equilateral triangle whose side s = 50 cm is

A)18.0 mJ
B)-18.0 mJ
C)21.6 mJ
D)-24.4 mJ
E)1.23 mJ

Question 79

Dielectric breakdown occurs in the air at an electric field strength of E_max = 3.0  10⁶ V/m.What is the maximum surface charge density that can be placed on a spherical conductor of radius 1.5 m before breakdown?

A)2.7  10^-5 C/m²
B)1.2  10^-5 C/m²
C)8.1  10^-5 C/m²
D)8.6  10^-6 C/m²
E)1.8  10^-5 C/m²

Question 80

Dielectric breakdown occurs in the air at an electric field strength of E_max = 3.0  10⁶ V/m.If the maximum potential at the surface of a spherical conductor is 5.0  10⁶ V,then calculate the radius of the sphere.

A)0.60 m
B)1.3 m
C)1.7 m
D)0.77 m
E)15 m