Deck 3: Electric Potential

Question 1

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 1

V

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

None of these is correct.

Question 3

Charges Q and q (Q $\neq$ q), separated by a distance d, produce a potential V_P = 0 at point P. This means that

A) no force is acting on a test charge placed at point P.
B) Q and q must have the same sign.
C) the electric field must be zero at point P.
D) the net work in bringing Q to distance d from q is zero.
E) the net work needed to bring a charge from infinity to point P is zero.

Answer 3

the net work needed to bring a charge from infinity to point P is zero.

Question 4

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 5

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 6

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 7

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 8

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 9

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 10

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 11

The electron volt is a unit of

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

Question 12

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 13

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 14

Correct units for electric potential are

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

Question 15

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 16

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 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

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 19

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 20

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 21

The electrostatic potential as a function of distance along a certain line in space is shown in graph (1). Which of the curves in graph (2) is most likely to represent the electric field as a function of distance along the same line?

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

Question 22

Use the following figure to answer the next problem: The electric field versus distance for a charge is plotted above. Use the reference point
V = 0 at r $\rightarrow$ infinity.

-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 23

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 24

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 25

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 26

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 F* 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 27

Use the following figure to answer the next four problems:
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 28

Use the following figure to answer the next four problems:
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 29

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 30

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 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 32

The figure shows two plates A and B. Plate A has a potential of 0 V and plate B a potential of 100 V. The dotted lines represent equipotential lines of 25, 50, and 75 V. A positive test charge of 1.6 × 10^-19 C at point x is transferred to point z. The energy gained or expended by the test charge is

A) 8 × 10^-18 J, gained.
B) 8 × 10^-18 J, expended.
C) 24 × 10^-18 J, gained.
D) 24 × 10^-8 J, expended.
E) 40 × 10^-8 J, gained.

Question 33

Charges +Q and -Q are arranged at the corners of a square as shown. When the electric field and the electric potential V are determined at P, the center of the square, we find that

A) E $\neq$ 0 and V > 0
B) E = 0 and V = 0
C) E = 0 and V > 0
D) E $\neq$ 0 and V < 0
E) None of these is correct.

Question 34

Two charges Q₁ (= +6 $\mu$ C) and Q₂ (= -2 $\mu$ 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 35

Use the following figure to answer the next four problems:
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 36

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

Question 37

Use the following figure to answer the next four problems:
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 38

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 39

Use the following figure to answer the next problem: The electric field versus distance for a charge is plotted above. Use the reference point
V = 0 at r $\rightarrow$ infinity.

-The potential for r < 1 m is

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

Question 40

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 41

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 42

The electric potential in a region of space is given by
V(x) = 50 V + (15 V/m) x.
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 43

The electric potential in a region of space is given by
V(x, y, z) = (10 V/m) x + (20 V/m) y + (30 V/m) z
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 44

The graph that best represents the electric potential of a uniformly charged spherical shell as a function of the distance from the center of the shell is

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

Question 45

Use the following figure to answer the next four problems:
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 46

Two charges Q₁ (= +6 $\mu$ C) and Q₂ (= -2 $\mu$ 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 $\mu$ 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 47

An isolated hollow spherical conductor of radius R is carrying a charge of Q. Graph (1) represents the potential V as a function of the distance r from the center of the sphere. The graph that represents the electric field as a function of distance is

A) 2
B) 3
C) 4
D) 5
E) 6

Question 48

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 49

The graph that represents the electric potential near an infinite plane of charge is

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

Question 50

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 51

The figure depicts a uniform electric field. The direction in which the increase in the electric potential is a maximum is

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

Question 52

The electric potential in a region of space is given by
V(x, y, z) = (10 V/m) x + (20 V/m) y + (30 V/m) z
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 53

The electric potential in a region of space is given by
V(x, y, z) = (10 V/m) x + (20 V/m) y + (30 V/m) z
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 54

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 55

The electric potential in a region of space is given by
V(x, y, z) = 50 V
The electric field in this region is

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

Question 56

Use the following figure to answer the next four problems:
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 57

The figure depicts a uniform electric field. The direction in which there is no change in the electric potential is

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

Question 58

Use the following figure to answer the next four problems:
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 59

If the potential V of an array of charges versus the distance from the charges is as shown in graph 1, which graph shows the electric field E as a function of distance r?

A) 2
B) 3
C) 4
D) 5
E) 6

Question 60

Use the following figure to answer the next four problems:
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 61

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 62

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 63

Two charged metal spheres are connected by a wire. Sphere A is larger than sphere B, as shown. The magnitude of the electric potential of sphere A

A) is greater than that at the surface of sphere B.
B) is less than that at the surface of sphere B.
C) is the same as that at the surface of sphere B.
D) could be greater than or less than that at the surface of sphere B, depending on the radii of the spheres.
E) could be greater than or less than that at the surface of sphere B, depending on the charges on the spheres.

Question 64

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 65

A charge of 100 nC resides on the surface of a spherical shell of radius 20 cm. The electric potential at a distance of 50 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 66

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 67

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 68

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 69

The potential of a spherical shell carrying 6.0 $\mu$ 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 70

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 71

The vector that best represents the direction of the electric field intensity at point x on the 20-V equipotential line is

A)
B)
C)
D)
E) None of these is correct.

Question 72

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 $\sigma$ = 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 73

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 74

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 75

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 76

A conducting sphere of radius r₁ = 10 cm and charge q₁ = 2 $\mu$ C is placed far apart from a second conducting sphere of radius r₂ = 30 cm and charge q₂ = 3 $\mu$ 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 77

The vector that best represents the direction of the electric field intensity at point x on the 200-V equipotential line is

A)
B)
C)
D)
E) None of these is correct.

Question 78

The figure shows portions of four equipotential surfaces whose potentials are related as follows: V₁ > V₂ > V₃ > V₄. The lines represent four paths (A $\rightarrow$ A', B $\rightarrow$ B', C $\rightarrow$ C', D $\rightarrow$ D') along which equal test charges are moved. The work involved can be said to be

A) the greatest for path A $\rightarrow$ A'.
B) the greatest for path B $\rightarrow$ B'.
C) the greatest for path C $\rightarrow$ C'.
D) the greatest for path D $\rightarrow$ D'.
E) the same for all paths.

Question 79

A conducting sphere of radius r₁ = 10 cm and charge q₁ = 2 $\mu$ C is placed far apart from a second conducting sphere of radius r₂ = 30 cm and charge q₂ = 3 $\mu$ 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 $\mu$ C
B) 2.5 $\mu$ C
C) 3 $\mu$ C
D) 1.25 $\mu$ C
E) none of the above

Question 80

The charge density of an infinite line of charge is $\lambda$ = 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