Deck 20: Electric Potential and Electric Potential Energy

Question 1

The work done in moving a positive charge against an electric field does not depend on the path chosen in moving the charge in that field. Based on the statement, what kind of force field is the electrostatic field?

A) discrete
B) quantized
C) polarized
D) conservative
E) nonconservative

Answer 1

conservative

Question 2

In the expression for the definition of capacitance C = Q/V, Q is the total charge on the plates of a capacitor.

Answer 2

False

Question 3

When a proton moves in a direction of the electric field, its potential increases but its potential energy decreases.

Answer 3

True

Question 4

A negative charge, if free, tries to move

A) from high potential to low potential.
B) from low potential to high potential.
C) toward infinity.
D) away from infinity.
E) in the direction of the electric field.

Question 5

Every point on an equipotential surface is at the same potential.

Question 6

The capacitance of a parallel plate capacitor is directly proportional to its plate separation.

Question 7

If you were a parallel plate capacitor manufacturer, state three ways you might make larger valued capacitors.

Question 8

When an electron moves in a direction opposite to the electric field, its potential increases but the potential energy decreases.

Question 9

The electron-volt is a unit of

A) charge.
B) potential.
C) electric field.
D) electric force.
E) energy.

Question 10

Unlike electric potential, the electric potential energy is a vector quantity.

Question 11

The direction of an electric field is from higher to lower potential.

Question 12

A capacitor, in addition to storing charge, also stores electrical energy.

Question 13

After being charged from a battery, the plates of a parallel plate capacitor are moved closer together. When they are half as far apart as originally, by how much does the stored energy change?

Question 14

The electric potential at a point P due to a positive charge is along the direction of that charge.

Question 15

The electric field between the plates of a parallel plate capacitor is inversely proportional to the plate separation.

Question 16

Equipotential lines and electric field lines meet perpendicular to one another.

Question 17

State three reasons for adding a dielectric material between the plates of a capacitor.

Question 18

Electric potential is a scalar quantity.

Question 19

A potential changes at the greatest rate in the direction of the gradient of the potential.

Question 20

For a proton moving in the direction of the electric field

A) its potential energy increases and its electric potential decreases.
B) its potential energy decreases and its electric potential increases.
C) its potential energy increases and its electric potential increases.
D) its potential energy decreases and its electric potential decreases.
E) both its potential energy and it electric potential remain constant.

Question 21

Which of the following will increase the capacitance of a parallel plate capacitor?

A) a decrease in the plate area and an increase in the plate separation
B) a decrease in the potential difference between the plates
C) an increase in the potential difference between the plates
D) an increase in the plate area and a decrease in the plate separation
E) none of the above

Question 22

A capacitor consists of a set of two parallel plates of area A separated by a distance d. This capacitor is connected to a battery that maintains a constant potential difference between the plates. A slab of a dielectric material is inserted in the region between the plates so as to completely fill it. What changes would you observe?

A) Only the charge in the capacitor would change.
B) Only the capacitance would change.
C) Both the charge in the capacitor and its capacitance would change.
D) Nothing would change.

Question 23

A capacitor consists of a set of two parallel plates of area A separated by a distance d. This capacitor is connected to a battery and charged until its plates carry charges +Q and -Q. If the separation between the plates is doubled, the potential difference between the plates will

A) double.
B) quadruple.
C) be cut in half.
D) be cut in fourth.
E) not change.

Question 24

A capacitor consists of a set of two parallel plates of area A separated by a distance d. This capacitor is connected to a battery that maintains a constant potential difference between the plates. If the separation between the plates is doubled, the magnitude of the charge on the plates will

A) double.
B) quadruple.
C) be cut in half.
D) be cut in fourth.
E) not change.

Question 25

FIGURE 20-2
The equipotential surfaces between two spherical conductors are shown in Figure 20-2, with the value of the potential marked for each line. What is the direction of the electric field at point F?

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

Question 26

FIGURE 20-1
Two parallel metal plates A and B carry positive and negative charges of equal strength, respectively, as shown in Figure 20-1. What is the correct direction for the equipotential lines for this charge configuration?
Choice I:
Vertical, along the y-axis
Choice II:
Horizontal, along the x-axis

A) Choice I
B) Choice II
C) neither Choice I nor Choice II
D) both Choice I and Choice II

Question 27

FIGURE 20-1
Two electric charges each equal to +Q, are separated by a distance d. If you make a graph of the electric potential as a function of the distance along the line connecting the two charges, the point exactly midway between the two charges would

A) be a relative maximum.
B) be a relative minimum.
C) be neither a relative maximum nor a relative minimum.
D) oscillate between being a relative maximum and a relative minimum.

Question 28

A negative charge is moved from point A to point B along an equipotential surface. Which of the following statements is true for this case?

A) The negative charge performs work in moving from point A to point B.
B) Work is required to move the negative charge from point A to point B.
C) Work is both required and performed in moving the negative charge from point A to point B.
D) No work is required to move the negative charge from point A to point B.

Question 29

Several electrons are placed on a hollow conducting sphere. They

A) clump together on the sphere's outer surface.
B) clump together on the sphere's inner surface.
C) become uniformly distributed on the sphere's outer surface.
D) become uniformly distributed on the sphere's inner surface.
E) become randomly distributed on the shere's outer and inner surfaces.

Question 30

FIGURE 20-1
Two electric charges each equal to -Q, are separated by a distance d. If you make a graph of the electric potential as a function of the distance along the line connecting the two charges, the point exactly midway between the two charges would

A) be a relative maximum.
B) be a relative minimum.
C) be neither a relative maximum nor a relative minimum.
D) oscillate between being a relative maximum and a relative minimum.

Question 31

A capacitor consists of a set of two parallel plates of area A separated by a distance d. This capacitor is connected to a battery and charged until its plates carry charges +Q and -Q. If the separation between the plates is doubled, the electrical energy stored in the capacitor will

A) double.
B) quadruple.
C) be cut in half.
D) be cut in fourth.
E) not change.

Question 32

An equipotential surface must be

A) parallel to the electric field at any point.
B) perpendicular to the electric field at any point.
C) randomly oriented with respect to the electric field.
D) equal to the electric field at any point.

Question 33

A surface on which all points are at the same potential is referred to as

A) a constant electric force surface.
B) a constant electric field surface.
C) an equipotential surface.
D) an equivoltage surface.
E) a dielectric surface.

Question 34

FIGURE 20-1
Two electric charges +Q and -Q, are separated by a distance d. If you make a graph of the electric potential as a function of the distance along the line connecting the two charges, the point exactly midway between the two charges would

A) be a relative maximum.
B) be a relative minimum.
C) be neither a relative maximum nor a relative minimum.
D) oscillate between being a relative maximum and a relative minimum.

Question 35

For an electron moving in a direction opposite to the electric field

A) its potential energy increases and its electric potential decreases.
B) its potential energy decreases and its electric potential increases.
C) its potential energy increases and its electric potential increases.
D) its potential energy decreases and its electric potential decreases.
E) both its potential energy and it electric potential remain constant.

Question 36

When a dielectric material is introduced between the plates of a parallel plate capacitor the capacitance increases by a factor of 4. What is the dielectric constant of the material introduced between the plates?

A) 0.4
B) 1/4
C) 2
D) 4
E) None of the other choices is correct.

Question 37

A dielectric material such as paper is placed between the plates of a capacitor holding a fixed charge. What happens to the electric field between the plates?

A) no change
B) becomes stronger
C) becomes weaker
D) reduces to zero

Question 38

A capacitor consists of a set of two parallel plates of area A separated by a distance d. This capacitor is connected to a battery that maintains a constant potential difference between the plates. If the separation between the plates is doubled, the magnitude of the electrical energy stored on the capacitor will

A) double.
B) quadruple.
C) be cut in half.
D) be cut in fourth.
E) not change.

Question 39

Which of the following expression(s) represents the electrical energy stored by a capacitor?

A) QV/2
B) CV²/2
C) Q²/2C
D) All of the expressions are correct.
E) None of the expressions is correct.

Question 40

Which of the following will increase the capacitance between the plates of a parallel plate capacitor?

A) Increase the charge on the plates.
B) Decrease the potential between the plates.
C) Increase the potential between the plates.
D) Introduce a dielectric material between the plates.
E) none of the above

Question 41

An electron is carried from the positive terminal to the negative terminal of a 9 V battery. How much work is required in carrying this electron?

A) 1.6 × 10^-19 J
B) 17 × 10^-19 J
C) 9 J
D) 14.4 × 10^-19 J
E) 14.4 × 10^-19 J/C

Question 42

A + 5.0-μC charge is moved from a negative to a positive plate of a parallel plate capacitor. In moving this charge 0.30 mJ of energy is used. What is the potential difference between the plates of this capacitor?

A) 60 V
B) 81 V
C) 55 V
D) 23 V
E) 0 V

Question 43

FIGURE 20-3
Two point charges of magnitude +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in Figure 20-3.
(a) What is the potential at point A due to these charges?
(b) What is the potential at point B due to these charges?
(c) What is the potential difference between points A and B?

Question 44

At a certain point in space there is a potential of 400 V. What is the potential energy of a +2-μC charge at that point in space?

A) 80 × 10^-6 J
B) 800 J
C) 400 J
D) 200 J
E) 8 × 10^-4 J

Question 45

FIGURE 20-5
Four equal point charges of magnitude 6.00 μC and of varying signs are placed at the corners of a square 2.00 m on each side, as shown in Figure 20-5. What is the electric potential at the center of this square due to these charges?

A) 76.4 kV
B) 0 V
C) 153 kV
D) 61.0 kV
E) 306 kV

Question 46

The potential energy at x = 8 m is -2000 V and at x = 2 m is +400 V. What is the magnitude and direction of the electric field?

A) 200 V/m directed parallel to the +x-axis
B) 300 V/m directed parallel to the +x-axis
C) 400 V/m directed parallel to the +x-axis
D) 500 V/m directed parallel to the +x-axis
E) 600 V/m directed parallel to the +x-axis

Question 47

At a certain point in space the electric potential is 20 V. A 4.0-μC charge is brought from infinity to that point. What is the electric potential energy of this charge at that point?

A) - 80 μJ
B) 80 μJ
C) - 20 μJ
D) 20 μJ
E) 4.0 μJ

Question 48

FIGURE 20-4
Four equal point charges of magnitude 6.00 μC are placed at the corners of a square 2.00 m on each side, as shown in Figure 20-4. What is the electric potential of these charges at the center of this square?

A) 76.4 kV
B) 38.2 kV
C) 306 kV
D) 153 kV
E) 61.0 kV

Question 49

A 2000 V/m electric field is directed along the +x-axis. If the potential at x = 10 m is 800 V, what is the potential at x = 6 m?

A) 8800 V
B) 2000 V
C) 7200 V
D) 4400 V
E) 1600 V

Question 50

The electric potential at the origin of an xy-coordinate system is 40 V. A -8.0-μC charge is brought from x = +∞ to that point. What is the electric potential energy of this charge at the origin?

A) -3.2 × 10^-4 J
B) 3.2 × 10^-4 J
C) -40 μJ
D) 40 μJ
E) 8.0 μJ

Question 51

A charged particle with charge + 5.0 μC is initially at rest. It is accelerated through a potential difference of 500 V. What is the kinetic energy of this charged particle?

A) 2.5 × 10^-3 J/m
B) 2.5 × 10^-3 J
C) 2500 J
D) 2500 J/m
E) 0 J

Question 52

Two point charges of magnitude 4.0 μC and -4.0 μC are situated along the x-axis at x₁ = 2.0 m and x₂ = -2.0 m, respectively. What is the electric potential energy of this system of charges?

A) -36 mJ
B) 36 mJ
C) 0 J
D) -72 mJ
E) 72 mJ

Question 53

An 800 V/m electric field is directed along the +x-axis. If the potential at x = 0 m is 2000 V, what is the potential at x = 2 m?

A) 200 V
B) 400 V
C) 600 V
D) 800 V
E) 1000 V

Question 54

An electron is initially at rest. It is accelerated through a potential difference of 400 V. What is the kinetic energy of this electron?

A) 6.4 × 10^-17 J
B) 400 J
C) 0 J
D) 800 J
E) 6400 J

Question 55

Two equal point charges of magnitude 4.0 μC are situated along the x-axis at x₁ = -2.0 m and x₂ = -2.0 m. What is the electric potential energy of this system of charges?

A) -36 mJ
B) 36 mJ
C) 0 J
D) -72 mJ
E) 72 mJ

Question 56

An electron, initially at rest is accelerated through a potential difference of 550 V. What is the speed of the electron due to this potential difference?

A) 1.44 × 10⁶ m/s
B) 1.59 × 10⁶ m/s
C) 6.10 × 10⁶ m/s
D) 18.7 × 10⁶ m/s
E) 13.9 × 10⁶ m/s

Question 57

Three charges are placed as follows along the x- and y-axes of an xy-coordinate system: q₁ = 2.00 μC at x₁ = 0 m, q₂ = 4.00 μC at x₂ = 3.00 m, and q₃ = 6.00 μC at y = 4.00 m. What is the electric potential energy of this system of charges?

A) -94.2 mJ
B) 94.2 mJ
C) 0 J
D) -90.0 mJ
E) 90.0 mJ

Question 58

Three charges are placed as follows along the x- and y-axis of an xy-coordinate system: q₁ = 2.00 μC at x₁ = 0 m, q₂ = -4.00 μC at x₂ = 3.00 m, and q₃ = 6.00 μC at y = 4.00 m. What is the electric potential energy of this system of charges?

A) -40.2 mJ
B) 40.2 mJ
C) -94.2 mJ
D) 94.2 mJ
E) 0 J

Question 59

A proton falls through a potential drop of 400 V. How much is the change of potential energy of this proton in falling through this potential drop?

A) 6.4 × 10^-16 J
B) -6.4 × 10^-16 J
C) 17 × 10^-16 J
D) -4000 J
E) 4000 J

Question 60

The potential difference between the plates of a parallel plate capacitor is 4.00 V. If the plate separation for this capacitor is 6.00 cm, what is the intensity of the electric field between the plates of this capacitor?

Question 61

FIGURE 20-9
Two point charges of +2.00 μC and +4.00 μC are placed at the origin and at y = -0.300 m, as shown in Figure 20-9. What is the electric field potential at a point P at a position x = 0.400 m due to these charges?

A) 117 × 10³ V
B) -11.7 × 10³ V
C) 11.7 × 10³ V
D) -36.0 × 10³ V
E) 36.0 × 10³ V

Question 62

A 4.0-μC charge is situated at the origin of an xy-coordinate system. What is the potential difference between a point x₁ = 2.0 m and another point x₂ = 5.0 m because of this charge?

A) - 11 × 10³ V
B) 11 × 10³ V
C) - 33 × 10³ V
D) 33 × 10³ V
E) 0 V

Question 63

FIGURE 20-10
Two point charges of magnitude +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in Figure 20-10. What is the potential at point B due to these two charges?

A) 1.13 × 10³ V
B) 11.3 × 10³ V
C) -11.3 × 10³ V
D) -113 × 10³ V
E) 113 × 10³ V

Question 64

FIGURE 20-7
Two identical charges of magnitude 6.0 μC are placed at the corners of the base of an equilateral triangle, as shown in Figure 20-7. What is the electric potential at the vertex, P, of the triangle due to these charges?

A) 54 kV
B) 108 V
C) 0 V
D) 90 kV
E) 27 kV

Question 65

A 4.0-μC charge is situated at the origin of an xy-coordinate system. What is the potential difference between a point x = 4.0 m and y = -4.0 m because of this charge?

A) 18 × 10³ V
B) -18 × 10³ V
C) 0 V
D) 36 × 10³ V
E) -36 × 10³ V

Question 66

Point charges of + 2.0 μC, + 4.0 μC, and + 6.0 μC are placed at the origin, the point y = -0.30 m, and x = 0.40 m, respectively. What is the electric potential energy of the system?

A) 94.0 mJ
B) 94.0 J/C
C) 940 mJ
D) 0 J
E) 940 J/C

Question 67

A 4.0-μC charge is situated at the origin of an xy-coordinate system. What is the magnitude and direction of the electric potential at x = 6.0 m?

A) 1500 V along the +x-axis
B) 4000 V along the +x-axis
C) 4000 V with no direction, as it is a scalar quantity
D) 6000 V along the +x-axis
E) 6000 V with no direction, as it is a scalar quantity

Question 68

FIGURE 20-8
Two charges of magnitude 6.0 μC, but opposite signs, are placed at the corners of the base of an equilateral triangle, as shown in Figure 20-8. What is the electric potential at the vertex, P, of the triangle due to these charges?

A) 27 kV
B) 54 kV
C) 90 kV
D) 108 V
E) 0 V

Question 69

A +8.00-μC charge is situated along the +y-axis at y = 0.400 m. What is the electric potential at the origin because of this charge?

A) +180 × 10³ V
B) -180 × 10³ V
C) 0 V
D) -288 × 10³ V
E) +288 × 10³ V

Question 70

Two point charges of magnitude 4.0 μC and -4.0 μC are situated along the x-axis at x₁ = 2.0 m and x₂ = -2.0 m, respectively. What is the electric potential at the origin of the xy-coordinate system?

A) -36 × 10³ V
B) 0 V
C) 36 × 10³ V
D) -48 × 10³ V
E) 48 × 10³ V

Question 71

A -4.0-μC charge is situated at the origin of an xy-coordinate system. Another -4.0 μC charge is at y = 4.0 m. What is the electric potential at a point x = 3.0 m due to these two charges?

A) -3600 V
B) 3600 V
C) -4800 V
D) 4800 V
E) 0 V

Question 72

FIGURE 20-10
Two point charges of magnitude +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in Figure 20-10. What is the potential at point A due to these charges?

A) +9.00 × 10³ V
B) -9.00 × 10³ V
C) -90.0 × 10³ V
D) +90.0 × 10³ V
E) +900 × 10³ V

Question 73

Two equal point charges of magnitude 4.0 μC are situated along the x-axis at x₁ = -2.0 m and x₂ = 2.0 m. What is the electric potential at the origin of the xy-coordinate system?

A) 0 V
B) -36 × 10³ V
C) 36 × 10³ V
D) -48 × 10³ V
E) 48 × 10³ V

Question 74

A -4.0-μC charge is situated at the origin of an xy-coordinate system. What is the potential difference between a point x = 4.0 m and y = 2.0 m because of this charge?

A) -9.0 × 10³ V
B) 9.0 × 10³ V
C) -36 × 10³ V
D) 36 × 10³ V
E) 0 V

Question 75

FIGURE 20-6
Four equal point charges of magnitude 6.00 μC and of varying signs are placed at the corners of a square 2.00 m on each side, as shown in Figure 20-6. What is the electric potential at the center of the square?

A) 0 V
B) 76.4 kV
C) 152.7 kV
D) 61.0 kV
E) 306 kV

Question 76

Two point charges q₁ = 4.0 μC and q₂ = -8.0 μC are placed along the x-axis at x₁ = 0 m and x₂ = 0.20 m, respectively. What is the electric potential energy of this system of charges?

A) +1.4 J
B) -1.4 J
C) -32 J
D) 4.0 J
E) -4.0 J

Question 77

Three equal charges of magnitude + 4.00 μC are placed at the corners of an equilateral triangle of side 2.00 cm. What is the electric field potential energy of the system of these charges?

A) 90.0 J
B) 900 mJ
C) 0 J
D) 216 mJ
E) 21.6 J

Question 78

The absolute value of the electric potential at a distance of 4 m from a certain point charge is 200 V. What is the absolute value of this potential at a distance of 8 m from the same point charge?

A) 50 V
B) 400 V
C) 100 V
D) 200 V
E) 600 V

Question 79

A -4.0-μC charge is situated at the origin of an xy-coordinate system. What is the magnitude and direction of an electric potential at x = 6.0 m?

A) 1500 V along the +x-axis
B) 6000 V along the +x-axis
C) -6000 V with no direction
D) 4000 V along the +x-axis
E) 4000 V with no direction

Question 80

A 4.0-μC charge is situated at the origin of an xy-coordinate system. What is the potential difference between the points x = 4.0 m and y = 2.0 m because of this charge?

A) -9.0 × 10³ V
B) 9.0 × 10³ V
C) -36 × 10³ V
D) 36 × 10³ V
E) 0 V