Deck 23: Electric Potential

Question 1

Three negative charges of equal magnitudes are positioned along the x-axis at x = -a, x=0, and x = +a respectively. The charge located at x=0 is moved away along the y-axis to a position (x,y) = (0, +a). How does the potential energy of the system of charges change as a result?

A)The potential energy may increase or decrease depending on the magnitude of the charges.
B)The potential energy increases.
C)The potential energy decreases.
D)The potential energy stays the same.
E)More information is needed to answer the question.

Answer 1

The potential energy decreases.

Question 2

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.

Answer 2

from low potential to high potential.

Question 3

The component of the electric field in any direction is equal to the negative of the rate of change of the electric potential with distance in that direction.

Answer 3

True

Question 4

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 5

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

Question 6

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.
E)Not enough information is given to make a statement about the work involved.

Question 7

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 8

If the electric field is zero in some region of space is the electric potential zero there as well? Explain.

Question 9

An equipotential surface must be

A)parallel to the electric field at every point.
B)oriented 30° with respect to the electric field at every point.
C)oriented 60° with respect to the electric field at every point.
D)perpendicular to the electric field at every point.
E)equal to the electric field at every point.

Question 10

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

Question 11

The potential outside a uniformly charged sphere is the same as if all the charge were concentrated at its center.

Question 12

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

Question 13

The potential of a uniformly charged sphere is lowest at

A)infinity.
B)a distance from the sphere equal to its radius.
C)a distance from the sphere equal to its diameter.
D)the surface of the sphere.
E)the center of the sphere.

Question 14

All points on the perpendicular bisector of the line joining two equal but opposite charges have a potential of zero.

Question 15

Explain why equipotential surfaces are always perpendicular to the electric field vectors.

Question 16

The direction in which the potential changes at the greatest rate is in the direction

A)of the gradient of the potential.
B)perpendicular to the electric field.
C)perpendicular to the gradient of the potential.
D)of the partial derivative with respect to x.
E)cannot be determined

Question 17

The change in electric potential energy, Ub - Ua, is the work done on a charge by the electric force as it moves from point a to point b.

Question 18

How much work is required to move a charge from one location on an equipotential to another point on the same equipotential? Explain.

Question 19

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

Question 20

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

Question 21

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 22

The voltage between two parallel plates separated by a distance of 3.0 cm is 120 V. The electric field between the plates is

A)3.6 V/m.
B)up to 4000 V/m depending on position.
C)2000 V/m halfway between the plate.
D)4000 V/m.
E)7.2 V/m.

Question 23

Two uniformly distributed rings of charge, one of total charge Q₁ and radius r₁ and the other of total charge Q₂ and radius r₂, have the same center. The potential at the center is

Question 24

A charge Q distributed uniformly along the edge of a ring of radius R. What is the electric potential due to this charge at a distance x = R from the center the ring along its axis?

Question 25

If the electric field is 12 V/m in the positive x-direction, what is the potential difference between the origin, (0, 0), and the point (3.0 m, 4.0 m)?

A)48 V with the origin at the higher potential
B)48 V with the origin at the lower potential
C)36 V with the origin at the lower potential
D)36 V with the origin at the higher potential
E)cannot be determined

Question 26

If an electric field of magnitude 25 V/m makes an angle of 30° with a path of length 10 m, then the integral of E∙dl over this path has a value of

A)30 V.
B)250 V.
C)125 V.
D)217 V.
E)-250 V.

Question 27

FIGURE 23-1
Fig. 23-1 shows equipotentials surrounding a pair of charges Q_A and Q_B. The value of the potential half-way between the charges is indicated. Which of the statements below applies to the charges?

A)The two charges have the same sign and equal magnitudes.
B)Nothing can be said about the charges.
C)The two charges have the same sign but different magnitudes.
D)The two charges have opposite signs and equal magnitudes.
E)The two charges have opposite signs and different magnitudes.

Question 28

Computer monitors are often referred to as CRT's. CRT stands for

A)computer registration tube.
B)color relay transmission.
C)computer resource transmission.
D)nothing; it's computer jargon.
E)cathode ray tube.

Question 29

A half-ring (semicircle) of uniformly distributed charge Q has radius r. The potential at its center is

Question 30

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 31

Two equal charges Q are separated by a distance d. One of the charges is released and moves away from the other due to the force between them. When the moving charge is a distance 3d from the other charge, what is its kinetic energy?

Question 32

One electron-volt corresponds to

A)8.0 × 10^-20 J.
B)1.6 × 10^-19 J.
C)9.5 × 10^-17 J.
D)1.9 × 10^-16 J.

Question 33

Electric dipoles always consist of two charges that are

A)equal in magnitude; opposite in sign.
B)equal in magnitude; both are negative.
C)equal in magnitude; both are positive.
D)unequal in magnitude; opposite in sign.
E)unequal in magnitude; both are negative.

Question 34

Cathode rays are now known to be

A)electrons.
B)visible light rays.
C)protons.
D)x-rays.
E)short wavelength light rays.

Question 35

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 36

FIGURE 23-2
Fig. 23-2 shows two arcs of a circle on which charges +Q and -Q have been spread uniformly. What is the value of the electric potential at the center of the circle?

Question 37

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 38

Three electric charges Q_A = q, Q_B = -q, and Q_C = -2q are located at the points A (x = + a, y = 0), B (x = -a, y = 0), and C (x = 0, y = +2a) respectively. What is the value of the electric potential at the origin?

Question 39

The energy acquired by a particle carrying a charge equal to that on the electron as a result of moving through a potential difference of one volt is referred to as

A)a joule.
B)an electron-volt.
C)a proton-volt.
D)a neutron-volt.
E)a coulomb.

Question 40

FIGURE 23-3
Two point charges of magnitude +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in Fig. 23-3.
(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 41

FIGURE 23-10
The equipotential surfaces between two spherical conductors are shown in Fig. 23-10, with the value of the potential marked for each line. What is the potential difference between points G and D?

A)+160 V
B)-160 V
C)+320 V
D)0 V
E)None of the other choices is correct.

Question 42

FIGURE 23-12
Fig. 23-12 shows the variations of the electric potential V (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 electric field along the x axis?

A)E is positive from x = -2 to x = 2.
B)E is positive from x = -2 to x = 0, and negative from 0 to x= 2.
C)E is negative from x = -2 to x = 0, and positive from 0 to x= 2.
D)E is negative from x = -2 to x = 2.
E)More information is needed to answer the question.

Question 43

A charge of 1.5 μC is located at (0, 0) and a charge of 2.1 μC is located at (4 m, 0). What is the potential at (4 m, 3 m)?

A)7000 V
B)9000 V
C)9000 V at 37°
D)7000 V at 37°
E)cannot be determined

Question 44

Two charges Q_A = +q and Q_B = - 3q are located on the x-axis at x= 0 and x= d respectively. Where is the electric potential equal to zero?

A)x= 3d/4
B)x= d/3
C)x = d/4
D)x= 2d/3
E)x= d/2

Question 45

Two electric charges Q_A = + 1.0 μC and Q_B= - 2.0 μC are located 0.50 m apart. How much work is needed to move the charges apart and double the distance between them?

A)-36 × 10^-3J
B)+18 × 10^-3
C)0
D)+36 × 10^-3
E)-18 × 10^-3

Question 46

A large plate carries a uniform charge density σ = 8.85 × 10^-9 C/ m². A pattern showing equipotential surfaces with a 5 V potential difference would appear as

A)a series of planes perpendicular to the plate, 1 cm apart.
B)a series of lines perpendicular to the plate, 1 cm apart.
C)a series of lines parallel to the plate, 1 cm apart.
D)a series of circles of radius 1 cm, parallel to the plate.
E)a series of planes parallel to the plate, 1 cm apart.

Question 47

FIGURE 23-9
Two point charges of magnitude +4.0 μC and -4.0 μC are placed as shown in Fig. 23-9. What is the potential difference between points A and B?

A)48 V
B)96 V
C)0 V
D)96 × 10³V
E)48 × 10³V

Question 48

FIGURE 23-11
Fig. 23-11 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 of r is the magnitude of the electric field the largest?

A)from r = 2 m to r = 4 m
B)from r = 4 m to r = 6 m
C)from r = 0 to r = 2 m
D)The magnitude of the field is the same everywhere.
E)More information is needed to answer the question.

Question 49

The equipotential surfaces between two spherical conductors are shown in Fig. 23-10, with the value of the potential marked for each line. What is the potential difference between points A and G?

A)320 V
B)160 V
C)-160 V/m
D)0 V
E)None of the other choices is correct.

Question 50

FIGURE 23-4
Three point charges of -2.00 μC, +4.00 μC, and +6.00 μC are placed along the x axis as shown in Fig. 23-4. What is the electrical potential at point P due to these charges?

A)-307 × 10³V
B)+307 × 10³V
C)-154 × 10³V
D)+154 × 10³V
E)0 V

Question 51

FIGURE 23-5
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 Fig. 23-5. 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 52

FIGURE 23-8
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 Fig. 23-8. 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 53

Four point charges, each of charge 2.5 x 10^-5, are located on the x- and y-axes, one at each of the locations (0, 2.0 m), (0, -2.0 m), (2.0 m, 0), and (-2.0 m, 0). The potential at the origin is

A)2.3 × 10⁵ V.
B)4.5 × 10⁵ V.
C)3.5 × 10⁵ V.
D)1.1 × 10⁵ V.
E)0.

Question 54

FIGURE 23-6
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 Fig. 23-6. 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 55

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 56

Two charges Q_A = +2 μC and Q_B = - 6μC are located on the x-axis at x_A= - 1 cm and x_B= +2 cm respectively. Where should a third charge, Q_C = + 3μC, be placed on the positive x-axis so that the potential at the origin is equal to zero?

A)x = 4 cm
B)x = +1 cm
C)x =+2 cm
D)x = 3 cm
E)x = 5 cm

Question 57

FIGURE 23-7
Two identical charges of magnitude 6.0 μC are placed at the corners of the base of an equilateral triangle, as shown in Fig. 23-7. 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 58

If the potential is given by 6/ x², the x-component of the electric field is

A)-12 x^-3.
B)-6x.
C)12 x^-3.
D)12x.
E)6x.

Question 59

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 × 10³V
D)-48 × 10³V
E)48 × 10³V

Question 60

Three charges Q_A = -2.0 μC, Q_B= 6.0 μC, and Q_C= -4.0 μC are located along the y-axis at y_A= -4.0 cm, y_B = 0, and y_C = 2.0 cm respectively. Calculate the electric potential at the point x = 6.0 cm on the x-axis.

A)0.81 × 10⁵ V
B)-0.81 × 10⁵ V
C)0.41 × 10⁵ V
D)0
E)-0.41 × 10⁵ V

Question 61

If a charge of 12 μC is located 5.0 cm from a charge of 6.5 μC, the potential energy of this arrangement is

A)1.4 × 10^-5 J.
B)14 J.
C)0.
D)2.8 × 10^-4 J.
E)281 J.

Question 62

If an electron is accelerated from rest through a potential difference of 25,000 volts in a color television picture tube, its kinetic energy will be

A)16 J.
B)2.5 × 10⁴ J.
C)4.0 × 10^-5J.
D)1.6 J.
E)4.0 × 10^-15 J.

Question 63

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 64

The electric potential of a charge distribution is given by the equation V(x) = 3 x² y² + y z³ - 2 z³x, where x, y, z are measured in meters and V is measured in volts. Calculate the magnitude of the electric field vector at the position (x,y,z) = (1.0, 1.0, 1.0).

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 65

If the potential is given by V = xy - 3 z^-2, then the electric field has a y-component of

A)x + y - 6 z^-3.
B)-y.
C)-x.
D)x + y.
E)cannot be determined

Question 66

If a particle with a charge of 2 coulombs moves through a potential difference of 12 volts, its change in kinetic energy will a have magnitude of

A)12 J.
B)6 J.
C)8 J.
D)1/6 J.
E)24 J.

Question 67

If an electron is accelerated through a potential difference of 500 V between two parallel plates separated by a distance of 2.0 cm. The change in kinetic energy of the electron during this motion is

A)100 eV.
B)2000 eV.
C)250 eV.
D)500 eV.
E)1000 eV.

Question 68

The electric potential of a charge distribution is given by V(x, y) = 2xy - x² - y. At which point is the electric field equal to zero?

A)x = 0.5, y = 1
B)x = 1, y = 1
C)x = 1, y = 0.5
D)x = 0.5, y = 0.5
E)x =0, y = 0

Question 69

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 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 70

An electron is accelerated from rest through a potential difference of 1000 volts giving it a kinetic energy of

A)1.6 × 10^-22 eV.
B)0.001 eV.
C)1.6 × 10^-16 J.
D)1.6 × 10^-22 J.
E)1.6 × 10^-16 eV.