Deck 19: Electric Potential Energy and the Electric Potential

Question 1

Two point charges are held at the corners of a rectangle as shown in the figure. The lengths of sides of the rectangle are 0.050 m and 0.150 m. Assume that the electric potential is defined to be zero at infinity.

-What is the electric potential energy of a +3.0 $\mu$ C charge placed at corner A?

A)0.10 J
B)0.18 J
C)2.3 J
D)3.6 J
E)zero joules

Answer 1

0.18 J

Question 2

Two point charges are located at two of the vertices of a right triangle, as shown in the figure. If a third charge -q is brought from infinity and placed at the third vertex, what will its electric potential energy be? Use the following values: a = 0.35 m; b = 0.65 m, and q = 3.0 × 10^-6 C.

A)-1.7 J
B)-0.14 J
C)-0.028 J
D)+0.85 J
E)+1.7 J

Answer 2

-0.14 J

Question 3

The electric potential at a certain point is space is 12 V. What is the electric potential energy of a -3.0 $\mu$ C charge placed at that point?

A)+4 $\mu$ J
B)-4 $\mu$ J
C)+36 $\mu$ J
D)-36 $\mu$ J
E)zero µJ

Answer 3

-36 $\mu$ J

Question 4

A proton moves in a constant electric field from point A to point B. The magnitude of the electric field is 6.4 × 10⁴ N/C; and it is directed as shown in the drawing, the direction opposite to the motion of the proton. If the distance from point A to point B is 0.50 m, what is the change in the proton's electric potential energy, EPE_A - EPE_B?

A)-2.4 × 10^-15 J
B)-3.2 × 10^-15 J
C)+1.2 × 10^-15 J
D)-5.1 × 10^-15 J
E)-1.8 × 10^-15 J

Question 5

Complete the following statement: The electron volt is a unit of

A)energy.
B)electric field strength.
C)electric force.
D)electric potential difference.
E)electric power.

Question 6

Two point charges are held at the corners of a rectangle as shown in the figure. The lengths of sides of the rectangle are 0.050 m and 0.150 m. Assume that the electric potential is defined to be zero at infinity.
Determine the electric potential at corner A.

A)+6.0 × 10⁴ V
B)-2.4 × 10⁵ V
C)+4.6 × 10⁵ V
D)-7.8 × 10⁵ V
E)zero volts

Question 7

P and Q are points within a uniform electric field that are separated by a distance of 0.2 m as shown. The potential difference between P and Q is 75 V.

-How much work is required to move a +150 $\mu$ C point charge from P to Q?

A)0.023 J
B)0.056 J
C)75 J
D)140 J
E)2800 J

Question 8

Which one of the following statements is true concerning the work done by an external force in moving an electron at constant speed between two points in an electrostatic field?

A)The work done is always zero joules.
B)The work done is always positive.
C)The work done only depends on the speed of the electron.
D)The work done depends on the total distance covered.
E)The work done depends only on the displacement of the electron.

Question 9

Which one of the following statements best explains why it is possible to define an electrostatic potential in a region of space that contains an electrostatic field?

A)Work must be done to bring two positive charges closer together.
B)Like charges repel one another and unlike charges attract one another.
C)A positive charge will gain kinetic energy as it approaches a negative charge.
D)The work required to bring two charges together is independent of the path taken.
E)A negative charge will gain kinetic energy as it moves away from another negative charge.

Question 10

Two point charges are held at the corners of a rectangle as shown in the figure. The lengths of sides of the rectangle are 0.050 m and 0.150 m. Assume that the electric potential is defined to be zero at infinity.
What is the potential difference, V_B - V_A, between corners A and B?

A)-8.4 × 10⁵ V
B)-7.8 × 10⁵ V
C)-7.2 × 10⁵ V
D)-6.0 × 10⁵ V
E)zero volts

Question 11

Three point charges -Q, -Q, and +3Q are arranged along a line as shown in the sketch. What is the electric potential at the point P?

A)+kQ/R
B)-2kQ/R
C)-1.6kQ/R
D)+1.6kQ/R
E)+4.4kQ/R

Question 12

Two positive point charges are separated by a distance R. If the distance between the charges is reduced to R/2, what happens to the total electric potential energy of the system?

A)The total electric potential energy is doubled.
B)The total electric potential energy remains the same.
C)The total electric potential energy increases by a factor of 4.
D)The total electric potential energy is reduced to one-half of its original value.
E)The total electric potential energy is reduced to one-fourth of its original value.

Question 13

A completely ionized beryllium atom (net charge = +4e) is accelerated through a potential difference of 6.0 V. What is the increase in kinetic energy of the atom?

A)zero eV
B)0.67 eV
C)4.0 eV
D)6.0 eV
E)24 eV

Question 14

P and Q are points within a uniform electric field that are separated by a distance of 0.2 m as shown. The potential difference between P and Q is 75 V.
Determine the magnitude of this electric field.

A)15 V/m
B)75 V/m
C)375 V/m
D)750 V/m
E)1100 V/m

Question 15

A charge q = -6.0 µC is moved 0.25 m horizontally to point P in a region where an electric field is 250 V/m directed vertically, as shown. What is the change in the electric potential energy of the charge?

A)-2.4 × 10^-5 J
B)-1.5 × 10^-4 J
C)zero joules
D)+1.5 × 10^-4 J
E)+2.4 × 10^-5 J

Question 16

A +1.0 $\mu$ C point charge is moved from point A to B in the uniform electric field as shown. Which one of the following statements is necessarily true concerning the potential energy of the point charge?

A)The potential energy increases by 6.0 × 10^-6J.
B)The potential energy decreases by 6.0 × 10^-6 J.
C)The potential energy decreases by 9.0 × 10^-6 J.
D)The potential energy increases by 10.8 × 10^-6 J.
E)The potential energy decreases by 10.8 × 10^-6 J.

Question 17

Four point charges are individually brought from infinity and placed at the corners of a square as shown in the figure. Each charge has the identical value +Q. The length of the diagonal of the square is 2a.
What is the magnitude of the electric field at P, the center of the square?

A)kQ/a²
B)2kQ/a²
C)4kQ/a²
D)kQ/4a²
E)zero V/m

Question 18

If the work required to move a +0.25 C charge from point A to point B is +175 J, what is the potential difference between the two points?

A)zero volts
B)44 V
C)88 V
D)350 V
E)700 V

Question 19

Four point charges are individually brought from infinity and placed at the corners of a square as shown in the figure. Each charge has the identical value +Q. The length of the diagonal of the square is 2a.
What is the electric potential at P, the center of the square?

A)kQ/a
B)2kQ/a
C)4kQ/a
D)kQ/4a
E)zero volts

Question 20

Two point charges are arranged along the x axis as shown in the figure. At which of the following values of x is the electric potential equal to zero? Note: At infinity, the electric potential is zero.

A)+0.05 m
B)+0.29 m
C)+0.40 m
D)+0.54 m
E)+0.71 m

Question 21

The sketch below shows cross sections of equipotential surfaces between two charged conductors that are shown in solid grey. Various points on the equipotential surfaces near the conductors are labeled A, B, C, ..., I.
What is the magnitude of the electric field at point A?

A)10 V/m
B)25 V/m
C)30 V/m
D)75 V/m
E)100 V/m

Question 22

Two charges of opposite sign and equal magnitude Q = 0.82 C are held 2.0 m apart as shown in the figure.
Determine the electric potential at the point P.

A)1.1 × 10⁹ V
B)2.2 × 10⁹ V
C)4.5 × 10⁹ V
D)9.0 × 10⁹ V
E)zero volts

Question 23

The sketch below shows cross sections of equipotential surfaces between two charged conductors that are shown in solid grey. Various points on the equipotential surfaces near the conductors are labeled A, B, C, ..., I.

-How much work is required to move a -1.0 $\mu$ C charge from B to D to C?

A)+2.0 × 10^-5 J
B)-2.0 × 10^-5 J
C)+4.0 × 10^-5 J
D)-4.0 × 10^-5 J
E)zero joules

Question 24

The sketch below shows cross sections of equipotential surfaces between two charged conductors that are shown in solid grey. Various points on the equipotential surfaces near the conductors are labeled A, B, C, ..., I.
What is the direction of the electric field at B?

A)toward A
B)toward D
C)toward C
D)into the page
E)up and out of the page

Question 25

The sketch below shows cross sections of equipotential surfaces between two charged conductors that are shown in solid grey. Various points on the equipotential surfaces near the conductors are labeled A, B, C, ..., I.
At which of the labeled points will the electric field have the greatest magnitude?

A)G
B)I
C)A
D)H
E)D

Question 26

The sketch below shows cross sections of equipotential surfaces between two charged conductors that are shown in solid grey. Various points on the equipotential surfaces near the conductors are labeled A, B, C, ..., I.
What is the potential difference between points B and E?

A)10 V
B)30 V
C)40 V
D)50 V
E)60 V

Question 27

The sketch below shows cross sections of equipotential surfaces between two charged conductors that are shown in solid grey. Various points on the equipotential surfaces near the conductors are labeled A, B, C, ..., I.

-How much work is required to move a -1.0 $\mu$ C charge from A to E?

A)+3.0 × 10^-5 J
B)-4.0 × 10^-5 J
C)+7.0 × 10^-5 J
D)-7.0 × 10^-5 J
E)zero joules

Question 28

Which one of the following statements concerning electrostatic situations is false?

A)E is zero everywhere inside a conductor.
B)Equipotential surfaces are always perpendicular to E.
C)Zero work is needed to move a charge along an equipotential surface.
D)If V is constant throughout a region of space, then E must be zero in that region.
E)No force component acts along the path of a charge as it is moved along an equipotential surface.

Question 29

Two point charges are separated by 1.00 × 10-2 m. One charge is -2.8 × 10-8 C; and the other is +2.8 × 10-8 C. The points A and B are located 2.5 × 10-3 m from the lower and upper point charges as shown.
If a proton, which has a charge of +1.60 × 10^-19 C, is moved from rest at A to rest at B, what is change in electrical potential energy of the proton?

A)+2.1 × 10^-14 J
B)+3.2 × 10^-14 J
C)- 4.3 × 10^-15 J
D)- 5.4 × 10^-15 J
E)zero joules

Question 30

The sketch below shows cross sections of equipotential surfaces between two charged conductors that are shown in solid grey. Various points on the equipotential surfaces near the conductors are labeled A, B, C, ..., I.

-A point charge gains 50 $\mu$ J of electric potential energy when it is moved from point D to point G. Determine the magnitude of the charge.

A)1.0 $\mu$ C
B)1.3 $\mu$ C
C)25 $\mu$ C
D)50 $\mu$ C
E)130 $\mu$ C

Question 31

The sketch shows cross sections of equipotential surfaces between two charged conductors shown in solid black. Points on the equipotential surfaces near the conductors are labeled A, B, C, ..., H.
How much work is required to move a +6.0 µC point charge from B to F to D to A?

A)+1.2 × 10^-3 J
B)-1.2 × 10^-3 J
C)+3.6 × 10^-3 J
D)-3.6 × 10^-3 J
E)zero joules

Question 32

The sketch below shows cross sections of equipotential surfaces between two charged conductors that are shown in solid grey. Various points on the equipotential surfaces near the conductors are labeled A, B, C, ..., I.
A positive point charge is placed at F. Complete the following statement: When it is released,

A)no force will be exerted on it.
B)a force will cause it to move toward E.
C)a force will cause it to move toward G.
D)a force will cause it to move away from E.
E)it would subsequently lose kinetic energy.

Question 33

Two charges of opposite sign and equal magnitude Q = 0.82 C are held 2.0 m apart as shown in the figure.
How much work is required to move a 1.0 C charge from infinity to the point P?

A)zero joules
B)2.2 × 10⁹ J
C)4.5 × 10⁹ J
D)9.0 × 10⁹ J
E)infinity

Question 34

The sketch shows cross sections of equipotential surfaces between two charged conductors shown in solid black. Points on the equipotential surfaces near the conductors are labeled A, B, C, ..., H.
What is the direction of the electric field at point E?

A)toward G
B)toward B
C)toward H
D)toward C
E)toward F

Question 35

The sketch shows cross sections of equipotential surfaces between two charged conductors shown in solid black. Points on the equipotential surfaces near the conductors are labeled A, B, C, ..., H.
What is the magnitude of the potential difference between points A and H?

A)100 V
B)200 V
C)400 V
D)600 V
E)700 V

Question 36

Which one of the following statements best describes the equipotential surfaces surrounding a point charge?

A)The equipotential surfaces are planes extending radially outward from the charge.
B)The equipotential surfaces are curved planes surrounding the charge, but only one passes through the charge.
C)The equipotential surfaces are concentric cubes with the charge at the center.
D)The equipotential surfaces are concentric spheres with the charge at the center.
E)The equipotential surfaces are concentric cylinders with the charge on the axis at the center.

Question 37

A charge is located at the center of sphere A (radius R_A = 0.0010 m), which is in the center of sphere B (radius R_B = 0.0012 m). Spheres A and B are both equipotential surfaces. What is the ratio V_A/V_B of the potentials of these surfaces?

A)0.42
B)0.83
C)1.2
D)1.4
E)2.4

Question 38

Two point charges are separated by 1.00 × 10-2 m. One charge is -2.8 × 10-8 C; and the other is +2.8 × 10-8 C. The points A and B are located 2.5 × 10-3 m from the lower and upper point charges as shown.
If an electron, which has a charge of 1.60 × 10^-19 C, is moved from rest at A to rest at B, what is the change in electric potential energy of the electron?

A)+4.3 × 10^-15 J
B)+5.4 × 10^-15 J
C)-2.1 × 10^-14 J
D)-3.2 × 10^-14 J
E)zero joules

Question 39

The sketch below shows cross sections of equipotential surfaces between two charged conductors that are shown in solid grey. Various points on the equipotential surfaces near the conductors are labeled A, B, C, ..., I.
At which of the labeled points will an electron have the greatest potential energy?

A)A
B)D
C)G
D)H
E)I

Question 40

Two charges of opposite sign and equal magnitude Q = 0.82 C are held 2.0 m apart as shown in the figure.
Determine the magnitude of the electric field at the point P.

A)2.8 × 10⁸ V/m
B)4.4 × 10⁸ V/m
C)5.6 × 10⁸ V/m
D)9.2 × 10⁸ V/m
E)zero V/m

Question 41

A capacitor is initially charged to 3 V. It is then connected to a 6 V battery. What is the ratio of the final to the initial energy stored in the capacitor?

A)3
B)5
C)6
D)7
E)9

Question 42

A uniform electric field of 8 V/m exists between the plates of a parallel plate capacitor. How much work is required to move a +20 $\mu$ C point charge from the negative plate to the positive plate if the plate separation is 0.050 m?

A)0.4 J
B)1.6 J
C)8 × 10^-4 J
D)8 × 10^-5 J
E)8 × 10^-6 J

Question 43

A parallel plate capacitor has plates of area 2.0 × 10^-3 m² and plate separation 1.0 × 10^-4 m. Determine the capacitance of this system if air fills the volume between the plates.

A)1.1 × 10^-10 F
B)1.8 × 10^-10 F
C)3.2 × 10^-10 F
D)4.4 × 10^-10 F
E)5.3 × 10^-10 F

Question 44

A parallel plate capacitor has a potential difference between its plates of 1.6 V and a plate separation distance of 2.5 mm. What is the magnitude of the electric field if a material that has a dielectric constant of 3.4 is inserted between the plates?

A)110 V/m
B)170 V/m
C)190 V/m
D)240 V/m
E)290 V/m

Question 45

The plates of a parallel plate capacitor each have an area of 0.40 m² and are separated by a distance of 0.02 m. They are charged until the potential difference between the plates is 3000 V. The charged capacitor is then isolated.
Determine the value of the capacitance.

A)9.0 × 10^-11 F
B)1.8 × 10^-10 F
C)3.6 × 10^-10 F
D)4.8 × 10^-10 F
E)6.4 × 10^-10 F

Question 46

A capacitor has a very large capacitance of 10 F. The capacitor is charged by placing a potential difference of 2 V between its plates. How much energy is stored in the capacitor?

A)2000 J
B)500 J
C)100 J
D)40 J
E)20 J

Question 47

The plates of a parallel plate capacitor each have an area of 0.40 m² and are separated by a distance of 0.02 m. They are charged until the potential difference between the plates is 3000 V. The charged capacitor is then isolated.

-How much work is required to move a -4.0 $\mu$ C charge from the negative plate to the positive plate of this system?

A)-1.2 × 10^-2 J
B)+1.2 × 10^-2 J
C)-2.4 × 10^-2 J
D)+2.4 × 10^-2 J
E)-5.4 × 10^-2 J

Question 48

Which one of the following changes will necessarily increase the capacitance of a capacitor?

A)decreasing the charge on the plates
B)increasing the charge on the plates
C)placing a dielectric between the plates
D)increasing the potential difference between the plates
E)decreasing the potential difference between the plates

Question 49

The plates of a parallel plate capacitor each have an area of 0.40 m² and are separated by a distance of 0.02 m. They are charged until the potential difference between the plates is 3000 V. The charged capacitor is then isolated.
Determine the magnitude of the electric field between the capacitor plates.

A)60 V/m
B)120 V/m
C)1.0 × 10⁵ V/m
D)1.5 × 10⁵ V/m
E)3.0 × 10⁵ V/m

Question 50

The plates of a parallel plate capacitor each have an area of 0.40 m² and are separated by a distance of 0.02 m. They are charged until the potential difference between the plates is 3000 V. The charged capacitor is then isolated.
Suppose that a dielectric sheet is inserted to completely fill the space between the plates and the potential difference between the plates drops to 1000 V. Determine the dielectric constant.

A)0.333
B)0.666
C)3.0
D)6.0
E)2000

Question 51

A parallel plate capacitor with plates of area A and plate separation d is charged so that the potential difference between its plates is V. If the capacitor is then isolated and its plate separation is decreased to d/2, what happens to the potential difference between the plates?

A)The final potential difference is 4V.
B)The final potential difference is 2V.
C)The final potential difference is 0.5V.
D)The final potential difference is 0.25V.
E)The final potential difference is V.

Question 52

A parallel plate capacitor has plates of area 2.0 × 10^-3 m² and plate separation 1.0 × 10^-4 m. Air fills the volume between the plates. What potential difference is required to establish a 3.0 $\mu$ C charge on the plates?

A)9.3 × 10² V
B)2.4 × 10⁴ V
C)1.7 × 10⁴ V
D)6.9 × 10³ V
E)3.7 × 10⁵ V

Question 53

A parallel plate capacitor is fully charged at a potential V. A dielectric with constant $\kappa$ = 4 is inserted between the plates of the capacitor while the potential difference between the plates remains constant. Which one of the following statements is false concerning this situation?

A)The energy density remains unchanged.
B)The capacitance increases by a factor of four.
C)The stored energy increases by a factor of four.
D)The charge on the capacitor increases by a factor of four.
E)The electric field between the plates increases by a factor of four.

Question 54

A parallel plate capacitor with plates of area A and plate separation d is charged so that the potential difference between its plates is V. If the capacitor is then isolated and its plate separation is decreased to d/2, what happens to its capacitance?

A)The capacitance is twice its original value.
B)The capacitance is four times its original value.
C)The capacitance is eight times its original value.
D)The capacitance is one half of its original value.
E)The capacitance is unchanged.

Question 55

The plates of a parallel plate capacitor each have an area of 0.40 m² and are separated by a distance of 0.02 m. They are charged until the potential difference between the plates is 3000 V. The charged capacitor is then isolated.
Determine the magnitude of the charge on either capacitor plate.

A)1.8 × 10^-7 C
B)2.7 × 10^-7 C
C)4.9 × 10^-7 C
D)5.4 × 10^-7 C
E)6.8 × 10^-7 C

Question 56

A potential difference of 120 V is established between two parallel metal plates. The magnitude of the charge on each plate is 0.020 C. What is the capacitance of this capacitor?

A)170 µF
B)24 µF
C)7.2 µF
D)0.12 F
E)2.4 F

Question 57

Complete the following statement: When a dielectric with constant $\kappa$ is inserted between the plates of a charged isolated capacitor

A)the capacitance is reduced by a factor $\kappa$ .
B)the charge on the plates is reduced by a factor of $\kappa$ .
C)the charge on the plates is increased by a factor of $\kappa$ .
D)the electric field between the plates is reduced by a factor of $\kappa$ .
E)the potential difference between the plates is increased by a factor of $\kappa$ .

Question 58

The magnitude of the charge on the plates of an isolated parallel plate capacitor is doubled. Which one of the following statements is true concerning the capacitance of this parallel-plate system?

A)The capacitance is decreased to one half of its original value.
B)The capacitance is increased to twice its original value.
C)The capacitance remains unchanged.
D)The capacitance depends on the electric field between the plates.
E)The capacitance depends on the potential difference across the plates.

Question 59

The plates of a parallel plate capacitor each have an area of 0.40 m² and are separated by a distance of 0.02 m. They are charged until the potential difference between the plates is 3000 V. The charged capacitor is then isolated.
Suppose that a dielectric sheet is inserted to completely fill the space between the plates and the potential difference between the plates drops to 1000 V. What is the capacitance of the system after the dielectric is inserted?

A)1.8 × 10^-10 F
B)2.7 × 10^-10 F
C)5.4 × 10^-10 F
D)6.2 × 10^-10 F
E)6.8 × 10^-10 F

Question 60

The effective area of each plate of a parallel plate capacitor is 2.1 m². The capacitor is filled with neoprene rubber ( $\kappa$ = 6.4). When a 6.0-V potential difference exists across the plates of the capacitor, the capacitor stores 4.0 µC of charge. Determine the plate separation of the capacitor.

A)7.2 × 10^-5 m
B)3.0 × 10^-4 m
C)1.8 × 10^-4 m
D)5.3 × 10^-4 m
E)8.2 × 10^-5 m

Question 61

Two positive charges are located at points A and B as shown in the figure. The distance from each charge to the point P is a = 2.0 m.
Determine the electric potential at the point P.

A)1.35 × 10⁴ V
B)1.89 × 10⁴ V
C)2.30 × 10⁴ V
D)2.70 × 10⁴ V
E)3.68 × 10⁴ V

Question 62

The figure below shows four parallel plate capacitors: A, B, C, and D. Each capacitor carries the same charge q and has the same plate area A. As suggested by the figure, the plates of capacitors A and C are separated by a distance d while those of B and D are separated by a distance 2d. Capacitors A and B are maintained in vacuum while capacitors C and D contain dielectrics with constant  = 5.
Which list below places the capacitors in order of increasing capacitance?

A)A, B, C, D
B)B, A, C, D
C)A, B, D, C
D)B, A, D, C
E)D, C, B, A

Question 63

The figure below shows four parallel plate capacitors: A, B, C, and D. Each capacitor carries the same charge q and has the same plate area A. As suggested by the figure, the plates of capacitors A and C are separated by a distance d while those of B and D are separated by a distance 2d. Capacitors A and B are maintained in vacuum while capacitors C and D contain dielectrics with constant  = 5.
Which capacitor is storing the greatest amount of electric potential energy?

A)A
B)B
C)C
D)D
E)Since all four carry the same charge, each will store the same amount of energy.

Question 64

The figure below shows four parallel plate capacitors: A, B, C, and D. Each capacitor carries the same charge q and has the same plate area A. As suggested by the figure, the plates of capacitors A and C are separated by a distance d while those of B and D are separated by a distance 2d. Capacitors A and B are maintained in vacuum while capacitors C and D contain dielectrics with constant  = 5.
Which capacitor has the largest potential difference between its plates?

A)A
B)B
C)C
D)D
E)A and D are the same and larger than B or C.

Question 65

Two positive charges are located at points A and B as shown in the figure. The distance from each charge to the point P is a = 2.0 m.
Which statement is true concerning the direction of the electric field at P?

A)The direction is toward A.
B)The direction is toward B.
C)The direction is directly away from A.
D)The direction makes a 45° angle above the horizontal direction.
E)The direction makes a 135° angle below the horizontal direction.

Question 66

An isolated system consists of two conducting spheres A and B. Sphere A has five times the radius of sphere B. Initially, the spheres are given equal amounts of positive charge and are isolated from each other. The two spheres are then connected by a conducting wire.
Note: The potential of a sphere of radius R that carries a charge Q is V = kQ/R, if the potential at infinity is zero.
Which one of the following statements is true after the spheres are connected by the wire?

A)The electric potential of A is 1/25 as large as that of B.
B)The electric potential of A equals that of B.
C)The electric potential of A is 25 times larger than that of B.
D)The electric potential of A is 1/5 as large as that of B.
E)The electric potential of A is five times larger than that of B.

Question 67

An isolated system consists of two conducting spheres A and B. Sphere A has five times the radius of sphere B. Initially, the spheres are given equal amounts of positive charge and are isolated from each other. The two spheres are then connected by a conducting wire.
Note: The potential of a sphere of radius R that carries a charge Q is V = kQ/R, if the potential at infinity is zero.
Determine the ratio of the charge on sphere A to that on sphere B, q_A/q_B, after the spheres are connected by the wire.

A)1
B)1/5
C)5
D)25
E)1/25

Question 68

Two positive charges are located at points A and B as shown in the figure. The distance from each charge to the point P is a = 2.0 m.
Suppose that the charges are rearranged as shown in this figure. Which one of the following statements is true for this new arrangement?

A)The electric field will be zero, but the electric potential remains unchanged.
B)Both the electric field and the electric potential are zero at P.
C)The electric field will remain unchanged, but the electric potential will be zero.
D)The electric field will remain unchanged, but the electric potential will decrease.
E)Both the electric field and the electric potential will be changed and will be non-zero.

Question 69

At what distance from a 1.0-C charge is the electric potential equal to 12 V?

A)8.3 × 10⁷ m
B)7.5 × 10⁸ m
C)9.0 × 10⁸ m
D)1.1 × 10⁹ m
E)3.0 × 10⁹ m

Question 70

Two positive charges are located at points A and B as shown in the figure. The distance from each charge to the point P is a = 2.0 m.
Determine the magnitude of the electric field at the point P.

A)3.38 × 10³ V/m
B)6.75 × 10³ V/m
C)9.55 × 10³ V/m
D)1.35 × 10⁴ V/m
E)2.70 × 10⁴ V/m