Deck 21: Electric Potential

Question 1

If the result of your calculation of a quantity has SI units of kg ∙ m/(s² ∙C), that quantity could be

A) an electric field strength.
B) a dielectric constant.
C) an electric potential difference.
D) a capacitance
E) an electric potential energy.

Answer 1

A

Question 2

As an electron moves in the direction the electric field lines

A) it is moving from low potential to high potential and gaining electric potential energy.
B) it is moving from low potential to high potential and losing electric potential energy.
C) it is moving from high potential to low potential and gaining electric potential energy.
D) it is moving from high potential to low potential and losing electric potential energy.
E) both its electric potential and electric potential energy remain constant.

Answer 2

C

Question 3

A proton and an electron are released from rest, with only the electrostatic force acting. Which of the following statements must be true about them as they move toward each other? (There could be more than one correct choice.)

A) Their electric potential energy keeps increasing.
B) Their kinetic energy keeps increasing.
C) Their electric potential energy keeps decreasing.
D) Their kinetic energy keeps decreasing.
E) Their acceleration keeps decreasing.

Answer 3

B, C

Question 4

Two protons are released from rest, with only the electrostatic force acting. Which of the following statements must be true about them as they move apart? (There could be more than one correct choice.)

A) Their electric potential energy keeps increasing.
B) Their kinetic energy keeps increasing.
C) Their electric potential energy keeps decreasing.
D) Their kinetic energy keeps decreasing.
E) Their acceleration keeps decreasing.

Question 5

If the result of your calculation of a quantity has SI units kg ∙ m²/(s² ∙C), that quantity could be

A) an electric field strength.
B) a dielectric constant.
C) an electric potential difference.
D) a capacitance
E) an electric potential energy.

Question 6

The potential (relative to infinity) at the midpoint of a square is 3.0 V when a point charge of +Q is located at one of the corners of the square. What is the potential (relative to infinity) at the center when each of the other corners is also contains a point charge of +Q?

A) 0 V
B) 3.0 V
C) 9.0 V
D) 12 V

Question 7

The electric potential at a distance of 4 m from a certain point charge is 200 V relative to infinity. What is the potential (relative to infinity) at a distance of 2 m from the same charge?

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

Question 8

Two protons are fired toward each other in a particle accelerator, with only the electrostatic force acting. Which of the following statements must be true about them as they move closer together? (There could be more than one correct choice.)

A) Their electric potential energy keeps increasing.
B) Their kinetic energy keeps increasing.
C) Their electric potential energy keeps decreasing.
D) Their kinetic energy keeps decreasing.
E) Their acceleration keeps decreasing.

Question 9

The electron-volt is a unit of

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

Question 10

If the electric field between the plates of a given air-filled capacitor is weakened by removing charge from the plates, the capacitance of that capacitor

A) increases.
B) decreases.
C) does not change.
D) It cannot be determined from the information given.

Question 11

Four charged particles (two having a charge +Q and two having a charge -Q) are arranged in the xy-plane as shown in the figure. The charges are all equidistant from the origin. The amount of work required to move a positively charged particle from point P to point O (both of which are on the z-axis) is

A) zero.
B) positive.
C) negative.
D) depends on the path in which the charged is moved.

Question 12

A proton is accelerated from rest through a potential difference V₀ and gains a speed v₀. If it were accelerated instead through a potential difference of 2V₀, what speed would it gain?

A) 8v₀
B) 4v₀
C) 2v₀
D) v₀

Question 13

If the result of your calculations for a quantity has SI units of C² ∙ s²/(kg ∙ m²), that quantity could be

A) an electric potential difference.
B) a dielectric constant.
C) an electric field strength.
D) a capacitance.
E) an electric potential energy.

Question 14

A region of space contains a uniform electric field, directed toward the right, as shown in the figure. Which statement about this situation is correct?

A) The potential at all three locations is the same.
B) The potentials at points A and B are equal, and the potential at point C is higher than the potential at point A.
C) The potential at points A and B are equal, and the potential at point C is lower than the potential at point A.
D) The potential at point A is the highest, the potential at point B is the second highest, and the potential at point C is the lowest.

Question 15

A hydrogen atom consists of a proton and an electron. If the orbital radius of the electron increases, the electric potential energy of the electron due to the proton

A) increases.
B) decreases.
C) remains the same.
D) depends on the zero point of the potential.

Question 16

Four charged particles (two having a charge +Q and two having a charge -Q) are arranged in the xy-plane, as shown in the figure. These particles are all equidistant from the origin. The electric potential (relative to infinity) at point P on the z-axis due to these particles, is

A) zero.
B) positive.
C) negative.
D) impossible to determine based on the information given.

Question 17

As a proton moves in a direction perpendicular to the electric field lines

A) it is moving from low potential to high potential and gaining electric potential energy.
B) it is moving from low potential to high potential and losing electric potential energy.
C) it is moving from high potential to low potential and gaining electric potential energy.
D) it is moving from high potential to low potential and losing electric potential energy.
E) both its electric potential and electric potential energy remain constant.

Question 18

Which statements must be true about the surface of a charged conductor in which no charge is moving? (There could be more than one correct choice.)

A) The electric field is zero at the surface.
B) The electric potential of the surface is zero.
C) The electric field is constant at the surface.
D) The electric potential is constant over the surface.
E) The electric field is perpendicular to the surface.

Question 19

As a proton moves in the direction the electric field lines

A) it is moving from low potential to high potential and gaining electric potential energy.
B) it is moving from low potential to high potential and losing electric potential energy.
C) it is moving from high potential to low potential and gaining electric potential energy.
D) it is moving from high potential to low potential and losing electric potential energy.
E) both its electric potential and electric potential energy remain constant.

Question 20

If the electric potential at a point in space is zero, then the electric field at that point must be

A) negative.
B) zero.
C) uniform.
D) positive.
E) impossible to determine based on the information given.

Question 21

A parallel-plate capacitor is connected to a battery and becomes fully charged. The capacitor is then disconnected, and the separation between the plates is increased in such a way that no charge leaks off. As the plates are being separated, the energy stored in this capacitor

A) increases.
B) decreases.
C) does not change.
D) become zero.

Question 22

Which of the following changes will increase the capacitance of a parallel-plate capacitor? (There could be more than one correct choice.)

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) decrease the separation between the plates

Question 23

An ideal parallel-plate capacitor having circular plates of diameter D that are a distance d apart stores energy U when it is connected across a fixed potential difference. If you want to triple the amount of energy stored in this capacitor by changing only the size of its plates, the diameter should be changed to

A) 9D.
B) 3D.
C) D
D)
E)

Question 24

At a distance d from a point charge Q, the energy density in its electric field is u. If we double the charge, what is the energy density at the same point?

A) 16u
B) 8u
C) 4u
D) 2u
E) u

Question 25

Which of the following will increase the capacitance of a parallel-plate capacitor? (There could be more than one correct choice.)

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) an increase in the charge on the plates

Question 26

An ideal parallel-plate capacitor consists 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 across the plates. If the separation between the plates is now doubled, the amount of 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 27

A parallel-plate 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 across the plates. A slab of a dielectric material is inserted in the region between the plates and completely fills it. What changes would you observe as the dielectric is inserted? (There could be more than one correct choice.)

A) Only the charge on the plates of the capacitor would change.
B) Only the capacitance would change.
C) Both the charge on the plates of the capacitor and its capacitance would change.
D) The potential difference across the plates would increase.
E) Nothing would change.

Question 28

Doubling the potential across a given capacitor causes the energy stored in that capacitor to

A) quadruple.
B) double.
C) reduce to one-half.
D) reduce to one-fourth.

Question 29

A battery charges a parallel-plate capacitor fully and then is removed. The plates are then slowly pulled apart. What happens to the potential difference between the plates as they are being separated?

A) It increases.
B) It decreases.
C) It remains constant.
D) It cannot be determined from the information given.

Question 30

The plates of a parallel-plate capacitor are maintained with constant voltage by a battery as they are pulled apart. What happens to the strength of the electric field between the plates during this process?

A) It increases.
B) It decreases.
C) It remains constant.
D) It cannot be determined from the information given.

Question 31

An ideal parallel-plate capacitor consists 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, and the battery is then disconnected. If the separation between the plates is now 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

When a dielectric material is introduced between the plates of a parallel-plate capacitor and completely fills the space, the capacitance increases by a factor of 4. What is the dielectric constant of the material that was introduced?

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

Question 33

Two ideal parallel-plate capacitors are identical in every respect except that one has twice the plate area of the other. If the smaller capacitor has capacitance C, the larger one has capacitance

A) C/2.
B) C.
C) 2C.
D) 4C.

Question 34

A dielectric material such as paper is inserted between the plates of a capacitor as the capacitor holds a fixed charge on its plates. What happens to the electric field between the plates as the dielectric is inserted?

A) There is no change in the field.
B) The field becomes stronger.
C) The field becomes weaker.
D) The field reduces to zero.

Question 35

When a certain capacitor carries charges of ±10 µC on its plates, the potential difference cross the plates is 25 V. Which of the following statements about this capacitor are true? (There could be more than one correct choice.)

A) If we double the charges on the plates to ±20 µC, the capacitance of the capacitor will also double.
B) If we double the charges on the plates to ±20 µC, the potential difference across the plates will also double.
C) If we double the charges on the plates to ±20 µC, the capacitance of the capacitor will not change.
D) If we double the charges on the plates to ±20 µC, the potential difference across the plates will decrease by a factor of two.

Question 36

The plates of a parallel-plate capacitor are maintained with constant potential by a battery as they are pulled apart. During this process, the amount of charge on the plates

A) must increase.
B) must decrease.
C) must remain constant.
D) could either increase or decrease. There is no way to tell from the information given.

Question 37

An ideal parallel-plate capacitor has a capacitance of C. If the area of the plates is doubled and the distance between the plates is halved, what is the new capacitance?

A) C/4
B) C/2
C) 2C
D) 4C

Question 38

An capacitor consists of two large parallel plates of area A separated by a very small distance d. This capacitor is connected to a battery and charged until its plates carry charges +Q and -Q, and then disconnected from the battery. If the separation between the plates is now 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 39

An ideal parallel-plate capacitor consists of two parallel plates of area A separated by a distance d. This capacitor is connected across a battery that maintains a constant potential difference between the plates. If the separation between the plates is now 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 40

Doubling the capacitance of a capacitor that is holding a constant charge causes the energy stored in that capacitor to

A) quadruple.
B) double.
C) decrease to one-half.
D) decrease to one-fourth.

Question 41

A 4.0-g bead carries a charge of 20 μC. The bead is accelerated from rest through a potential difference V, and afterward the bead is moving at 2.0 m/s. What is the magnitude of the potential difference V?

A) 800 kV
B) 400 kV
C) 800 V
D) 400 V
E) 200 V

Question 42

A proton that is initially at rest is accelerated through an electric potential difference of magnitude 500 V. How much kinetic energy does it gain? (e = 1.60 × 10^-19

A) 500 J
B) 8.0 × 10^-17 J
C)
C) 1.6 × 10^-19 J
D) 800 J

Question 43

How much work is needed to carry an electron from the positive terminal to the negative terminal of a 9.0-V battery. (e = 1.60 × 10^-19 C , m_electron = 9.11 × 10^-31 kg)

A) 1.6 × 10^-19 J
B) 17 × 10^-19 J
C) 9.0 J
D) 14.4 × 10^-19 J
E) 14.4 × 10^-19 J/C

Question 44

A proton that is initially at rest is accelerated through an electric potential difference of magnitude 500 V. What speed does the proton gain? (e = 1.60 × 10^-19 C , m_proton = 1.67 × 10^-27 kg)

A) 2.2 × 10⁵ m/s
B) 3.1 × 10⁵ m/s
C) 9.6 × 10⁵ m/s
D) 1.1 × 10⁵ m/s

Question 45

A tiny particle with charge + 5.0 μC is initially moving at 55 m/s. It is then accelerated through a potential difference of 500 V. How much kinetic energy does this particle gain during the period of acceleration?

A) 1.0 × 10⁴ J
B) 2.5 × 10^-3 J
C) 100 J
D) 2500 J

Question 46

How much kinetic energy does a proton gain if it is accelerated, with no friction, through a potential difference of 1.00 V? The proton is 1836 times heavier than an electron, and e = 1.60 × 10^-19 C.

A) 1836 eV
B) 1.00 eV
C) 1.60 × 10^-19 eV
D) 1.00 J
E) 1836 J

Question 47

Two very small +3.00-μC charges are at the ends of a meter stick. Find the electric potential (relative to infinity) at the center of the meter stick. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A) 0.00 V
B) 2.70 × 10⁴ V
C) 5.40 × 10⁴ V
D) 1.08 × 10⁵ V

Question 48

A +4.0-μC and a -4.0-μC point charge are placed as shown in the figure. What is the potential difference between points A and B? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A) 48 V
B) 96 V
C) 0 V
D) 96 kV
E) 48 kV

Question 49

How much work must we do on an electron to move it from point A, which is at a potential of +50V, to point B, which is atC)
a potential of -50 V, along the semicircular path shown in the figure? Assume the system is isolated from outside forces. (e = 1.60 × 10^-19

A) 1.6 J
B) 1.60 × 10^-17 J
C) -1.60 × 10^-17 J
D) -1.6 J
E) This cannot be determined because we do not know the distance traveled.

Question 50

A 6.9 μC negative point charge has a positively charged particle in an elliptical orbit about it. If the mass of the positively charged particle is and its distance from the point charge varies from to , what is the maximum potential difference through which the positive object moves? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A) 12 MV
B) 3.9 MV
C) -5.2 MV
D) 19 MV

Question 51

If a Cu²⁺ ion that is initially at rest accelerates through a potential difference of 12 V without friction, how much kinetic energy will it gain? (e = 1.60 × 10^-19 C)

A) 3.0 eV.
B) 6.0 eV.
C) 12 eV.
D) 24 eV.

Question 52

If it takes 50 J of energy to move 10 C of charge from point A to point B, what is the magnitude of the potential difference between points A and B?

A) 500 V
B) 50 V
C) 5.0 V
D) 0.50 V

Question 53

If an electron is accelerated from rest through a potential difference of 1500 V, what speed does it reach? (e = 1.60 × 10^-19 C , m_electron = 9.11 × 10^-31 kg)

A) 2.3 × 10⁷ m/s
B) 1.9 × 10⁷ m/s
C) 1.5 × 10⁷ m/s
D) 1.1 × 10⁷ m/s

Question 54

Three point charges, -2.00 μC, +4.00 μC, and +6.00 μC, are located along the x-axis as shown in the figure. What is the electric potential (relative to infinity) at point P due to these charges? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A) -307 kV
B) +307 k V
C) -154 kV
D) +154 kV
E) 0.00 kV

Question 55

Four 2.0-µC point are at the corners of a rectangle with sides of length 3.0 cm and 4.0 cm. What is the electric potential (relative to infinity) at the midpoint of the rectangle? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A) 1.3 MV
B) 2.9 MV
C) 3.5 MV
D) 7.8 MV

Question 56

At a distance d from a point charge Q, the energy density in its electric field is u. If we now go to a distance d/2 from the charge, what is the energy density at the new location?

A) 16u
B) 8u
C) 4u
D) 2u
E) u

Question 57

After a proton with an initial speed of 1.50 × 10⁵ m/s has increased its speed by accelerating through a potential difference of 0.100 kV, what is its final speed? (e = 1.60 × 10^-19 C , m_proton = 1.67 × 10^-27 kg)

A) 4.56 × 10⁵ m/s
B) 2.04 × 10⁵ m/s
C) 3.55 × 10⁵ m/s
D) 8.80 × 10⁵ m/s
E) 1.55 × 10⁶ m/s

Question 58

A sphere with radius 2.0 mm carries a charge. What is the potential difference, between point B, which is from the center of the sphere, and point A, which is from the center of the sphere? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A) 1500 V
B) -1500 V
C) 170 V
D) -0.63 V

Question 59

Two 3.0 μC charges lie on the x-axis, one at the origin and the other at What is the potential (relative to infinity) due to these charges at a point at on the x-axis? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A) 11,000 V
B) 9000 V
C) 14,000 V
D) 3400 V

Question 60

A proton with a speed of 2.0 x m/s accelerates through a potential difference and thereby increases its speed to 4.0 x m/s. Through what magnitude potential difference did the proton accelerate? (e = 1.60 × 10^-19 C , m_proton = 1.67 × 10^-27 kg)

A) 630 V
B) 210 V
C) 840 V
D) 1000 V
E) 100 V

Question 61

A +5.0-µC point charge is 12 cm from a -5.0-µC point charge. What is the magnitude of the electric field they produce at the point on the line connecting them where their electric potential (relative to infinity) is zero? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A) 0 N/C
B) 12.5 MN/C
C) 0.75 MN/C
D) 25 MN/C
E) 1.5 MN/C

Question 62

A 7.0-μC point charge and a point charge are initially extremely far apart. How much work does it take to bring the point charge to the point , and the point charge to the point (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A) 95 J
B) 190 J
C) 63 J
D) 16 J

Question 63

The three point charges shown in the figure form an equilateral triangle with sides 4.9 cm long. What is the electric potential (relative to infinity) at the point indicated with the dot, which is equidistant from all three charges? Assume that the numbers in the figure are all accurate to two significant figures. (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A) 0.00 V
B) 1300 V
C) 640 V
D) 1900 V

Question 64

An electric dipole with ±5.0 μC point charges is positioned so that the positive charge is to the right of the origin and the negative charge is at the origin. How much work does it take to bring a point charge from very far away to the point x = 3.0 mm, y = 0.0 mm? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A) 23 J
B) 110 J
C) 19 J
D) 49 J

Question 65

Two point charges of +2.00 μC and +4.00 μC are at the origin and at the point x = 0.000 m, y = -0.300 m, as shown in the figure. What is the electric potential due to these charges, relative to infinity, at the point P at x = 0.400 m on the x-axis? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A) 117 kV
B) 15.7 kV
C) 11.7 kV
D) 56.0 kV
E) 36.0 kV

Question 66

A +7.5-nC point charge is 5.0 cm from a -9.4-µC point charge in your laboratory in California. How much work would you have to do if you left the +7.5-nC charge in the lab but took the -9.4-µC charge to New York City? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Question 67

An alpha particle (a helium nucleus, having charge +2e and mass 6.64 × 10^-27 kg) moves head-on at a fixed gold nucleus (having charge +79e). If the distance of closest approach is 2.0 × 10^-10 m, what was the speed of the alpha particle when it was very far away from the gold? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C², e = 1.60 × 10^-19

A) 2.3 × 10⁵ m/s
B) 4.6 × 10⁵ m/s
C)
C) 2.3 × 10⁶ m/s
D) 4.6 × 10⁶ m/s

Question 68

A very small 4.8-g particle carrying a charge of +9.9 μC is fired with an initial speed of directly toward a second small 7.8-g particle carrying a charge of + The second particle is held fixed throughout this process. If these particles are initially very far apart, what is the closest they get to each other? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Question 69

Two tiny particles having charges q₁ = +56.0 nC and ^q₂ = -46.0 nC are separated by and held in place, as shown in the figure. A third particle, having a charge of is placed at the point A, which is 0.18 m to the left of ^q₂. How much work is needed to move the third particle from point A to point B, which is 0.40 m to the left of ^q₁. All the points in the figure lie on the same line. (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Question 70

How much energy is necessary to place three +2.0-µC point charges at the vertices of an equilateral triangle of side 2.0 cm if they started out extremely far away? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A) 4.5 J
B) 5.4 J
C) 6.7 J
D) 7.6 J

Question 71

Four +6.00-µC point charges are at the corners of a square 2.00 m on each side. What is the electric potential of these charges, relative to infinity, at the center of this square? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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

Question 72

Two 5.0-µC point charges are 12 cm apart. What is the electric potential (relative to infinity) of this combination at the point where the electric field due to these charges is zero? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A) 0.75 MV
B) 1.5 MV
C) 0.0 MV
D) 25 MV
E) 12.5 MV

Question 73

Two tiny grains of sand having charges of 4.0 μC and -4.0 μC are situated along the x-axis at x₁ = 2.0 m and x₂ = -2.0 m. What is electric potential energy of these grains relative to infinity? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

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

Question 74

Two +6.0-µC charges are placed at two of the vertices of an equilateral triangle having sides 2.0 m long. What is the electric potential at the third vertex, relative to infinity, due to these charges? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

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

Question 75

Point charges +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in the figure. What is the potential at point B due to these charges? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A) 8.99 kV
B) 11.2 kV
C) 89.9 kV
D) 899 kV
E) 112 kV

Question 76

Point charges +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in the figure. What is the potential at point A, relative to infinity, due to these charges? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A) 0.899 kV
B) 8.99 kV
C) 89.9 kV
D) 899 kV
E) 8990 kV

Question 77

A square is 1.0 m on a side. Point charges of +4.0 μC are placed in two diagonally opposite corners. In the other two corners are placed charges of +3.0 μC and -3.0 μC. What is the potential (relative to infinity) at the midpoint of the square? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A) 1.0 × 10⁴ V
B) 1.0 × 10⁵ V
C) 1.0 × 10⁶ V
D) 0 V
E) infinite

Question 78

Three point charges are placed at the following points in a horizontal x-y plane: is at is at and is at Calculate the electrical potential (relative to infinity) at the origin due to these three point charges. (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Question 79

Point charges +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in the figure. What is the potential difference V_A - V_B? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A) +203 kV
B) -203 kV
C) -22.5 kV
D) +22.5 kV
E) 0.00 kV

Question 80

Four point charges of magnitude 6.00 μC and are at the corners of a square 2.00 m on each side. Two of the charges are positive, and two are negative. What is the electric potential at the center of this square, relative to infinity, due to these charges? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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