Deck 17: Electrostatics II: Electric Potential Energy and Electric Potential

Question 1

The electrostatic potential energy of a positively charged body is greatest at point _____.

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

Answer 1

E

Question 2

The voltage between the cathode and the screen of a computer monitor is 12 kV. If we assume a speed of zero for an electron as it leaves the cathode, what is its speed just before it hits the screen?

A) 8.8 × 10⁷ m/s
B) 6.5 × 10⁷ m/s
C) 4.2 × 10¹⁵ m/s
D) 7.7 × 10¹⁵ m/s
E) 5.3 × 10⁷ m/s

Answer 2

6.5 × 10⁷ m/s

Question 3

Which of the curves in the graph represents the electrostatic potential energy of a small negative charge plotted as a function of its distance from another positive point charge located at the origin?

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

Answer 3

5

Question 4

Four point charges q₁ = 1 $\mu$ C, q₂ = 2 $\mu$ C, q₃ = 3 $\mu$ C, and q₄ = 4 $\mu$ C are located at the corners of a square whose side s = 1.00 m. The electrostatic potential energy of this system of charges is

A) 0.167 J
B) 0.176 J
C) 0.286 J
D) 0.337 J
E) 0.492 J

Question 5

The electrostatic potential energy of the system of point charges q₁ = 1 μC, q₂ = 2 μC, and q₃ = 3 μC at the corners of the equilateral triangle whose side s = 30 cm is

A) 1.1 J.
B) 0.99 J.
C) 0.63 J.
D) 0.33 J.
E) 0.11 J.

Question 6

The work required to bring a negatively charged body from very far is greatest for point _____.

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

Question 7

The electrostatic potential energy of the system of point charges q₁ = 1 μC, q₂ = -2 μC, and q₃ = 3 μC at the corners of the equilateral triangle whose side s = 40 cm is

A) 1.10 J.
B) 0.990 J..
C) -0.631 J.
D) 0.330 J.
E) -0.113 J.

Question 8

The work required to bring a positively charged body from very far away is greatest for point _____.

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

Question 9

The electrostatic potential energy of the system of point charges q₁ = -1 ?C, q₂ = -2 ?C, and q₃ =-3 ?C at the corners of the equilateral triangle whose side s = 30 cm is

A) "-1.1 J."
B) "-0.99 J."
C) "-0.33 J."
D) "0.33 J."
E) "0.11 J."

Question 10

Two protons in a nucleus of ²³⁸U are 6.0 × 10^-15 m apart. The electrostatic potential energy of the pair is approximately

A) zero.
B) 4.7 × 10^-34 J.
C) 4.3 × 10^-24 J.
D) 3.8 × 10^-14 J.
E) 2.4 × 10⁴ J.

Question 11

The voltage between the cathode and the screen of a television set is 22 kV. If we assume a speed of zero for an electron as it leaves the cathode, what is its speed just before it hits the screen?

A) 8.8 × 10⁷ m/s
B) 2.8 × 10⁶ m/s
C) 6.2 × 10⁷ m/s
D) 7.7 × 10¹⁵ m/s
E) 5.3 × 10⁷ m/s

Question 12

Three charges are brought from infinity and placed at the corners of an equilateral triangle. Which of the following statements is true?

A) The work required to assemble the charges is always positive.
B) The electrostatic potential energy of the system is always positive.
C) The electrostatic potential energy does not depend on the order the charges are placed at the corners.
D) The work required to assemble the charges depends on which charge is placed at which corner.
E) The electrostatic potential energy depends on which charge is placed at which corner.

Question 13

The electrostatic potential energy of the system of point charges q₁ = -1 μC, q₂ = 2 μC, and q₃ = 3 μC at the corners of the equilateral triangle whose side s = 50 cm is

A) 18.0 mJ.
B) -18.0 mJ.
C) 21.6 mJ.
D) -24.4 mJ.
E) 1.23 mJ.

Question 14

Which of the following statements is false?

A) The total work required to assemble a collection of discrete charges is the electrostatic potential energy of the system.
B) The potential energy of a pair of positively charged bodies is positive.
C) The potential energy of a pair of oppositely charged bodies is positive.
D) The potential energy of a pair of oppositely charged bodies is negative.
E) The potential energy of a pair of negatively charged bodies is negative.

Question 15

The electrostatic potential energy of two protons separated by 2.6 × 10^-15 m is approximately

A) zero.
B) 4.7 × 10^-34 J.
C) 4.3 × 10^-24 J.
D) 3.8 × 10^-14 J.
E) 8.9 × 10^-14 J.

Question 16

Which of the curves in the graph represents the electrostatic potential energy of a small positive charge plotted as a function of its distance from another positive point charge located at the origin?

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

Question 17

Four point charges q₁ = -1 $\mu$ C, q₂ = 2 $\mu$ C, q₃ = 3 $\mu$ C, and q₄ = 4 $\mu$ C are located at the corners of a square whose side s = 1.00 m. The electrostatic potential energy of this system of charges is

A) 0.140 J.
B) 0.176 J.
C) 0.286 J.
D) 0.337 J.
E) 0.492 J.

Question 18

A charge of 2.0 mC is located in a uniform electric field of intensity 4.0 × 10⁵ N/C. How much work is required to move this charge 20 cm along a path making an angle of 60° with the electric field?

A) 0.14 J
B) 0.34 J
C) 80 J
D) 14 J
E) 8.0 J

Question 19

A charge of 5.0 mC is located in a uniform electric field of intensity 3.5 × 10⁵ N/C. How much work is required to move this charge 50 cm along a path making an angle of 33° with the electric field?

A) 0.27 J
B) 0.16 J
C) 0.54 J
D) 0.74 kJ
E) 7.3 mJ

Question 20

The electrostatic potential energy of a negatively charged body is greatest at point _____.

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

Question 21

When 5.0 C of charge moves at constant speed along a path between two points differing in potential by 12 V, the amount of work done by the field is

A) 2.4 J.
B) 0.42 J.
C) 5.0 J.
D) 12 J.
E) 60 J.

Question 22

Two parallel metal plates 0.35 cm apart have a potential difference between them of 175 V. The electric force on a positive charge of 6.4 × 10^-19 C at a point midway between the plates is approximately

A) 4.8 × 10^-18 N.
B) 2.4 × 10^-17 N.
C) 1.6 × 10^-18 N.
D) 4.8 × 10^-16 N.
E) 3.2 × 10^-14 N.

Question 23

Two parallel horizontal plates are spaced 0.40 cm apart in air. You introduce an oil droplet of mass 4.9 × 10^-17 kg between the plates. If the droplet carries two electronic charges and if there were no air buoyancy, you could hold the droplet motionless between the plates if you kept the potential difference between them at

A) 60 V.
B) 12 V.
C) 3.0 V.
D) 0.12 kV.
E) 6.0 V.

Question 24

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

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

Question 25

When 2.0 C of charge moves at constant speed along a path between two points differing in potential by 6.0 V, the amount of work done by the field is

A) 2 J.
B) 3 J.
C) 6 J.
D) 12 J.
E) 24 J.

Question 26

A uniform electric field exists between two parallel plates separated by 1.2 cm. The intensity of the field is 23 kN/C. What is the potential difference between the plates?

A) 7.5 MV
B) 0.30 kV
C) 3.0 MV
D) 15 kV
E) None of these is correct.

Question 27

The electrical potential 2.5 cm from a point charge of Q₁ = +4.5 × 10^-9 C and 2.0 cm from a second charge Q₂ is 3.2 kV. Find Q₂.

A) 2.7 × 10^-9 C
B) 4.4 × 10^-9 C
C) 1.1 × 10^-8 C
D) 3.5 × 10^-9 C
E) 5.5 × 10^-9 C

Question 28

A uniform electric field exists between two parallel plates separated by 2.0 cm. The intensity of the field is 15 kN/C. What is the potential difference between the plates?

A) 0.75 MV
B) 30 kV
C) 15 kV
D) 0.30 kV
E) 54 kV

Question 29

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

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

Question 30

Two parallel horizontal plates are spaced 0.60 cm apart in air. You introduce an oil droplet of mass 7.4 × 10^-17 kg between the plates. If the droplet carries 5 electronic charges and if there were no air buoyancy, you could hold the droplet motionless between the plates if you kept the potential difference between them at

A) 5.4 V.
B) 27 V.
C) 3.0 V.
D) 0.54 V.
E) 0.27 kV.

Question 31

The magnitude of the electric field in a region is given by E = kQ / r² where Q is the charge. What is the potential difference between r = a to r = b?

A)
B)
C)
D)
E) None of the above.

Question 32

Two parallel metal plates 5.0 cm apart have a potential difference between them of 75 V. The electric force on a positive charge of 3.2 × 10^-19 C at a point midway between the plates is approximately

A) 4.8 × 10^-18 N.
B) 4.8 × 10^-16 N.
C) 2.4 × 10^-17 N..
D) 9.6 × 10^-17 N.
E) 1.6 × 10^-18 N.

Question 33

Electric field in a region is created by a point charge Q located at r = 0. What is the potential difference as one moves from a closer point r = a to a farther location r = b?

A)
B)
C)
D)
E) None of the above.

Question 34

A lithium nucleus with a charge of 31.6 × 10^-19) C and a mass of 71.67 × 10^-27) kg, and an alpha particle with a charge of 21.6 × 10^-19) C and a mass of 41.67 × 10^-27) kg, are at rest. They could be accelerated to the same kinetic energy by

A) accelerating them through the same electrical potential difference.
B) accelerating the alpha particle through V volts and the lithium nucleus through 2V/3 volts.
C) accelerating the alpha particle through V volts and the lithium nucleus through 7V/4 volts.
D) accelerating the alpha particle through V volts and the lithium nucleus through 7V/6 volts.
E) None of these procedures.

Question 35

An electric dipole that has a positive charge of 4.8 × 10^-19 C is separated from a negative charge of the same magnitude by 6.4 × 10^-10 m. The electric potential at a point 9.2 × 10^-10 m from each of the two charges is

A) 9.4 V.
B) zero.
C) 4.2 V.
D) 5.1 × 10⁹ V.
E) 1.7 V.

Question 36

Correct units for electric potential are

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

Question 37

The concept of difference in electric potential is most closely associated with

A) the mechanical force on an electron.
B) the number of atoms in one gram-atom.
C) the charge on one electron.
D) the resistance of a certain specified column of mercury.
E) the work per unit quantity of electricity.

Question 38

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

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

Question 39

The potential at a point due to a unit positive charge is found to be V. If the distance between the charge and the point is tripled, the potential becomes

A) V/3.
B) 3V.
C) V/9.
D) 9V.
E) 1/V².

Question 40

The electron volt is a unit of

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

Question 41

A metal sphere with a radius of 10 cm is used to accumulate charges until the electric field at the surface is 3.0 MV/m. How much charge can be accumulated on this sphere?

A) 67 μC
B) 33 μC
C) 13 μC
D) 6.7 μC
E) 3.3 μC

Question 42

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

A) 1.
B) 2.
C) 3.
D) 4.
E) None of these is correct.

Question 43

Which point in the electric field in the diagram is at the highest potential?

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

Question 44

Which of the following statements regarding electric potential is true?

A) The units of electric potential are N/C.
B) Electric potential is a vector quantity.
C) Equipotential surfaces are at right angles to lines of force.
D) Potential differences can be measured directly with a ballistic galvanometer.
E) Equipotential surfaces for an isolated point charge are cubes concentric with the charge.

Question 45

Which point in the electric field in the diagram is at the lowest potential?

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

Question 46

A metal sphere with a radius of 8.0 cm is used to accumulate charges until the electric field at the surface is 3.0 MV/m. How much charge can be accumulated on this sphere?

A) 2.1 μC
B) 3.3 μC
C) 1.3 nC
D) 6.7 μC
E) 4.2 μC

Question 47

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

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

Question 48

Which of the points shown in the diagram are at the same potential?

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

Question 49

Two charges Q₁ = +6 $\mu$ C) and Q₂ = -2 $\mu$ C) are brought from infinity to positions on the x-axis of x = -4 cm and x = +4 cm, respectively. Is it possible to bring a third charge
Q₃ = +3 $\mu$ C) from infinity to a point on the x-axis between the charges where the potential is zero, and if so, where would this position be?

A) It is not possible.
B) x = 0 cm
C) x = +2 cm
D) x = +6 cm
E) x = +1.5 cm

Question 50

The potential on the surface of a solid conducting sphere of radius r = 20 cm is 100 V. The potential at r = 10 cm is

A) 100 V.
B) 50 V.
C) 25 V.
D) zero.
E) cannot be determined.

Question 51

Two equal positive charges are placed x m apart. The equipotential lines are at 100 V interval.The potential for line c is

A) "-100 V."
B) "+0 V."
C) "-200 V."
D) "+200 V."
E) "zero."

Question 52

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

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

Question 53

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

A) 1.
B) 2.
C) 3.
D) 4.
E) None of these is correct.

Question 54

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

A) the greatest for path A → A'.
B) the greatest for path B → B'.
C) the greatest for path C → C'.
D) the greatest for path D → D'.
E) the same for all paths.

Question 55

Two flat parallel plates are d = 0.40 cm apart. The potential difference between the plates is 360 V. The electric field at the point P at the center is approximately

A) 90 kN/C.
B) 3.6 kN/C.
C) 0.9 kN/C.
D) zero.
E) 3.6 × 10⁵ N/C.

Question 56

From a very large distance, a proton charge = e, mass = 1.67 × 10^-27 kg) with initial kinetic energy 3 MeV is fired head-on toward a fixed stationary uranium nucleus charge 92e, mass = 3.95 × 10^-25 kg). Calculate how close to the uranium the proton gets before it comes to rest. Assume the uranium nucleus does not move.)

A) 2.75 × 10⁵ m
B) 4.40 × 10^-8 m
C) 4.40 × 10^-14 m
D) 2.10 × 10^-7 m
E) None of the above.

Question 57

The electrical potential 2.0 cm from a point charge of Q₁ = +6.5 × 10^-9 C and 3.5 cm from a second charge Q₂ is 1.2 kV. Find Q₂.

A) -6.7 × 10^-9 C
B) -3.8 × 10^-9 C
C) -1.0 × 10^-9 C
D) 3.8 × 10^-9 C
E) 1.0 × 10^-9 C

Question 58

Two large metallic plates are parallel to each other and charged. The distance between the plates is d. The potential difference between the plates is V. The magnitude of the electric field in the region between the plates and away from the edges is given by

A) d/V.
B) V²/d.
C) dV.
D) V/d².
E) None of these is correct.

Question 59

Two charges Q₁ = +6 $\mu$ C) and Q₂ = -2 $\mu$ C) are brought from infinity to positions on the x-axis of x = -4 cm and x = +4 cm, respectively. How much work was done in bringing the charges together?

A) -1.80 × 10⁶ J
B) -9.00 × 10⁵ J
C) -16.9 J
D) -1.35 J
E) None of the above.

Question 60

Two equal positive charges are placed x m apart. The equipotential lines are at 100 V interval.The work required to move a third charge, q = -e, from the+0 V line to b is

A) "-0 eV."
B) "-100 eV."
C) "-200 eV."
D) "-200 eV.".
E) "zero."

Question 61

An 80-nF capacitor is charged to a potential of 500 V. How much charge accumulates on each plate of the capacitor?

A) 4.0 × 10^-4 C
B) 4.0 × 10^-5 C
C) 4.0 × 10^-10 C
D) 1.6 × 10^-10 C
E) 1.6 × 10^-7 C

Question 62

When a small, positively charged metal ball comes in contact with the interior of a positively charged metal shell,

A) the charge on the ball becomes negative.
B) the amount of positive charge on the ball increases.
C) the positive charge on the shell decreases.
D) the charge on the shell and the ball reach the same value.
E) the ball loses all of its excess charge.

Question 63

A capacitor of capacitance C holds a charge Q when the potential difference across the plates is V. If the charge Q on the plates is doubled to 2Q,

A) the capacitance becomes 1/2)V.
B) the capacitance becomes 2C.
C) the potential changes to 1/2)V.
D) the potential changes to 2V.
E) the potential does not change.

Question 64

What is the approximate radius of an equipotential spherical surface of 30 V about a point charge of +15 nC if the potential at an infinite distance from the surface is zero?

A) 1.0 m
B) 2.1 m
C) 3.0 m
D) 4.5 m
E) 6.8 m

Question 65

A solid spherical conductor of radius 15 cm has a charge Q = 6.5 nC on it. A second, initially uncharged, spherical conductor of radius 10 cm is moved toward the first until they touch and is then moved far away from it. How much charge is there on the second sphere after the two spheres have been separated?

A) 2.6 nC
B) 2.2 nC
C) 3.2 nC
D) 3.9 nC
E) 4.3 nC

Question 66

A solid spherical conductor of radius 15 cm has a charge Q = 6.5 nC on it. A second, initially uncharged, spherical conductor of radius 10 cm is moved toward the first until they touch and is then moved far away from it. How much charge is there on the first sphere after the two spheres have been separated?

A) 2.6 nC
B) 2.2 nC
C) 3.2 nC
D) 3.9 nC
E) 4.3 nC

Question 67

A solid conducting sphere of radius r_a is placed concentrically inside a conducting spherical shell of inner radius r_b1 and outer radius r_b2. The inner sphere carries a charge Q while the outer sphere does not carry any net charge. The potential for r < r_a is

A) .
B) .
C) .
D) .
E) zero.

Question 68

Dielectric breakdown occurs in the air at an electric field strength of E_max = 3.0 × 10⁶ V/m. If the maximum charge that can be placed on a spherical conductor is 2.0 × 10^-3 C before breakdown, calculate the diameter of the sphere.

A) 6.0 m
B) 4.9 m
C) 1.2 m
D) 2.5 m
E) 3.0 m

Question 69

We give the same charge to a metal sphere of radius R and a metal cone of radius R and height 2R. The shaded regions in the figure are of equal area. Which region has the greatest surface charge density?

A) 1
B) 2
C) 3
D) 4
E) All have equal charge densities.

Question 70

The dielectric strength of the atmosphere is of the order of

A) 1 V/m.
B) 10² V/m.
C) 10⁴ V/m.
D) 10⁶ V/m.
E) 10⁸ V/m.

Question 71

A solid spherical conductor of radius 20 cm has a charge Q = 25 nC on it. A second, initially uncharged, spherical conductor of radius 12 cm is moved toward the first until they touch and is then moved far away from it. How much charge is there on the second sphere after the two spheres have been separated?

A) 15 nC
B) 9.4 nC
C) 25 nC
D) 3.9 nC
E) 2.1 nC

Question 72

A charged metal ball is lowered into an insulated metal can and permitted to touch the inside of the can. The ball is then withdrawn and hung on a stand. A second uncharged ball will be attracted to

A) the outside of the can.
B) the inside of the can.
C) the outside and the inside of the can.
D) the metal ball and the inside of the can.
E) the metal ball, the inside of the can, and the outside of the can.

Question 73

A solid conducting sphere of radius r_a is placed concentrically inside a conducting spherical shell of inner radius r_b1 and outer radius r_b2. The inner sphere carries a charge Q while the outer sphere does not carry any net charge. The potential for r_b1 < r < r_b2 is

A) .
B) .
C) .
D) .
E) zero.

Question 74

A metal ball of charge +Q is lowered into an insulated, uncharged metal shell and allowed to rest on the bottom of the shell. When the charges reach equilibrium,

A) the outside of the shell has a charge of -Q and the ball has a charge of +Q.
B) the outside of the shell has a charge of +Q and the ball has a charge of +Q.
C) the outside of the shell has a charge of zero and the ball has a charge of +Q.
D) the outside of the shell has a charge of +Q and the ball has zero charge.
E) the outside of the shell has a charge of +Q and the ball has a charge of -Q.

Question 75

Dielectric breakdown occurs in the air at an electric field strength of E_max = 3.0 × 10⁶ V/m. If the maximum potential at the surface of a spherical conductor is 5.0 × 10⁶ V, then calculate the radius of the sphere.

A) 0.60 m
B) 1.3 m
C) 1.7 m
D) 0.77 m
E) 15 m

Question 76

If the area of the plates of a parallel-plate capacitor is doubled, the capacitance is

A) not changed.
B) doubled.
C) halved.
D) increased by a factor of 4.
E) decreased by a factor of 1/4.

Question 77

If a capacitor of capacitance 2.0 μF is given a charge of 1.0 mC, the potential difference across the capacitor is

A) 0.50 kV.
B) 2.0 V.
C) 2.0 μV.
D) 0.50 V.
E) None of these is correct.

Question 78

Dielectric breakdown occurs in the air at an electric field strength of E_max = 3.0 × 10⁶ V/m. What is the maximum surface charge density that can be placed on a spherical conductor of radius 1.5 m before breakdown?

A) 2.7 × 10^-5 C/m²
B) 1.2 × 10^-5 C/m²
C) 8.1 × 10^-5 C/m²
D) 8.6 × 10^-6 C/m²
E) 1.8 × 10^-5 C/m²

Question 79

What is the approximate radius of an equipotential spherical surface of 100 V about a point charge of +45 nC if the potential at an infinite distance from the surface is zero?

A) 1.0 m
B) 2.1 m
C) 3.0 m
D) 4.5 m
E) 4.0 m

Question 80

An electric charge q is placed on an isolated metal sphere of radius r₁. If an uncharged sphere of radius r₂ with r₂ > r₁) is then connected to the first sphere, the spheres will have equal

A) and like charges on their surfaces.
B) electric fields.
C) potentials.
D) capacitances.
E) but opposite charges on their surfaces.