Deck 23: Electric Potential

Question 1

Equipotential lines and electric field lines are always

A)disjoint.
B)parallel.
C)perpendicular.
D)None are correct.

Answer 1

perpendicular.

Question 2

A point charge of 5.0 is located at (2.5 m,4.1 m).A second point charge of is located at (-2.0 m,1.0 m).What is the electric potential at the origin?

A)1.4 * 10³ V
B)2.6 * 10³ V
C)3.7 * 10³ V
D)5.2 * 10³ V
E)7.9 * 10³ V

Answer 2

1.4 * 10³ V

Question 3

A 5.0 V battery is connected to two parallel metal plates placed in a vacuum.An electron is accelerated from rest from the negative plate toward the positive plate.What kinetic energy does the electron have as it just reaches the positive plate?

A)5.6 * 10^-19 J
B)6.1 * 10^-19 J
C)8.0 * 10^-19 J
D)8.9 * 10^-19 J
E)9.7 * 10^-19 J

Answer 3

8.0 * 10^-19 J

Question 4

At a distance d from a charge,the electric potential is V.What would be the electric potential a distance d/2 from the same charge?

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

Question 5

A particle (charge 4.0 µC)is released from rest at a point on the x- axis,x = 5.0 cm.It begins to move due to the presence of a 3.0-µC charge that remains fixed at the origin.What is the kinetic energy of the particle at the instant it passes the point x = 12 cm?

A)1.26 J
B)12.6 mJ
C)-1.26 J
D)-12.6 mJ

Question 6

Consider two isolated metal spheres,the first with a charge of 8.7 and a radius of 25 cm and the second uncharged with a radius of 5.4 cm.What is the charge on the larger sphere after a long thin metal wire is used to connect the two spheres?

A)0
B)1.5
C)4.4
D)7.2
E)8.7

Question 7

Two protons are released simultaneously from rest when the two are 1.00 nm apart.What is the speed of either at the instant when the two are separated by 5.0 nm?

A)10.5 km/s
B)10.5 m/s
C)14.9 km/s
D)14.9 m/s

Question 8

Four identical point charges Q are placed at the corners of a rectangle which measures 3.00 m * 5.00 m.The potential at the geometric center of this rectangle is 32.2 V assuming that the electric potential is zero at infinity.The charge Q is

A)1.35 nC.
B)2.61 nC.
C)3.24 nC.
D)4.89 nC.
E)5.72 nC.

Question 9

In large televisions,electrons are accelerated from rest by a potential difference of 20 kV and shot onto a phosphorescent screen to produce an image.What is the speed of the electrons when they reach the screen?

A)1.4 * 10⁶ m/s
B)1.3 * 10⁷ m/s
C)4.4 * 10⁷ m/s
D)5.9 * 10⁷ m/s
E)8.4 * 10⁷ m/s

Question 10

Two point charges are located at two corners of a triangle as shown.What is the electric potential at the right corner of the triangle?

A)2.1 * 10⁵ V
B)3.4 * 10⁵ V
C)4.5 * 10⁵ V
D)6.3 * 10⁵ V
E)7.2 * 10⁵ V

Question 11

Consider two isolated metal spheres,the first with a charge of 8.7 and a radius of 25 cm and the second uncharged with a radius of 5.4 cm.What is the charge on the smaller sphere after a long thin metal wire is used to connect the two spheres?

A)0
B)1.5
C)4.4
D)7.2
E)8.7

Question 12

Four identical point charges (+ 2.50 nC)are placed at the corners of a rectangle which measures 2.00 m * 4.00 m.If the electric potential is taken to be zero at infinity,what is the potential at the geometric center of this rectangle?

A)8.99 V
B)19.9 V
C)20.1 V
D)30.0 V
E)40.2 V

Question 13

How much charge must be placed on a 10 cm diameter metal sphere so that the electric potential at the center of the sphere is 1.0 V? Assume that the electric potential is zero at points infinitely far away from the sphere.

A)2.8 * 10^-13 C
B)1.1 * 10^-12 C
C)5.6 * 10^-12 C
D)1.1 * 10^-11 C
E)2.2 * 10^-11 C

Question 14

Electric field lines always point

A)from higher potential to lower potential.
B)from lower potential to higher potential.
C)in the same direction as the equipotential lines.
D)in the opposite direction as the equipotential lines.

Question 15

An insulating sheet in the xz-plane is uniformly charged with charge surface density $\sigma$ = 6.2 * 10^-6 C/m².What is the change in electric potential when a charge of Q=3.3 $\mu$ C is moved from a position that is 6.2 m away from the sheet to a position that is 1.3 m away from the sheet?

A)1.7 * 10⁶ V
B)-1.7 * 10⁶ V
C)3.4 * 10⁶ V
D)-3.4 * 10⁶ V
E)9.1 * 10⁵ V

Question 16

A negative charge is released and moves along an electric field line.This negative charge moves to a position of

A)lower potential and lower potential energy.
B)lower potential and higher potential energy.
C)higher potential and lower potential energy.
D)higher potential and higher potential energy.

Question 17

In the opposite corners of a square there are two identical ions.Each has a charge of + e.The length of one side of he square is L.What is the net electric potential caused by the two positive ions at both of the empty corners of the square?

A)ke/2L
B)ke/L
C) ke/L
D)2ke/L

Question 18

An electron is accelerated from rest through a potential difference of 450 V.What is its final speed?

A)0.81 * 10⁷ m/s
B)1.3 * 10⁷ m/s
C)2.9 * 10⁷ m/s
D)4.1 * 10⁷ m/s

Question 19

When two charges are separated by a distance d,their electric potential energy is equal to U.What would be their electric potential energy if the separation distance was d/2?

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

Question 20

A charge Q = -7.8 $\mu$ C is uniformly distributed on a thin plastic ring.The radius of the ring is 4.3 cm.Calculate the electric potential at the center of the ring.Assume that the electric potential is zero at points infinitely far away from the ring.

A)-3.8 * 10⁷ V
B)3.8 * 10⁷ V
C)0 V
D)-1.6 * 10⁶ V
E)1.6 * 10⁶ V

Question 21

The amount of work done to move a positive charge Q on an equipotential surface of 1000 V compared to that on an equipotential surface of 10 V is

A)the same.
B)less.
C)more.
D)dependent on distance travelled.

Question 22

Two parallel plates are held at a potential of + 220 V and + 130 V.If the plates have area of 44 cm² and are separated by a distance of 7.3 mm,what is the magnitude of the electric field between the plates?

A)54 V/m
B)132 N/C
C)12,000 N/C
D)20 kV/m
E)30,000 N/C

Question 23

A ring of radius 20 cm has a charge of 2 nC on it.What is the electric potential in the center of the ring?

A)0 V
B)8.9 V
C)4.5 V
D)89 V
E)45 V

Question 24

Two metallic spheres have radii of 10 cm and 5 cm,respectively.The electric field strength on the surface of each sphere is 3600 N/C.The two spheres are then connected together by a long,thin metal wire.Determine the electric field strength on the surface of 10-cm radius sphere while they are connected.

A)3600 N/C
B)3000 N/C
C)6000 N/C
D)4500 N/C

Question 25

Two metallic spheres have radii of 10 cm and 5 cm,respectively.The electric field strength on the surface of each sphere is 3600 N/C.The two spheres are then connected together by a long,thin metal wire.Determine the electric field strength on the surface of 5-cm radius sphere while they are connected.

A)3600 N/C
B)3000 N/C
C)6000 N/C
D)4500 N/C

Question 26

In an effort to produce nuclear fusion you fire a deuterium nuclei (q = + 1e,m = 3.34 * 10^-27kg)directly at another (fixed)hydrogen nucleus.How fast must you fire the deuterium for it to approach within 2.0 * 10^-15 m of the nuclei?

A)8.3 * 10⁶ m/s
B)5.4 * 10⁷ m/s
C)1.4 * 10⁸ m/s
D)1.9 * 10¹⁴ m/s
E)2.1 * 101⁶ m/s

Question 27

The 10-cm long plastic rod in the figure has a non-uniform linear charge density $\lambda$ = cx,where c = 10^-6 C/m² and x is measured from the left end of the rod.Find the electric potential at point P on the y axis,a distance of 3 cm above the left end of the rod.

A)5.9 * 10² V
B)6.5 * 10¹ V
C)9.0 * 10² V
D)1.3 * 10³ V
E)6.7 * 10² V

Question 28

A cartoon dog obtains a voltage of 17,000 V in his fur by scuffing his feet on the carpet.If he can be treated as a sphere of radius 12 cm,how much charge is on his fur?

A)1.2 * 10^-8 C
B)2.7 * 10^-8 C
C)3.4 * 10^-8 C
D)1.4 * 10^-7 C
E)2.3 * 10^-7 C

Question 29

What is the potential energy of a system of three 2 $\mu$ C charges arranged in an equilateral triangle of side 20 cm?

A)0.54 J
B)0.32 J
C)0.74 J
D)0.18 J
E)0.26 J

Question 30

A 20-g ball with 2 $\mu$ C of charge is placed 1 m away from a fixed 1-C charge and released.How fast is the charge moving a very long time later?

A)2500 m/s
B)750 m/s
C)3400 m/s
D)1300 m/s
E)4200 m/s

Question 31

The electric potential at a point is space is given by the relation V = 23x - 27y + 11y² + 72.What is the x-component of the electric field (in V/m)at the point r = (3.0,2.0,1.0)?

A)-23
B)-95
C)95
D)-17
E)-29

Question 32

An electric potential is given by V=4x² + 2y² + x + z + 2 volts.What is the magnitude of the electric field at the point (2,2,2)?

A)9 N/C
B)25 N/C
C)30 N/C
D)19 N/C
E)13 N/C

Question 33

An electric potential is given by V=4x² + 2y² + x + z + 2 volts.What is the electric field at the point (2,2,2)?

A)-2i - 3j N/C
B)-17i - 8j + k N/C
C)-16i - 4j + k N/C
D)-10i - 5j - 2k N/C
E)-3i - 8j N/C

Question 34

Two charged particles,Q₁ = + 12.0 mC,Q₂ = -5.0mC are placed on a line.At what finite locations along the line may the electric potential be equal to zero? I.in between the particles,closer to the positive particle
II.in between the particles,closer to the negative particle
III.not in between,but closer to the positive particle
IV.not in between,but closer to the negative particle
V.It can never be zero.

A)I only
B)II only
C)V only
D)I and IV
E)II and IV

Question 35

The electric potential at a point is space is given by the relation V = 23x - 27y + 11y² + 72.What is the magnitude of the force on a 3.4 $\mu$ C charge at the point r = (3.0,2.0,1.0)?

A)38 $\mu$ N
B)62 $\mu$ N
C)97 $\mu$ N
D)11 $\mu$ N
E)120 $\mu$ N

Question 36

The potential energy of a system of three equal charges arranged in an equilateral triangle is 0.54 J If the length of one side of this triangle is 33 cm,what is the charge of one of the three charges?

A)4.3 $\mu$ C
B)2.0 $\mu$ C
C)1.7 $\mu$ C
D)2.6 $\mu$ C
E)3.7 $\mu$ C

Question 37

Two charged particles,Q₁ = + 12.0 mC,Q₂ = + 5.0mC are placed on a line.At what finite locations along the line may the electric potential be equal to zero? I.in between the particles,closer to the positive particle
II.in between the particles,closer to the negative particle
III.not in between,but closer to the positive particle
IV.not in between,but closer to the negative particle
V.It can never be zero.

A)I only
B)II only
C)V only
D)I and IV
E)II and IV

Question 38

The potential energy of a system of three 2 $\mu$ C charges arranged in an equilateral triangle is 0.54 J What is the length of one side of this triangle?

A)20 cm
B)51 cm
C)85 cm
D)33 cm
E)62 cm

Question 39

The electric potential inside a 10-m long linear particle accelerator is given by V = 3,000 - 5x² volts,where x is the distance from the left plate along the accelerator tube,as shown in the figure.If a proton is released from rest at position x = 4.4 m,what is the impact speed of the proton when (and if)it collides with one of the plates?

A)never collides
B)8.15 * 10² m/s
C)1.36 * 10³ m/s
D)2.78 * 10⁵ m/s

Question 40

The electric potential at a point is space is given by the relation V = 23x - 27y + 11y² + 72.What is the magnitude of the electric field (in V/m)at the point r = (3.0,2.0,1.0)?

A)5
B)23
C)29
D)59
E)131

Question 41

A charge 12 µC is placed at the center of a conducting spherical shell of radius 2.3 m.Find the electric potential at R = 0.7m.

A)7.54 * 10^-5 V
B)2.84 * 10^-3 V
C)67.8 V
D)8.23 * 10³ V
E)1.54 * 10⁵ V

Question 42

A quarter of 24.26 mm diameter is given a charge of + 10 nC.The potential energy of an electron 1 cm above the quarter is

A)-1.12 * 10^-15 J.
B)-7.92 * 10^-16 J.
C)-7.41 * 10^-17 J.
D)-12.5 * 10^-18 J.
E)-43.1 * 10^-18 J.

Question 43

An electron (mass: 9.11 * 10^-31 kg)and a proton (mass: 1.67 * 10^-27 kg)are each accelerated from rest through a potential difference of 15 V that spans 15 cm.Which one takes less time to cover the 15 cm distance?

A)It's a tie-each reaches 15cm at the same time.
B)There isn't enough information given to answer this question.
C)The electron beats the proton.
D)The proton beats the electron.

Question 44

In Rutherford's famous experiment,alpha particles of mass 6.64 * 10^-27 kg and charge + 2e were fired directly at a gold nucleus (charge + 79e)with a speed of 3 * 10⁷ m/s.Due to the Coulomb repulsive force the alpha particles slowed down and eventually came to rest momentarily before turning around.The distance alpha particles came closest to the gold nucleus before turning around was

A)27.4 fm.
B)15.1 fm.
C)12.1 fm.
D)9.8 fm.
E)5.4 fm.

Question 45

A 250-g metal ball with a charge of 0.50 mC has a kinetic energy of 6.0 * 10⁸ J.It is traveling directly at an infinite plane of charge with a charge density of 33 C/m².If it is currently 2.0 m away from the plane of charge,how close will it come to the plane before stopping?

A)0.32 m
B)0.64 m
C)1.36 m
D)1.68 m
E)It will hit the charged plane.

Question 46

A positive point charge q₁ = 3.70 $\mu$ C is located at the origin (x=0,y=0).The charge is held fixed.Another point charge q2 = 6.90 $\mu$ C starts at the point (0.170 m,0).What is the magnitude of the work required to move q₂ to (0,0.370 m)(in J)?

A)0.730
B)0.912
C)1.140
D)1.425
E)1.782

Question 47

A solid metal ball with a radius of 30 cm has a net charge of 77 nC.If the electric potential is zero far away from the ball,what is the electric potential at the center of the ball?

A)0 V
B)770 V
C)2300 V
D)6100 V
E)7700 V

Question 48

There are two fixed point charges located on the x-axis.A charge of + 3.3 mC is located at x = + 2.0 m and a charge of -4.4 mC is located at x = -5.0 m.At what position on the x-axis is the electric potential equal to zero?

A)-1.5 m
B)-1.2 m
C)-1.0 m
D)-0.3 m
E)+ 23 m
F) The potential will be zero at more than one of the locations given.

Question 49

An electric potential has the value (22V/m)(y)- (13V/m² )(z-3m)².What is the magnitude of electric field at the origin?

A)78 V/m
B)100 V/m
C)92 V/m
D)81 V/m
E)56 V/m

Question 50

A 12-V battery is connected between a hollow metal sphere with a radius of 1 m and ground as shown in the figure.What is the electric potential inside the hollow metal sphere?

A)-12 V
B)-2.9 V
C)0 V
D)2.9 V
E)12 V

Question 51

Over a certain region of space the electric potential is V (Volt)= 3x - 5x²yz + 3yz².The magnitude of the electric field at a point P (1m,1m,2m)is

A)7.1 N/C.
B)12.9 N/C.
C)15.8 N/C.
D)18.5 N/C.
E)25.1 N/C.

Question 52

An infinite plane of charge has a planar charge density of + 2.2 nC/m² and is located in the yz plane at x=0.A + 3.3 nC fixed point charge is located at x = + 1.0 m.At what position on the x-axis between x = 0.0 m and x = + 1.0 m is the electric potential a minimum?

A)0.49 m
B)0.31 m
C)0.65 m
D)0.51 m
E)0.69 m

Question 53

An infinite plane of charge has a planar charge density of + 2.2 nC/m² and is located in the yz plane at x=0.What fixed point charge should be placed on the x-axis at x = + 1.0 m to make the electric potential a minimum on the x-axis at x=+0.65 m?

A)+ 5.0 nC
B)+ 7.8 nC
C)+ 3.3 nC
D)+ 1.7 nC
E)+ 4.4 nC

Question 54

A proton (mass: 1.67 * 10^-27 kg)is brought to within 1.0 pm of the center of a gold (Z = 79)nucleus,and released.How fast is it going when it is very far away from the gold nucleus?

A)4.7 * 10⁶ m/s
B)3.3 * 10⁶ m/s
C)5.3 * 10⁵ m/s
D)3.8 * 10⁵ m/s

Question 55

A line of charge of magnitude 2.60 $\mu$ C is uniformly distributed on a 90.0 degree arc with radius R = 3.00 m.What is the magnitude of the electric potential at point P (in V)?

A)7791
B)8804
C)9949
D)11,242
E)12,704

Question 56

How much work would be required to move an electron from 0.0529 * 10^-9 m from a proton to four times that distance?

A)5.4 * 10^-18J
B)3.3 * 10^-18J
C)1.6 * 10^-18J
D)None are correct.

Question 57

The period of motion of a proton (mass: 1.67 * 10^-27 kg)in a one-dimensional electrical potential (17 mV/m²)x² executes simple harmonic motion with what frequency?

A)200 Hz
B)290 Hz
C)1276 Hz
D)1830 Hz
E)Not enough information is given.

Question 58

An infinite plane of charge has a uniform planar charge density and is located in the yz plane at x=0.A fixed point charge placed on the x-axis at x = + 1.0 m and the electric potential is a minimum on the x-axis at x=+0.31 m.What is the planar charge density on the plane?

A)+ 1.1 nC/m²
B)+ 0.91 nC/m²
C)+ 1.7 nC/m²
D)+ 2.2 nC/m²
E)+ 3.5 nC/m²

Question 59

An electric potential has the value (22V/m)(y)- (13V/m² )(z-3m)².What is the electric field at the origin?

A)-22V/m ŷ
B)-78V/m ẑ
C)+ 56V/m
D)-22V/m ŷ - 78V/m ẑ
E)+ 22 V/m ŷ + 78V/m ẑ

Question 60

What is the magnitude of the electric potential at point P (in V)at a distance R = 3.50 m from a point charge Q of magnitude 4.00 $\mu$ C?

A)10,274
B)14,898
C)21,602
D)31,322
E)45,418

Question 61

The potential energy stored in a system consisting of an electric dipole in a constant electric field is maximum when the angle between the electric dipole moment and the electric field is:

A)0 ^$\circ$
B)90 ^$\circ$
C)180 ^$\circ$
D)the potential energy is independent of the angle between these two vectors

Question 62

A metal sphere of radius R = 30 cm carries a total charge Q = 2.0 $\mu$ C.A charge is located 5 m from the center of the sphere.How much work does it take to move the charge to a point exactly on the opposite side of the sphere,5 m away from the center,on the negative x-axis?

A)1440 J
B)0 J
C)-1440 J
D)3.2 * 10^-6 J
E)-3.2 * 10^-6 J

Question 63

A point charge is moved against a potential difference of + 20 V.The work done by the force moving the charge is 25 µJ.What is the charge?

A)5.0 µC
B)2.5 µC
C)1.3 µC
D)0.80 µC
E)1.0 µC

Question 64

A force does 25 µJ of work moving a point charge of 5 µC against a potential difference What is the potential difference?

A)5.0 V
B)20 V
C)25 V
D)0.20 V
E)125 V

Question 65

The potential energy stored in a system consisting of an electric dipole in a constant electric field is zero when the angle between the electric dipole moment and the electric field is:

A)0 ^$\circ$
B)90 ^$\circ$
C)180 ^$\circ$
D)the potential energy is independent of the angle between these two vectors

Question 66

A point charge of 5 µC is moved against a potential difference of + 20 V.What is the work done by the force moving the charge?

A)100 µJ
B)25 µJ
C)5 µJ
D)4 µJ
E)0.1 µJ

Question 67

The potential energy stored in a system consisting of an electric dipole in a constant electric field is minimum when the angle between the electric dipole moment and the electric field is:

A)0 ^$\circ$
B)90 ^$\circ$
C)180 ^$\circ$
D)the potential energy is independent of the angle between these two vectors

Question 68

Two isolated spheres hold the same charge,but sphere A has twice the radius of sphere B.How is the voltage near the surface of sphere A related to the voltage near the surface of sphere B?

A)V_A = V_B
B)V_A = 2V_B
C)2V_A = V_B
D)V_A = 4V_B

Question 69

For the set up shown,which statement concerning the point P is true?

A)The potential is zero and the field is to the right.
B)The potential is zero and the field is to the left.
C)The potential is negative and the field is zero.
D)The potential is positive and the field is zero.
E)The potential is zero and the field is zero.

Question 70

Which of the following statements concerning the electric potential due to the two charges shown below is true? Assume V = 0 at infinity.

A)The potential is always positive in the A region.
B)The potential is always positive in the B region.
C)The potential is always positive in the C region.
D)The potential is always negative in the B region.
E)The potential cannot change sign in the B region.

Question 71

An electron is placed in an electric field and is allowed to accelerate for a distance of 1 m.If the strength of the electric field is E = 200 V/m then what is the final velocity of the electron,assuming it starts from rest?

A)3.5 * 10⁸ m/s
B)1.2 * 10⁴ m/s
C)7.2 * 10² m/s
D)4.1 * 10³ m/s
E)8.4 * 10⁶ m/s

Question 72

Two charges Q₁ = 4.4 $\mu$ C and Q₂ = -3.9 $\mu$ C are located on the x-axis at x₁ = -80 m and x₂ = 87 m.What is the electric potential at x = 52 m?

A)0.125 V
B)-0.125 V
C)0 V
D)703 V
E)-703 V

Question 73

Two isolated spheres have the same electric potential at their surface,but sphere A has twice the charge of sphere B.How is the radius of sphere A related to the radius of sphere B?

A)R_A = 2R_B
B)R_A = R_B
C)2R_A = R_B
D)R_A = 4R_B

Question 74

Which of the following statements is true?

A)If a metal sphere is charged,the extra charge will be uniformly distributed over the volume of the sphere.
B)On the line between two positive charges,the electric field is never zero.
C)A positive charge will always be attracted to a metal surface,but a negative charge will be repelled.
D)Good insulators do not conduct electricity well because they are usually doped with small amounts of impurities.
E)On the line between two positive charges,the electric potential is never zero.

Question 75

Two isolated spheres have the same electric potential at their surface,but sphere A has twice the radius of sphere B.How is the charge on sphere A related to the charge on sphere B?

A)Q_A = Q_B
B)Q_A = 2Q_B
C)2Q_A = Q_B
D)Q_A = 4Q_B