Deck 21: Electric Potential

Question 1

A 1.0 μF capacitor has a potential difference of 6.0 V applied across its plates.If the potential difference across its plates is increased to 8.0 V,how much additional energy does the capacitor store?

A)14 μJ
B)28 μJ
C)2.0 μJ
D)4.0 μJ

Answer 1

14 μJ

Question 2

Two parallel plates are separated by 1.0 mm.If the potential difference between them is 3.0 V,what is the magnitude of their surface charge densities?

A)27 nC/m²
B)0.16 mC/m²
C)53 nC/m²
D)0.33 mC/m²

Answer 2

27 nC/m²

Question 3

A proton with speed 1.5 × 10⁵ m/s falls through a potential difference of 100 volts,gaining speed.What is the speed reached?

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

Answer 3

2.04 × 10⁵ m/s

Question 4

Two parallel circular plates with radius 7.0 mm carrying equal-magnitude surface charge densities of ±3.0 μC/m² are separated by a distance of 1.0 mm.How much stored energy do the plates have?

A)78 nJ
B)25 nJ
C)7.9 nJ
D)250 nJ

Question 5

A 6.0 μC negative charge is attracted to a large,well-anchored,positive charge.How much kinetic energy does the negatively charged object gain if the potential difference through which it moves is 3 mV?

A)18 nJ
B)0.50 kJ
C)0.50 J
D)6.0 μJ

Question 6

Two parallel plates that are initially uncharged are separated by 1.2 mm.What charge must be transferred from one plate to the other if 11.0 kJ of energy are to be stored in the plates? The area of each plate is 19.0 mm².

A)56 μC
B)39 μC
C)78 μC
D)3.5 mC

Question 7

A charge of 3.0 μC and a second charge are initially far apart.If it takes 29 J of work to bring them to a final configuration in which the 3.0 μC is at x = 1.0 mm,y - 1.0 mm,and the other charge is at x = 1.0 mm,y = 3.0 mm,find the magnitude of the unknown charge.(The value of k is 9.0  109 N·m²/C². )

A)2.15 μC
B)4.30 μC
C)10.74 μC
D)4.30 nC

Question 8

Consider the group of charges in this figure.All three charges have Q = 2.4 nC.What is their electric potential energy?

A)4.1 × 10^-6 J
B)4.6 × 10^-6 J
C)4.2 × 10^-6 J
D)4.4 × 10^-6 J

Question 9

A 3.0 pF capacitor consists of two parallel plates that have surface charge densities of ±1.0 nC/mm².If the potential between the plates is 23.0 kV,find the surface area of one of the plates.

A)69 mm²
B)0.014 mm²
C)35 mm²
D)0.0072 mm²

Question 10

A sphere with radius 2.0 mm carries a 1.0 μC charge.What is the potential difference,VB - VA,between point B 4.0 m from the center of the sphere and point A 9.0 m from the center of the sphere? (The value of k is 9.0  109 N·m²/C². )

A)1300 V
B)-1300 V
C)140 V
D)-0.45 V

Question 11

A 100.0 pF capacitor consists of two circular plates of radius 0.40 mm.How far apart are the plates? (The value of εo is 8.85  10-12 C²/N·m². )

A)0.044 μm
B)0.022 μm
C)0.0050 μm
D)0.0025 μm

Question 12

An electron was accelerated from rest through a potential difference of 9900 V.What is its speed?

A)5.9 × 10⁷ m/s
B)4.9 × 10⁷ m/s
C)3.9 × 10⁷ m/s
D)2.9 × 10⁷ m/s

Question 13

A 3.0 μC point charge and a 9.0 μC point charge are initially infinitely far apart.How much work does it take to bring the 3.0 μC point charge to x = 3.0 mm,y = 0.0 mm,and the 9.0 μC point charge to x = -3.0 mm,y = 0.0 mm? (The value of k is 9.0  10⁹ N·m²/C². )

A)41 J
B)81 J
C)27 J
D)6.8 J

Question 14

A parallel-plate capacitor has a voltage of 391 V applied across its plates,then the voltage source is removed.What is the voltage across its plates if the space between them becomes filled with mica? (The dielectric constant for mica is 5.4 and for air is 1.0006. )

A)72 V
B)2110 V
C)641 V
D)18,675 V

Question 15

A dipole with ±6.0 μC charges is positioned so that the positive charge is 1.0 mm to the right of the origin and the negative charge is at the origin.How much work does it take to bring a 10.0 μC charge from infinity to a position x = 3.0 mm,y = 0.0 mm? (The value of k is 9.0  10⁹ N·m²/C². )

A)90 J
B)450 J
C)75 J
D)200 J

Question 16

A parallel-plate capacitor has a potential energy due to its charge of 6.00 mJ.It is accidentally filled with water in such a way as not to discharge its plates.How much energy does it continue to store after it is filled? (The dielectric constant for water is 78 and for air is 1.0006. )

A)0.077 mJ
B)468 mJ
C)0.04 mJ
D)6.00 mJ

Question 17

Point charges,Q₁ = +46 nC and Q₂ = -75 nC,are placed as shown.In the figure,an external force transports an electron from point A to point B.The work done by the external force is closest to:

A)+ 730 eV
B)+ 610 eV
C)+ 480 eV
D)- 730 eV
E)- 480 eV

Question 18

A parallel-plate capacitor consists of two parallel,square plates that have dimensions 1.0 cm by 1.0 cm.If the plates are separated by 1.0 mm,and the space between them is filled with teflon,what is the capacitance? (The dielectric constant for teflon is 2.1. )

A)1.9 pF
B)0.44 pF
C)2.1 pF
D)0.88 pF

Question 19

Three charges form an equilateral triangle with 1.6 cm long sides.What is the electric potential at the point indicated with the dot?

A)zero
B)3900 V
C)1900 V
D)5800 V

Question 20

A proton with a speed of 2.0 x 10⁵ m/s falls through a potential difference V and thereby increases its speed to 4.0 × 10⁵ m/s.Through what potential difference did the proton fall?

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

Question 21

Four charged particles (two having a charge +Q and two having a charge -Q)are distributed on the xy-plane,as shown below.Each charge is equidistant from the origin.The voltage is zero at infinity.The voltage at location P,which is on the z axis,is

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

Question 22

Two equal positive charges are separated by a fixed distance.If you put a third positive charge midway between these two charges,its electrical potential energy (relative to infinity)is zero because the electrical forces due to the two fixed charges just balance each other.

Question 23

When the electric field is zero at a point,the potential must also be zero there.

Question 24

Two equal but opposite point charges are held a distance D apart,and a third point charge Q is placed midway between them.When Q is released it will remain at rest because its potential energy is zero at the midpoint.

Question 25

If the potential is constant on a surface,then any electric field present can only be perpendicular to that surface.

Question 26

Suppose you have two point charges,+Q and -q.As you pull them farther and farther apart,you increase the potential energy of this system relative to infinity.

Question 27

A parallel plate capacitor contains a positively charged plate on the left,and a negatively charged plate on the right.An electron in between the plates is moving to the right.Which statement is true?

A)The potential energy of the electron is increasing and it is moving to a region having a lower potential.
B)The potential energy of the electron is increasing and it is moving to a region having a higher potential.
C)The potential energy of the electron is decreasing and it is moving to a region having a lower potential.
D)The potential energy of the electron is decreasing and it is moving to a region having a higher potential.

Question 28

A small object carries a charge of 10.0 μC.If the object is so small that it can be regarded as a point charge,what is the energy density at a distance of 2.0 m from the charge? (The value of k is 9.0  10⁹ N·m²/C². )

A)2.2 mJ/m³
B)4.5 mJ/m³
C)9.0 mJ/m³
D)18 mJ/m³

Question 29

A uniform electric field has the strength of 5.0 N/C.What is the electric energy density of the field? (The value of εo is 8.85  10-12 C²/N·m². )

A)1.1 × 10^-10 J/m³
B)2.2 × 10^-11 J/m³
C)1.4 × 10¹² J/m³
D)2.8 × 10¹² J/m³

Question 30

Four identical positive point charges lie at the corners of a square.The electrical potential at the center of this square is zero because the electric fields all cancel at that point.

Question 31

The potential is zero on the surface of a conductor in electrostatic equilibrium.

Question 32

Suppose a region of space has a uniform electric field,directed toward the right,as shown in the figure.Which statement is true?

A)The voltage at all three locations is the same.
B)The voltage at points A and B are equal,and the voltage at point C is higher than the voltage at point A.
C)The voltage at points A and B are equal,and the voltage at point C is lower than the voltage at point A.
D)The voltage at point A is the highest,the voltage at point B is the second highest,and the voltage at point C is the lowest.
E)None of the above

Question 33

Suppose you have two positive point charges and want to move them closer together.To do the least amount of work,you should move them directly toward each other;any other path will require more work because the charges must move through a greater distance.

Question 34

If the electric field is zero everywhere inside a region of space,the potential must also be zero in that region.

Question 35

As an electron moves from a high potential to a low potential,its electrical potential energy

A)increases.
B)decreases.
C)remains constant.

Question 36

If the electrical potential in a region is constant,the electric field must be zero everywhere in that region.

Question 37

Four charged particles (two having a charge +Q and two having a charge -Q)are distributed on the xy-plane,as shown below.Each charge is equidistant from the origin.The voltage is zero at infinity.The amount of work required to move a positively charged particle from point P to point O (which is on the z-axis,below the origin)is

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

Question 38

If an object is at zero potential,it must be uncharged.

Question 39

You want to put an electron somewhere between the plates of a parallel plate capacitor so that it will have the maximum electrical potential energy relative to one of the plates.The best place to put it is at the inner surface of the negative plate.

Question 40

The capacitance of a capacitor depends on

A)the charge on it.
B)the potential difference across it.
C)the energy stored in it.
D)More than one of these
E)None of these

Question 41

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

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

Question 42

A proton is accelerated from rest through a potential difference V_o and gains a speed vo.If it were accelerated instead through a potential difference of 2V_o,it would gain a speed:

A)8 v_o
B)4 v_o
C)2 v_o
D)v_o

Question 43

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

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

Question 44

Two conductors are joined by a long copper wire.Thus

A)each conductor carries the same free charge.
B)each conductor must be at the same potential.
C)the electric field at the surface of each conductor is the same.
D)no free charge can be present on either conductor.
E)the potential on the wire is the average of the potential of each conductor.

Question 45

A parallel-plate capacitor having circular plates of diameter D and 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 46

A proton is projected toward a fixed nucleus of charge +Ze with velocity vo.Initially the two particles are very far apart.When the proton is a distance R from the nucleus its velocity has decreased to 1/2 v_o.How far from the nucleus will the proton be when its velocity has dropped to 1/4 v_o?

A)1/16 R
B)1/4 R
C)1/2 R
D)4/5 R
E)None of these