Deck 20: Electric Potential and Capacitance

Question 1

A particle (mass = 6.7*10 ^{- 27} kg,charge = 3.2 *10 ^{- 19} C)moves along the positive x axis with a speed of 4.8 *10⁵ m/s.It enters a region of uniform electric field parallel to its motion and comes to rest after moving 2.0 m into the field.What is the magnitude of the electric field?

A)2.0 kN/C
B)1.5 kN/C
C)1.2 kN/C
D)3.5 kN/C
E)2.4 kN/C

Answer 1

1.2 kN/C

Question 2

Particle A (mass = m,charge = Q)and B (mass = m,charge = 5 Q)are released from rest with the distance between them equal to 1.0 m.If Q = 12 $\mu$ C,what is the kinetic energy of particle B at the instant when the particles are 3.0 m apart?

A)8.6 J
B)3.8 J
C)6.0 J
D)2.2 J
E)4.3 J

Answer 2

2.2 J

Question 3

Point charges q and Q are positioned as shown.If q = +2.0 nC,Q = -2.0 nC,a = 3.0 m,and b = 4.0 m,what is the electric potential difference,V_A -V_B?

A)8.4 V
B)6.0 V
C)7.2 V
D)4.8 V
E)0 V

Answer 3

4.8 V

Question 4

An electron (m = 9.1 *10 ^{- 31} kg,q = -1.6*10 ^{- 19} C)starts from rest at point A and has a speed of 5.0 *10⁶ m/s at point B.Only electric forces act on it during this motion.Determine the electric potential difference V_A -V_B.

A)-71 V
B)+71 V
C)-26 V
D)+26 V
E)-140 V

Question 5

A proton (m = 1.7 *10 ^{- 27} kg,q = +1.6 *10 ^{- 19} C)starts from rest at point A and has a speed of 40 km/s at point B.Only electric forces act on it during this motion.Determine the electric potential difference V_B - V_A.

A)+8.5 V
B)-8.5 V
C)-4.8 V
D)+4.8 V
E)-17 V

Question 6

A proton (mass = 1.67*10 ^{- 27} kg,charge = 1.60*10 ^{- 19} C)moves from point A to point B under the influence of an electrostatic force only.At point A the proton moves with a speed of 60 km/s.At point B the speed of the proton is 80 km/s.Determine the potential difference V_B- V_A.

A)+15 V
B)-15 V
C)-33 V
D)+33 V
E)-20 V

Question 7

Points A [at (2,3)m] and B [at (5,7)m] are in a region where the electric field is uniform and given by $\overrightarrow { \mathbf { E } } = ( 4 \tilde { \mathbf { i } } + 3 \tilde { \mathbf { j } } )$ N/C.What is the potential difference V_A - V_B?

A)33 V
B)27 V
C)30 V
D)24 V
E)11 V

Question 8

What is the speed of a proton that has been accelerated from rest through a potential difference of 4.0 kV?

A)1.1*10⁶ m/s
B)9.8 *10⁵ m/s
C)8.8 * 10⁵ m/s
D)1.2 *10⁶ m/s
E)6.2* 10⁵ m/s

Question 9

A charged particle (q = -8.0 mC),which moves in a region where the only force acting on the particle is an electric force,is released from rest at point A.At point B the kinetic energy of the particle is equal to 4.8 J.What is the electric potential difference V_B- V_A?

A)-0.60 kV
B)+0.60 kV
C)+0.80 kV
D)-0.80 kV
E)+0.48 kV

Question 10

A particle (charge = Q)is kept in a fixed position at point P,and a second particle (charge = q)is released from rest when it is a distance R from P.If Q = +2.0 mC,q = -1.5 mC,and R = 30 cm,what is the kinetic energy of the moving particle after it has moved a distance of 10 cm?

A)60 kJ
B)45 kJ
C)75 kJ
D)90 kJ
E)230 kJ

Question 11

A particle (charge = +2.0 mC)moving in a region where only electric forces act on it has a kinetic energy of 5.0 J at point A.The particle subsequently passes through point B which has an electric potential of +1.5 kV relative to point A.Determine the kinetic energy of the particle as it moves through point B.

A)3.0 J
B)2.0 J
C)5.0 J
D)8.0 J
E)10.0 J

Question 12

A particle (charge = 40 $\mu$ C)moves directly toward a second particle (charge = 80 $\mu$ C)which is held in a fixed position.At an instant when the distance between the two particles is 2.0 m,the kinetic energy of the moving particle is 16 J.Determine the distance separating the two particles when the moving particle is momentarily stopped.

A)0.75 m
B)0.84 m
C)0.95 m
D)0.68 m
E)0.56 m

Question 13

A particle (charge 7.5 $\mu$ C)is released from rest at a point on the x axis,x = 10 cm.It begins to move due to the presence of a 2.0- $\mu$ C charge which remains fixed at the origin.What is the kinetic energy of the particle at the instant it passes the point x = 1.0 m?

A)3.0 J
B)1.8 J
C)2.4 J
D)1.2 J
E)1.4 J

Question 14

A particle (charge = 50 $\mu$ C)moves in a region where the only force on it is an electric force.As the particle moves 25 cm from point A to point B,its kinetic energy increases by 1.5 mJ.Determine the electric potential difference,V_B - V_A.

A)-50 V
B)-40 V
C)-30 V
D)-60 V
E)+15 V

Question 15

If a = 30 cm,b = 20 cm,q = +2.0 nC,and Q = -3.0 nC in the figure,what is the potential difference V_A - V_B?

A)+60 V
B)+72 V
C)+84 V
D)+96 V
E)+48 V

Question 16

An alpha particle (m = 6.7* 10 ^{- 27} kg,q = +3.2 *10 ^{- 19} C)has a speed of 20 km/s at point A and moves to point B where it momentarily stops.Only electric forces act on the particle during this motion.Determine the electric potential difference V_A- V_B.

A)+4.2 V
B)-4.2 V
C)-9.4 V
D)+9.4 V
E)-8.4 V

Question 17

A particle (m = 2.0 $\mu$ g,q = -5.0 $\mu$ C)has a speed of 30 m/s at point A and moves (with only electric forces acting on it)to point B where its speed is 80 m/s.Determine the electric potential difference V_A - V_B.

A)-2.2 kV
B)+1.1 kV
C)-1.1 kV
D)+2.2 kV
E)+1.3 kV

Question 18

A proton (mass = 1.67 *10 ^{- 27} kg,charge = 1.60 *10 ^{- 19} C)moves from point A to point B under the influence of an electrostatic force only.At point A the proton moves with a speed of 50 km/s.At point B the speed of the proton is 80 km/s.Determine the potential difference V_B-V_A.

A)+20 V
B)-20 V
C)-27 V
D)+27 V
E)-40 V

Question 19

Point charges of equal magnitudes (25 nC)and opposite signs are placed on (diagonally)opposite corners of a 60-cm *80-cm rectangle.If point A is the corner of this rectangle nearest the positive charge and point B is located at the intersection of the diagonals of the rectangle,determine the potential difference,V_B -V_A.

A)-47 V
B)+94 V
C)zero
D)-94 V
E)+47 V

Question 20

Points A [at (3,6)m] and B [at (8,-3)m] are in a region where the electric field is uniform and given by $\overrightarrow { \mathrm { E } } = 12{ \tilde { i } }$ N/C.What is the electric potential difference V_A - V_B?

A)+60 V
B)-60 V
C)+80 V
D)-80 V
E)+50 V

Question 21

When a positive charge is released and moves along an electric field line,it 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.
E)greater magnitude of the electric field.

Question 22

Two identical particles,each with a mass of 4.5 $\mu$ g and a charge of 30 nC,are moving directly toward each other with equal speeds of 4.0 m/s at an instant when the distance separating the two is equal to 25 cm.How far apart will they be when closest to one another?

A)9.8 cm
B)12 cm
C)7.8 cm
D)15 cm
E)20 cm

Question 23

A particle (charge = 5.0 $\mu$ C)is released from rest at a point x = 10 cm.If a 5.0- $\mu$ C charge is held fixed at the origin,what is the kinetic energy of the particle after it has moved 90 cm?

A)1.6 J
B)2.0 J
C)2.4 J
D)1.2 J
E)1.8 J

Question 24

When introduced into a region where an electric field is present,a proton with initial velocity $\overrightarrow { \mathbf { v } }$ will eventually move

A)along an electric field line,in the positive direction of the line.
B)along an electric field line,in the negative direction of the line.
C)to a point of decreased potential.
D) as described in both (a)and (c).

Question 25

A system consisting of a positively-charged particle and an electric field

A)loses potential difference and kinetic energy when the charged particle moves in the direction of the field.
B)loses electric potential energy when the charged particle moves in the direction of the field.
C)loses kinetic energy when the charged particle moves in the direction of the field.
D)gains electric potential energy when the charged particle moves in the direction of the field.
E)gains potential difference and electric potential energy when the charged particle moves in the direction of the field.

Question 26

A 60- $\mu$ C charge is held fixed at the origin and a -20- $\mu$ C charge is held fixed on the x axis at a point x = 1.0 m.If a 10- $\mu$ C charge is released from rest at a point x = 40 cm,what is its kinetic energy the instant it passes the point x = 70 cm?

A)9.8 J
B)7.8 J
C)8.8 J
D)6.9 J
E)2.8 J

Question 27

When a charged particle is moved along an electric field line,

A)the electric field does no work on the charge.
B)the electrical potential energy of the charge does not change.
C)the electrical potential energy of the charge undergoes the maximum change in magnitude.
D)the voltage changes,but there is no change in electrical potential energy.
E)the electrical potential energy undergoes the maximum change,but there is no change in voltage.

Question 28

The electric field in a region of space is given by E_x = (3.0x)N/C,E_y = E_z = 0,where x is in m.Points A and B are on the x axis at x_A = 3.0 m and x_B = 5.0 m.Determine the potential difference V_B - V_A.

A)-24 V
B)+24 V
C)-18 V
D)+30 V
E)-6.0 V

Question 29

Two identical particles,each with a mass of 2.0 $\mu$ g and a charge of 25 nC,are released simultaneously from rest when the two are 4.0 cm apart.What is the speed of either particle at the instant when the two are separated by 10 cm?

A)7.3 m/s
B)9.8 m/s
C)9.2 m/s
D)6.5 m/s
E)4.6 m/s

Question 30

Can the lines in the figure below be equipotential lines?

A)No,because there are sharp corners.
B)No,because they are isolated lines.
C)Yes,because any lines within a charge distribution are equipotential lines.
D)Yes,they might be boundary lines of the two surfaces of a conductor.
E)It is not possible to say without further information.

Question 31

Identical 8.0- $\mu$ C point charges are positioned on the x axis at x = $\pm$ 1.0 m and released from rest simultaneously.What is the kinetic energy of either of the charges after it has moved 2.0 m?

A)84 mJ
B)54 mJ
C)96 mJ
D)63 mJ
E)48 mJ

Question 32

Two particles,each having a mass of 3.0 $\mu$ g and having equal but opposite charges of magnitude 5.0 nC,are released simultaneously from rest when the two are 5.0 cm apart.What is the speed of either particle at the instant when the two are separated by 2.0 cm?

A)2.1 m/s
B)1.5 m/s
C)1.8 m/s
D)2.4 m/s
E)3.2 m/s

Question 33

When introduced into a region where an electric field is present,an electron with initial velocity $\overrightarrow { \mathbf { v } }$ will eventually move

A)along an electric field line,in the positive direction of the line.
B)along an electric field line,in the negative direction of the line.
C)to a point of decreased potential.
D)to a point of increased potential.
E)as described in both (b)and (d).

Question 34

Four electrons move from point A to point B in a uniform electric field as shown below.Rank the electrons in diagrams I through IV by the changes in potential energy from most positive to most negative when traveling from A to B.

A)I = II = III = IV.
B)II = III > I > IV.
C)III > I = IV > II.
D)II > I = IV > III.
E)I > II = III > IV.

Question 35

When a negative charge is released and moves along an electric field line,it 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.
E)decreasing magnitude of the electric field.

Question 36

Two particles,each having a mass of 3.0 $\mu$ g and having equal but opposite charges of magnitude of 6.0 nC,are released simultaneously from rest when they are a very large distance apart.What distance separates the two at the instant when each has a speed of 5.0 m/s?

A)4.3 mm
B)8.6 mm
C)7.3 mm
D)5.6 mm
E)2.2 mm

Question 37

A particle (q = +5.0 $\mu$ C)is released from rest when it is 2.0 m from a charged particle which is held at rest.After the positively charged particle has moved 1.0 m toward the fixed particle,it has a kinetic energy of 50 mJ.What is the charge on the fixed particle?

A)-2.2 $\mu$ C
B)+6.7 $\mu$ C
C)-2.7 $\mu$ C
D)+8.0 $\mu$ C
E)-1.1 $\mu$ C

Question 38

Through what potential difference must an electron (starting from rest)be accelerated if it is to reach a speed of 3.0 *10⁷ m/s?

A)5.8 kV
B)2.6 kV
C)7.1 kV
D)8.6 kV
E)5.1 kV

Question 39

A system consisting of a negatively-charged particle and an electric field

A)gains potential difference and kinetic energy when the charged particle moves in the direction of the field.
B)loses electric potential energy when the charged particle moves in the direction of the field.
C)gains kinetic energy when the charged particle moves in the direction of the field.
D)gains electric potential energy when the charged particle moves in the direction of the field.
E)gains potential difference and electric potential energy when the charged particle moves in the direction of the field.

Question 40

Equipotentials are lines along which

A)the electric field is constant in magnitude and direction.
B)the electric charge is constant in magnitude and direction.
C)maximum work against electrical forces is required to move a charge at constant speed.
D)a charge may be moved at constant speed without work against electrical forces.
E)charges move by themselves.

Question 41

Identical point charges (+30 $\mu$ C)are placed at the corners of a rectangle (4.0 m *6.0 m).How much external energy is required to bring a charge of 55 $\mu$ C from infinity to the midpoint of one of the 6.0-m long sides of the rectangle?

A)22 J
B)16 J
C)13 J
D)19 J
E)8.0 J

Question 42

The Bohr model pictures a hydrogen atom in its ground state as a proton and an electron separated by the distance a₀ = 0.529 *10 ^{- 10} m.The electric potential created by the electron at the position of the proton is

A)-13.6 V.
B)+13.6 V.
C)-27.2 V.
D)+27.2 V.
E)+5.12*10⁹ V.

Question 43

Three identical point charges (+2.0 nC)are placed at the corners of an equilateral triangle with sides of 2.0-m length.If the electric potential is taken to be zero at infinity,what is the potential at the midpoint of any one of the sides of the triangle?

A)16 V
B)10 V
C)70 V
D)46 V
E)44 V

Question 44

Several charges in the neighborhood of point P produce an electric potential of 6.0 kV (relative to zero at infinity)and an electric field of $36 \hat { \mathbf { i } }$ N/C at point P.Determine the work required of an external agent to move a 3.0- $\mu$ C charge along the x axis from infinity to point P without any net change in the kinetic energy of the particle.

A)21 mJ
B)18 mJ
C)24 mJ
D)27 mJ
E)12 mJ

Question 45

Three charged particles are positioned in the xy plane: a 50-nC charge at y = 6 m on the y axis,a -80-nC charge at x = -4 m on the x axis,and a 70-nc charge at y = -6 m on the y axis.What is the electric potential (relative to a zero at infinity)at the point x = 8 m on the x axis?

A)+81 V
B)+48 V
C)+5.8 V
D)-72 V
E)-18 V

Question 46

Four identical point charges (+4.0 $\pm$ C)are placed at the corners of a square which has 20-cm sides.How much work is required to assemble this charge arrangement starting with each of the charges a very large distance from any of the other charges?

A)+2.9 J
B)+3.9 J
C)+2.2 J
D)+4.3 J
E)+1.9 J

Question 47

Four identical point charges (+6.0 nC)are placed at the corners of a rectangle which measures 6.0 m * 8.0 m.If the electric potential is taken to be zero at infinity,what is the potential at the geometric center of this rectangle?

A)58 V
B)63 V
C)43 V
D)84 V
E)11 V

Question 48

Four electrons move from point A to point B in a uniform electric field as shown below.Rank the electrons in diagrams I through IV by the changes in potential from most positive to most negative when traveling from A to B.

A)I = II = III = IV.
B)II = III > I > IV.
C)III > I = IV > II.
D)II > I = IV > III.
E)I > II = III > IV.

Question 49

Identical 2.0- $\mu$ C charges are located on the vertices of a square with sides that are 2.0 m in length.Determine the electric potential (relative to zero at infinity)at the center of the square.

A)38 kV
B)51 kV
C)76 kV
D)64 kV
E)13 kV

Question 50

Identical point charges (+20 $\mu$ C)are placed at the corners of an equilateral triangle with sides of 2.0-m length.How much external energy is required to bring a charge of 45 $\mu$ C from infinity to the midpoint of one side of the triangle?

A)26 J
B)16 J
C)23 J
D)21 J
E)12 J

Question 51

A +4.0- $\pm$ C charge is placed on the x axis at x = +3.0 m,and a -2.0- $\pm$ C charge is located on the y axis at y = -1.0 m.Point A is on the y axis at y = +4.0 m.Determine the electric potential at point A (relative to zero at the origin).

A)6.0 kV
B)8.4 kV
C)9.6 kV
D)4.8 kV
E)3.6 kV

Question 52

An electron is released form rest in a region of space where a uniform electric field is present.Joanna claims that its kinetic and potential energies both increase as it moves from its initial position to its final position.Sonya claims that they both decrease.Which one,if either,is correct?

A)Joanna,because the electron moves opposite to the direction of the field.
B)Sonya,because the electron moves opposite to the direction of the field.
C)Joanna,because the electron moves in the direction of the field.
D)Sonya,because the electron moves in the direction of the field.
E)Neither,because the kinetic energy increases while the electron moves to a point at a higher potential.

Question 53

Identical 4.0- $\pm$ C charges are placed on the y axis at y = $\pm$ 4.0 m.Point A is on the x axis at x = +3.0 m.Determine the electric potential of point A (relative to zero at the origin).

A)-4.5 kV
B)-2.7 kV
C)-1.8 kV
D)-3.6 kV
E)-14 kV

Question 54

The Bohr model pictures a hydrogen atom in its ground state as a proton and an electron separated by the distance a₀ = 0.529 * 10 ^{- 10} m.The electric potential created by the proton at the position of the electron is

A)-13.6 V.
B)+13.6 V.
C)-27.2 V.
D)+27.2 V.
E)+5.12 * 10⁹ V.

Question 55

A charge of +3.0 $\pm$ C is distributed uniformly along the circumference of a circle with a radius of 20 cm.How much external energy is required to bring a charge of 25 $\pm$ C from infinity to the center of the circle?

A)5.4 J
B)3.4 J
C)4.3 J
D)2.7 J
E)6.8 J

Question 56

An infinite plane of charge with $\sigma = + 55.5 \frac { p C } { \mathrm {~m} ^ { 2 } }$ is tilted at a 45 $\degree$ angle to the vertical direction as shown below.The potential difference,V_B -V_A,in volts,between points A and B,a 4.50 m distance apart,is

A)-7.06.
B)-9.98.
C)-14.11.
D)+7.06.
E)+9.98.

Question 57

An infinite plane of charge with $\sigma = + 55.5 \frac { p C } { \mathrm {~m} ^ { 2 } }$ is tilted at a 45 $\degree$ angle to the vertical direction as shown below.The potential difference,V_A -V_B,in volts,between points A and B,a 4.50 m distance apart,is

A)-7.06.
B)-9.98.
C)-14.11.
D)+7.06.
E)+9.98.

Question 58

Identical point charges (+50 $\pm$ C)are placed at the corners of a square with sides of 2.0-m length.How much external energy is required to bring a fifth identical charge from infinity to the geometric center of the square?

A)41 J
B)16 J
C)64 J
D)10 J
E)80 J

Question 59

Two charges lie on the x axis,+2q at the origin,and -3q at x = 5.0 m.The point on the x axis where the electric potential has a zero value (when the value at infinity is also zero)is

A)1.0 m.
B)2.0 m.
C)2.5 m.
D)3.0 m.
E)4.0 m.

Question 60

Two charges lie on the x axis,+3q at the origin,and -2q at x = 5.0 m.The point on the x axis where the electric potential has a zero value (when the value at infinity is also zero)is

A)1.0 m.
B)2.0 m.
C)2.5 m.
D)3.0 m.
E)4.0 m.

Question 61

For the potential $V = 3 x ^ { 2 } z - 2 y z ^ { 3 }$ ,what is the corresponding electric field at the point (2,2,2)?

A) $- 24 \tilde { \mathbf { i } } + 16 \tilde { \mathbf { j } } + 36 \tilde { \mathbf { k } }$
B) $12 \tilde { \mathbf { i } } - 16 \tilde { \mathbf { j } } + - 16 \tilde{ \mathbf { k } }$
C) $24 \tilde { \mathbf { i } } - 16 \tilde{ \mathbf { j } } - 36 \tilde { \mathbf { k } }$
D) $- 6 \tilde { \mathbf { i } } + 2 \tilde { \mathbf { j } } + 6 \tilde { \mathbf { k } }$
E)The correct answer is not given.

Question 62

A linear charge of nonuniform density $\lambda$ = bx,where b = 2.1 nC/m²,is distributed along the x axis from x = 2.0 m to x = 3.0 m.Determine the electric potential (relative to zero at infinity)of the point y = 4.0 m on the y axis.

A)36 V
B)95 V
C)10 V
D)17 V
E)15 V

Question 63

An electric dipole having dipole moment of magnitude p is placed in a uniform electric field having magnitude E.What is the magnitude of the greatest change in potential energy that can happen for this dipole in this field?

A)pE
B) $2 p E$
C)4pE
D) $\sqrt { 2 } p E$
E)No answer given is correct.

Question 64

A charge of 20 nC is distributed uniformly along the y axis from y = 0 to y = 4 m.Which of the following integrals is correct for the electric potential (relative to zero at infinity)at the point x = +3 m on the x axis?

A) $\int _ { 0 } ^ { 4 } \frac { 45 d y } { \left( y ^ { 2 } + 9 \right) ^ { 1 / 2 } }$
B) $\int _ { 0 } ^ { 4 } \frac { 180 d y } { \left( y ^ { 2 } + 9 \right) ^ { 1 / 2 } }$
C) $\int _ { 0 } ^ { 4 } \frac { 45 d y } { y ^ { 2 } + 9 }$
D) $\int _ { 0 } ^ { 4 } \frac { 180 d y } { y ^ { 2 } + 9 }$
E) $\int _ { 0 } ^ { 4 } \frac { 45 d y } { \left( y ^ { 2 } + 9 \right) ^ { 3 / 2 } }$

Question 65

A charge of uniform density (0.80 nC/m)is distributed along the x axis from the origin to the point x = 10 cm.What is the electric potential (relative to zero at infinity)at a point,x = 18 cm,on the x axis?

A)7.1 V
B)5.8 V
C)9.0 V
D)13 V
E)16 V

Question 66

A charge of 18 nC is uniformly distributed along the y axis from y = 3 m to y = 5 m.Which of the following integrals is correct for the electric potential (relative to zero at infinity)at the point x = +2 m on the x axis?

A) $\int _ { 3 } ^ { 5 } \frac { 81 d y } { \left( y ^ { 2 } + 4 \right) ^ { 1 / 2 } }$
B) $\int _ { 3 } ^ { 5 } \frac { 162 d y } { \left( y ^ { 2 } + 4 \right) ^ { 1 / 2 } }$
C) $\int _ { 3 } ^ { 5 } \frac { 81 d y } { y ^ { 2 } + 4 }$
D) $\int _ { 3 } ^ { 5 } \frac { 162 d y } { y ^ { 2 } + 4 }$
E) $\int _ { 3 } ^ { 5 } \frac { 81 d y } { y }$

Question 67

A charge of 4.0 nC is distributed uniformly along the x axis from x = +4 m to x = +6 m.Which of the following integrals is correct for the electric potential (relative to zero at infinity)at the origin?

A) $\int _ { 4 } ^ { 6 } \frac { 18 d x } { 4 - x }$
B) $\int _ { 4 } ^ { 6 } \frac { 36 d x } { x }$
C) $\int _ { 4 } ^ { 6 } \frac { 18 d x } { x }$
D) $\int _ { 4 } ^ { 6 } \frac { 36 d x } { 6 - x }$
E) $\int _ { 4 } ^ { 6 } \frac { 36 d x } { 4 + x }$

Question 68

Charge of uniform linear density 6.0 nC/m is distributed along the x axis from x = 0 to x = +3 m.Which of the following integrals is correct for the electric potential (relative to zero at infinity)at the point y = +4 m on the y axis?

A) $\int _ { 0 } ^ { 3 } \frac { 54 d x } { \left( x ^ { 2 } + 16 \right) ^ { 1 / 2 } }$
B) $\int _ { 0 } ^ { 3 } \frac { 18 d x } { \left( x ^ { 2 } + 16 \right) ^ { 1 / 2 } }$
C) $\int _ { 0 } ^ { 3 } \frac { 54 d x } { x ^ { 2 } + 16 }$
D) $\int _ { 0 } ^ { 3 } \frac { 18 d x } { x ^ { 2 } + 16 }$
E) $\int _ { 0 } ^ { 3 } \frac { 108 d x } { \left( x ^ { 2 } + 16 \right) ^ { 1 / 2 } }$

Question 69

A charge per unit length given by $\lambda$ (x)= bx,where b = 12 nC/m²,is distributed along the x axis from x = +9.0 cm to x = +16 cm.If the electric potential at infinity is taken to be zero,what is the electric potential at the point P on the y axis at y = 12 cm?

A)5.4 V
B)7.2 V
C)9.0 V
D)9.9 V
E)16 V

Question 70

A rod (length = 2.0 m)is uniformly charged and has a total charge of 5.0 nC.What is the electric potential (relative to zero at infinity)at a point which lies along the axis of the rod and is 3.0 m from the center of the rod?

A)22 V
B)19 V
C)16 V
D)25 V
E)12 V

Question 71

Charge of uniform linear density 3.0 nC/m is distributed along the x axis from x = 0 to x = 3 m.Which of the following integrals is correct for the electric potential (relative to zero at infinity)at the point x = +4 m on the x axis?

A) $\int _ { 0 } ^ { 3 } \frac { 27 d x } { x }$ .

B) $\int _ { 0 } ^ { 3 } \frac { 9 d x } { 4 - x }$

C) $\int _ { 0 } ^ { 3 } \frac { 27 d x } { 4 - x }$

D) $\int _ { 0 } ^ { 3 } \frac { 27 d x } { x }$

E) $\int _ { 0 } ^ { 3 } \frac { 27 d x } { 4 + x }$ .

Question 72

A charge of 20 nC is distributed uniformly along the x axis from x = -2.0 m to x = +2.0 m.What is the electric potential (relative to zero at infinity)at the point x = 5.0 m on the x axis?

A)57 V
B)48 V
C)38 V
D)67 V
E)100 V

Question 73

A charge of 10 nC is distributed uniformly along the x axis from x = -2 m to x = +3 m.Which of the following integrals is correct for the electric potential (relative to zero at infinity)at the point x = +5 m on the x axis?

A) $\int _ { - 2 } ^ { 3 } \frac { 90 d x } { x }$
B) $\int _ { - 2 } ^ { 3 } \frac { 90 d x } { 5 - x }$
C) $\int _ { - 2 } ^ { 3 } \frac { 18 d x } { x }$
D) $\int _ { - 2 } ^ { 3 } \frac { 18 d x } { 5 - x }$
E) $\int _ { - 2 } ^ { 3 } \frac { 90 d x } { 5 + x }$

Question 74

Charge of uniform density 12 nC/m is distributed along the x axis from x = 2.0 m to x = 5.0 m.What is the electric potential (relative to zero at infinity)at the origin (x = 0)?

A)91 V
B)99 V
C)82 V
D)74 V
E)140 V

Question 75

The electric field in the region defined by the y-z plane and the negative x axis is given by E = -ax,where a is a constant.(There is no field for positive values of x. )As -x increases in magnitude,relative to V = 0 at the origin,the electric potential in the region defined above is

A)a decreasing function proportional to -|x²|.
B)a decreasing function proportional to -|x|.
C)constant.
D)an increasing function proportional to +|x|.
E)an increasing function proportional to +|x²|.

Question 76

Which of the following represents the equipotential lines of a dipole?

A)
B)
C)
D)
E)

Question 77

Charge of uniform density (3.5 nC/m)is distributed along the circular arc shown.Determine the electric potential (relative to zero at infinity)at point P.

A)61 V
B)42 V
C)52 V
D)33 V
E)22 V

Question 78

A nonuniform linear charge distribution given by $\lambda$ (x)= bx,where b is a constant,is distributed along the x axis from x = 0 to x = +L.If b = 40 nC/m² and L = 0.20 m,what is the electric potential (relative to a potential of zero at infinity)at the point y = 2L on the y axis?

A)19 V
B)17 V
C)21 V
D)23 V
E)14 V

Question 79

The electric field in the region defined by the y-z plane and the positive x axis is given by E = ax,where a is a constant.(There is no field for negative values of x. )As x increases in magnitude,relative to V = 0 at the origin,the electric potential in the region defined above is

A)a decreasing function proportional to -|x²|.
B)a decreasing function proportional to -|x|.
C)constant.
D)an increasing function proportional to +|x|.
E)an increasing function proportional to +|x²|.

Question 80

Charge of uniform density 50 nC/m³ is distributed throughout the inside of a long nonconducting cylindrical rod (radius = 5.0 cm).Determine the magnitude of the potential difference of point A (2.0 cm from the axis of the rod)and point B (4.0 cm from the axis).

A)2.7 V
B)2.0 V
C)2.4 V
D)1.7 V
E)3.4 V