Question 1

Which statements are true for an electron moving in the direction of an electric field? (There may be more than one correct choice.)

Accepted Answer

A)  Its electric potential energy increases as it goes from high to low potential. 
B)  Its electric potential energy decreases as it goes from high to low potential. 
C)  Its potential energy increases as its kinetic energy decreases. 
D)  Its kinetic energy decreases as it moves in the direction of the electric field. 
E)  Its kinetic energy increases as it moves in the direction of the electric field. 
A)  Its electric potential energy increases as it goes from high to low potential. 
B)  Its electric potential energy decreases as it goes from high to low potential. 
C)  Its potential energy increases as its kinetic energy decreases. 
D)  Its kinetic energy decreases as it moves in the direction of the electric field. 
E)  Its kinetic energy increases as it moves in the direction of the electric field. A

Question 2

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

Accepted Answer

(a)153 kV 
(b)zero

Question 3

An electron is released from rest at a distance of 9.00 cm from a proton.If the proton is held in place,how fast will the electron be moving when it is 3.00 cm from the proton? (mel = 9.11 × 10-31 kg,
E = 1.60 × 10-19 C,k = 1/4πε0 = 8.99 × 109 N • m2/C2)

Accepted Answer

A)  75.0 m/s 
B)  106 m/s 
C)  130 m/s 
D)  1.06 × 103 m/s 
E)  4.64 × 105 m/s 
A)  75.0 m/s 
B)  106 m/s 
C)  130 m/s 
D)  1.06 × 103 m/s 
E)  4.64 × 105 m/s B

Question 4

A conducting sphere is charged up such that the potential on its surface is 100 V (relative to infinity).If the sphere's radius were twice as large,but the charge on the sphere were the same,what would be the potential on the surface relative to infinity?

Accepted Answer

A)  50 V 
B)  25 V 
C)  100 V 
D)  200 V 
A)  50 V 
B)  25 V 
C)  100 V 
D)  200 V

Question 5

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

Accepted Answer

A) True 
 B)False

Question 6

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

Accepted Answer

A) True 
 B)False

Question 7

A -3.0-μC point charge and a -9.0-μC point charge are initially extremely far apart.How much work does it take to bring the -3.0-μC charge to x = 3.0 mm,y = 0.00 mm and the -9.0-μC charge to x = -3.0 mm,y = 0.00 mm? (k = 1/4πε0 = 8.99 × 109 N • m2/C2)

Accepted Answer

A)  40 J 
B)  81 J 
C)  27 J 
D)  6.8 J 
A)  40 J 
B)  81 J 
C)  27 J 
D)  6.8 J

Question 8

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

Accepted Answer

A) True 
 B)False

Question 9

A conducting sphere of radius 20.0 cm carries an excess charge of +15.0 µC,and no other charges are present.(k = 1/4πε0 = 8.99 × 109 N • m2/C2)The potential (relative to infinity)due to this sphere at a point 12.0 cm from its center is closest to

Accepted Answer

A)  zero. 
B)  674 kV. 
C)  1130 kV. 
D)  3380 kV. 
E)  9380 kV. 
A)  zero. 
B)  674 kV. 
C)  1130 kV. 
D)  3380 kV. 
E)  9380 kV.

Question 10

A conducting sphere 45 cm in diameter carries an excess of charge,and no other charges are present.You measure the potential of the surface of this sphere and find it to be 14 kV relative to infinity.
(k = 1/4πε0 = 8.99 × 109 N • m2/C2)The excess charge on this sphere is closest to

Accepted Answer

A)  0.35 nC. 
B)  79 nC. 
C)  315 nC. 
D)  350 nC. 
E)  700 nC. 
A)  0.35 nC. 
B)  79 nC. 
C)  315 nC. 
D)  350 nC. 
E)  700 nC.

Question 11

If the potential in a region is given by V(x,y,z)= xy - 3z-2,then the y component of the electric field in that region is

Accepted Answer

A)  x + y - 6z-3. 
B)  -y. 
C)  -x. 
D)  x + y. 
A)  x + y - 6z-3. 
B)  -y. 
C)  -x. 
D)  x + y.

Question 12

A half-ring (semicircle)of uniformly distributed charge Q has radius R.What is the electric potential at its center?

Accepted Answer

The answer of A half-ring (semicircle)of uniformly distributed charge Q...

Question 13

A very small object carrying -6.0 μC of charge is attracted to a large,well-anchored,positively charged object.How much kinetic energy does the negatively charged object gain if the potential difference through which it moves is 3.0 mV? (k = 1/4πε0 = 8.99 × 109 N • m2/C2)

Accepted Answer

A)  18 nJ 
B)  0.50 kJ 
C)  0.50 J 
D)  6.0 μJ 
A)  18 nJ 
B)  0.50 kJ 
C)  0.50 J 
D)  6.0 μJ

Question 14

A tiny object carrying a charge of +3.00 μC and a second tiny charged object are initially very far apart.If it takes   of work to bring them to a final configuration in which the +3.00 μC object i is at
X = 1.00 mm,y = 1.00 mm,and the other charged object is at x = 1.00 mm,y = 3.00 mm,find the magnitude of the charge on the second object.(k = 1/4πε0 = 8.99 × 109 N • m2/C2)

Accepted Answer

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

Question 15

The figure shows an arrangement of two -4.5 nC charges,each separated by 5.0 mm from a proton.If the two negative charges are held fixed at their locations and the proton is given an initial velocity v as shown in the figure,what is the minimum initial speed v that the proton needs to totally escape from the negative charges? (k = 1/4πε0 = 8.99 × 109 N • m2/C2,e = 1.60 × 10-19 C,mproton = 1.67 × 10-27 kg)

Accepted Answer

A)  1.8 × 106 m/s 
B)  3.5 × 106 m/s 
C)  6.8 × 106 m/s 
D)  1.4 × 107 m/s 
A)  1.8 × 106 m/s 
B)  3.5 × 106 m/s 
C)  6.8 × 106 m/s 
D)  1.4 × 107 m/s

Question 16

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

Accepted Answer

(a)+8.99 ×

Question 17

A conducting sphere of radius R carries an excess positive charge and is very far from any other charges.Which one of the following graphs best illustrates the potential (relative to infinity)produced by this sphere as a function of the distance r from the center of the sphere?

Accepted Answer

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

Question 18

Two point charges of +2.0 μC and -6.0 μC are located on the x-axis at x = -1.0 cm and x = +2.0 cm respectively.Where should a third charge of +3.0-μC be placed on the +x-axis so that the potential at the origin is equal to zero? (k = 1/4πε0 = 8.99 × 109 N • m2/C2)

Accepted Answer

A)  x = 4.0 cm 
B)  x = 1.0 cm 
C)  x = 2.0 cm 
D)  x = 3.0 cm 
E)  x = 5.0 cm 
A)  x = 4.0 cm 
B)  x = 1.0 cm 
C)  x = 2.0 cm 
D)  x = 3.0 cm 
E)  x = 5.0 cm

Question 19

Consider the group of three+2.4 nC point charges shown in the figure.What is the electric potential energy of this system of charges relative to infinity? (k = 1/4πε0 = 8.99 × 109 N • m2/C2)

Accepted Answer

A)  4.1 × 10-6 J 
B)  4.6 × 10-6 J 
C)  4.2 × 10-6 J 
D)  4.4 × 10-6 J 
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 20

Two point charges,Q and -3Q,are located on the x-axis a distance d apart,with -3Q to the right of Q.Find the location of ALL the points on the x-axis (not counting infinity)at which the potential (relative to infinity)due to this pair of charges is equal to zero.

Accepted Answer

d/4 to the right of

Exam 25: Work and Energy in Electrostatics

Which statements are true for an electron moving in the direction of an electric field? (There may be more than one correct choice.)

An electron is released from rest at a distance of 9.00 cm from a proton.If the proton is held in place,how fast will the electron be moving when it is 3.00 cm from the proton? (mel = 9.11 × 10-31 kg, E = 1.60 × 10-19 C,k = 1/4πε0 = 8.99 × 109 N • m2/C2)

A conducting sphere is charged up such that the potential on its surface is 100 V (relative to infinity).If the sphere's radius were twice as large,but the charge on the sphere were the same,what would be the potential on the surface relative to infinity?

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

A -3.0-μC point charge and a -9.0-μC point charge are initially extremely far apart.How much work does it take to bring the -3.0-μC charge to x = 3.0 mm,y = 0.00 mm and the -9.0-μC charge to x = -3.0 mm,y = 0.00 mm? (k = 1/4πε0 = 8.99 × 109 N • m2/C2)

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

A conducting sphere of radius 20.0 cm carries an excess charge of +15.0 µC,and no other charges are present.(k = 1/4πε0 = 8.99 × 109 N • m2/C2)The potential (relative to infinity)due to this sphere at a point 12.0 cm from its center is closest to

A conducting sphere 45 cm in diameter carries an excess of charge,and no other charges are present.You measure the potential of the surface of this sphere and find it to be 14 kV relative to infinity. (k = 1/4πε0 = 8.99 × 109 N • m2/C2)The excess charge on this sphere is closest to

If the potential in a region is given by V(x,y,z)= xy - 3z-2,then the y component of the electric field in that region is

A half-ring (semicircle)of uniformly distributed charge Q has radius R.What is the electric potential at its center?

A very small object carrying -6.0 μC of charge is attracted to a large,well-anchored,positively charged object.How much kinetic energy does the negatively charged object gain if the potential difference through which it moves is 3.0 mV? (k = 1/4πε0 = 8.99 × 109 N • m2/C2)

A conducting sphere of radius R carries an excess positive charge and is very far from any other charges.Which one of the following graphs best illustrates the potential (relative to infinity)produced by this sphere as a function of the distance r from the center of the sphere?

Two point charges of +2.0 μC and -6.0 μC are located on the x-axis at x = -1.0 cm and x = +2.0 cm respectively.Where should a third charge of +3.0-μC be placed on the +x-axis so that the potential at the origin is equal to zero? (k = 1/4πε0 = 8.99 × 109 N • m2/C2)

Consider the group of three+2.4 nC point charges shown in the figure.What is the electric potential energy of this system of charges relative to infinity? (k = 1/4πε0 = 8.99 × 109 N • m2/C2)

Two point charges,Q and -3Q,are located on the x-axis a distance d apart,with -3Q to the right of Q.Find the location of ALL the points on the x-axis (not counting infinity)at which the potential (relative to infinity)due to this pair of charges is equal to zero.

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Acceleration

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Energy

Principle of Relativity

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Work

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Entropy

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Degradation of Energy

Electric Interactions

The Electric Field

Gausss Law

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Magnetic Interactions

Magnetic Fields of Charged Particles in Motion

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Changing Electric Fields

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Filters

An electron is released from rest at a distance of 9.00 cm from a proton.If the proton is held in place,how fast will the electron be moving when it is 3.00 cm from the proton? (m_el= 9.11 × 10^-31 kg, E = 1.60 × 10^-19 C,k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

A -3.0-μC point charge and a -9.0-μC point charge are initially extremely far apart.How much work does it take to bring the -3.0-μC charge to x = 3.0 mm,y = 0.00 mm and the -9.0-μC charge to x = -3.0 mm,y = 0.00 mm? (k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

A conducting sphere of radius 20.0 cm carries an excess charge of +15.0 µC,and no other charges are present.(k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)The potential (relative to infinity)due to this sphere at a point 12.0 cm from its center is closest to

A conducting sphere 45 cm in diameter carries an excess of charge,and no other charges are present.You measure the potential of the surface of this sphere and find it to be 14 kV relative to infinity. (k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)The excess charge on this sphere is closest to

If the potential in a region is given by V(x,y,z)= xy - 3z^-2,then the y component of the electric field in that region is

A very small object carrying -6.0 μC of charge is attracted to a large,well-anchored,positively charged object.How much kinetic energy does the negatively charged object gain if the potential difference through which it moves is 3.0 mV? (k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

Two point charges of +2.0 μC and -6.0 μC are located on the x-axis at x = -1.0 cm and x = +2.0 cm respectively.Where should a third charge of +3.0-μC be placed on the +x-axis so that the potential at the origin is equal to zero? (k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

Consider the group of three+2.4 nC point charges shown in the figure.What is the electric potential energy of this system of charges relative to infinity? (k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)