Question 1

Electric field and potential: 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  True

Question 2

Potential due to point-charges: A +4.0 μC-point charge and a -4.0-μC point charge are placed as shown in the figure. What is the potential difference, VA - VB, between points A and B? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Accepted Answer

A)  48 V 
B)  96 V 
C)  0.00 V 
D)  96 kV 
E)  48 kV 
A)  48 V 
B)  96 V 
C)  0.00 V 
D)  96 kV 
E)  48 kV D

Question 3

Potential due to point-charges: Four point charges of magnitude 6.00 μC and of varying signs are placed at the corners of a square 2.00 m on each side, as shown in the figure. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)   (a) What is the electric potential (relative to infinity) at the center of this square due to these charges?
(b) What is the magnitude of the electric field due to these charges at the center of the square?

Accepted Answer

(a) zero (b) 7.63 × 10⁴ N/C

Question 4

Potential energy of point-charges: 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

Question 5

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

Accepted Answer

A) True 
 B)False

Question 6

Potential energy of point-charges: 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 7

Potential energy of point-charges: Suppose you have two negative point charges. As you move them farther and farther apart, the potential energy of this system relative to infinity

Accepted Answer

A)  increases. 
B)  decreases. 
C)  stays the same. 
A)  increases. 
B)  decreases. 
C)  stays the same.

Question 8

Spheres of charge: 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 9

Potential due to point-charges: Three point charges of -2.00 μC, +4.00 μC, and +6.00 μC are placed along the x-axis as shown in the figure. What is the electrical potential at point P (relative to infinity) due to these charges? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Accepted Answer

A)  -307 kV 
B)  +307 kV 
C)  -154 kV 
D)  +154 kV 
E)  0 kV 
A)  -307 kV 
B)  +307 kV 
C)  -154 kV 
D)  +154 kV 
E)  0 kV

Question 10

Potential energy of point-charges: 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 11

Electric field and potential : The graph in the figure shows the variation of the electric potential V (measured in volts) as a function of the radial direction r (measured in meters). For which range or value of r is the magnitude of the electric field the largest?

Accepted Answer

A)  from r = 0 m to r = 3 m 
B)  from r = 3 m to r = 4 m 
C)  from r = 4 m to r = 6 m 
D)  at r = 3 m 
E)  at r = 4 m 
A)  from r = 0 m to r = 3 m 
B)  from r = 3 m to r = 4 m 
C)  from r = 4 m to r = 6 m 
D)  at r = 3 m 
E)  at r = 4 m

Question 12

Lines of charge: Two long conducting cylindrical shells are coaxial and have radii of 20 mm and 80 mm. The electric potential of the inner conductor, with respect to the outer conductor, is +600 V. An electron is released from rest at the surface of the outer conductor. What is the speed of the electron as it reaches the inner conductor? (e = 1.60 × 10-19 C, mel = 9.11 × 10-31 kg, k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Accepted Answer

A)  1.1 × 107 m/s 
B)  1.3 × 107 m/s 
C)  1.5 × 107 m/s 
D)  1.7 × 107 m/s 
E)  1.9 × 107 m/s 
A)  1.1 × 107 m/s 
B)  1.3 × 107 m/s 
C)  1.5 × 107 m/s 
D)  1.7 × 107 m/s 
E)  1.9 × 107 m/s

Question 13

Parallel plates: Two parallel conducting plates are separated by   and carry equal but opposite surface charge densities. If the potential difference between them is   what is the magnitude of the surface charge density on each plate? (ε0 = 8.85 × 10-12 C2/N ∙ m2)

Accepted Answer

A)  18 nC/m2 
B)  0.13 mC/m2 
C)  35 nC/m2 
D)  0.27 mC/m2 
A)  18 nC/m2 
B)  0.13 mC/m2 
C)  35 nC/m2 
D)  0.27 mC/m2

Question 14

Potential due to point-charges: The figure shows two arcs of a circle on which charges +Q and -Q have been spread uniformly. What is the value of the electric potential at the center of the circle?

Accepted Answer

The answer of Potential due to point-charges: The figure shows...

Question 15

Spheres of charge: A nonconducting sphere contains positive charge distributed uniformly throughout its volume. Which statements about the potential due to this sphere are true? All potentials are measured relative to infinity. (There may be more than one correct choice.)

Accepted Answer

A)  The potential is highest at the center of the sphere. 
B)  The potential at the center of the sphere is zero. 
C)  The potential at the center of the sphere is the same as the potential at the surface. 
D)  The potential at the surface is higher than the potential at the center. 
E)  The potential at the center is the same as the potential at infinity. 
A)  The potential is highest at the center of the sphere. 
B)  The potential at the center of the sphere is zero. 
C)  The potential at the center of the sphere is the same as the potential at the surface. 
D)  The potential at the surface is higher than the potential at the center. 
E)  The potential at the center is the same as the potential at infinity.

Question 16

Potential due to point-charges: 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

Question 17

Potential energy of point-charges: If an electron is accelerated from rest through a potential difference of 9.9 kV, what is its resulting speed? (e = 1.60 × 10-19 C, k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2, mel = 9.11 × 10-31 kg)

Accepted Answer

A)  5.9 × 107 m/s 
B)  4.9 × 107 m/s 
C)  3.9 × 107 m/s 
D)  2.9 × 107 m/s 
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 18

Potential energy of point-charges: 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 19

Electric field and potential: In a certain region, the electric potential due to a charge distribution is given by the equation V(x,y,z) = 3x2y2 + yz3 - 2z3x, where x, y, and z are measured in meters and V is in volts. Calculate the magnitude of the electric field vector at the position (x,y,z) = (1.0, 1.0, 1.0).

Accepted Answer

A)  4.3 V/m 
B)  2.0 V/m 
C)  -8.1 V/m 
D)  8.6 V/m 
E)  74 V/m 
A)  4.3 V/m 
B)  2.0 V/m 
C)  -8.1 V/m 
D)  8.6 V/m 
E)  74 V/m

Question 20

Electric field and potential: 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.

Exam 19: The First Law of Thermodynamics

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

Potential due to point-charges: A +4.0 μC-point charge and a -4.0-μC point charge are placed as shown in the figure. What is the potential difference, VA - VB, between points A and B? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Potential energy of point-charges: 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)

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

Potential energy of point-charges: Suppose you have two negative point charges. As you move them farther and farther apart, the potential energy of this system relative to infinity

Spheres of charge: 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?

Potential due to point-charges: Three point charges of -2.00 μC, +4.00 μC, and +6.00 μC are placed along the x-axis as shown in the figure. What is the electrical potential at point P (relative to infinity) due to these charges? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Potential energy of point-charges: 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)

Electric field and potential : The graph in the figure shows the variation of the electric potential V (measured in volts) as a function of the radial direction r (measured in meters). For which range or value of r is the magnitude of the electric field the largest?

Parallel plates: Two parallel conducting plates are separated by and carry equal but opposite surface charge densities. If the potential difference between them is what is the magnitude of the surface charge density on each plate? (ε0 = 8.85 × 10-12 C2/N ∙ m2)

Potential due to point-charges: The figure shows two arcs of a circle on which charges +Q and -Q have been spread uniformly. What is the value of the electric potential at the center of the circle?

Spheres of charge: A nonconducting sphere contains positive charge distributed uniformly throughout its volume. Which statements about the potential due to this sphere are true? All potentials are measured relative to infinity. (There may be more than one correct choice.)

Potential energy of point-charges: If an electron is accelerated from rest through a potential difference of 9.9 kV, what is its resulting speed? (e = 1.60 × 10-19 C, k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2, mel = 9.11 × 10-31 kg)

Electric field and potential: 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

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Potential due to point-charges: A +4.0 μC-point charge and a -4.0-μC point charge are placed as shown in the figure. What is the potential difference, V_A - V_B, between points A and B? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Potential due to point-charges: Three point charges of -2.00 μC, +4.00 μC, and +6.00 μC are placed along the x-axis as shown in the figure. What is the electrical potential at point P (relative to infinity) due to these charges? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Potential energy of point-charges: 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)

Parallel plates: Two parallel conducting plates are separated by and carry equal but opposite surface charge densities. If the potential difference between them is what is the magnitude of the surface charge density on each plate? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Potential energy of point-charges: If an electron is accelerated from rest through a potential difference of 9.9 kV, what is its resulting speed? (e = 1.60 × 10^-19 C, k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²,^m_el= 9.11 × 10^-31 kg)

Electric field and potential: 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