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.

Question 2

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 3

An extremely long thin wire carries a uniform linear charge density of 358 nC/m. Find the potential difference between points 5.0 m and 6.0 m from the wire, provided they are not near either end of the wire. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Accepted Answer

A)  1.2 kV 
B)  6.0 kV 
C)  0.21 kV 
D)  0.215 kV 
A)  1.2 kV 
B)  6.0 kV 
C)  0.21 kV 
D)  0.215 kV

Question 4

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 5

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 6

The potential as a function of position x is shown in the graph in the figure. Which statement about the electric field is true?

Accepted Answer

A)  The electric field is zero at x = 0, its magnitude is at a maximum at x = 5 cm, and the field is directed to the right there. 
B)  The electric field is zero at x = 5 cm, its magnitude is at a maximum at x = 0, and the field is directed to the right there. 
C)  The electric field is zero at x = 0, its magnitude is at a maximum at x = 15 cm, and the field is directed to the left there. 
D)  The electric field is zero at x = 10 cm, its magnitude is at a maximum at x = 5 cm, and the field is directed to the left there. 
A)  The electric field is zero at x = 0, its magnitude is at a maximum at x = 5 cm, and the field is directed to the right there. 
B)  The electric field is zero at x = 5 cm, its magnitude is at a maximum at x = 0, and the field is directed to the right there. 
C)  The electric field is zero at x = 0, its magnitude is at a maximum at x = 15 cm, and the field is directed to the left there. 
D)  The electric field is zero at x = 10 cm, its magnitude is at a maximum at x = 5 cm, and the field is directed to the left there.

Question 7

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 8

An alpha particle is a nucleus of helium. It has twice the charge and four times the mass of the proton. When they were very far away from each other, but headed toward directly each other, a proton and an alpha particle each had an initial speed of 0.0030c, where c is the speed of light. What is their distance of closest approach? Hint: There are two conserved quantities. Make use of both of them. (c = 3.00 × 108 m/s, k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2, e = 1.60 × 10-19 C, mproton = 1.67 x 10-27 kg)

Accepted Answer

A)  2.1 × 10-13 m 
B)  3.3 × 10-13 m 
C)  2.6 × 10-13 m 
D)  2.9 × 10-13 m 
A)  2.1 × 10-13 m 
B)  3.3 × 10-13 m 
C)  2.6 × 10-13 m 
D)  2.9 × 10-13 m

Question 9

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 10

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 11

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 12

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 13

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 14

A conducting sphere contains positive charge distributed uniformly over its surface. 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 lowest, but not zero, 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 lowest, but not zero, 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 15

A tiny object carrying a charge of +3.00 μC and a second tiny charged object are initially very far apart. If it takes 29.0 J 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

Exam 22: Electric Potential

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

An extremely long thin wire carries a uniform linear charge density of 358 nC/m. Find the potential difference between points 5.0 m and 6.0 m from the wire, provided they are not near either end of the wire. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

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

The potential as a function of position x is shown in the graph in the figure. Which statement about the electric field is true?

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)

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

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)

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?

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

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

A conducting sphere contains positive charge distributed uniformly over its surface. 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.)

Units, Physical Quantities, and Vectors

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Filters

An extremely long thin wire carries a uniform linear charge density of 358 nC/m. Find the potential difference between points 5.0 m and 6.0 m from the wire, provided they are not near either end of the wire. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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)

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