1. Halliday/Resnick/Walker Fundamentals of Physics
Classroom Response System Questions
Chapter 23 Gauss’ Law
Interactive Lecture Questions

2. The end of a garden hose is enclosed in a mesh sphere of radius 4 cm. If the hose delivers five liters per minute, how much water flows through the sphere each minute?
a) liters
b) liters
c) 3.2 liters
d) 5.0 liters
e) 20 liters

3. The end of a garden hose is enclosed in a mesh sphere of radius 4 cm. If the hose delivers five liters per minute, how much water flows through the sphere each minute?
a) liters
b) liters
c) 3.2 liters
d) 5.0 liters
e) 20 liters

4. 23. 2. 2. The a solid brass sphere of radius 3 cm is placed 0
The a solid brass sphere of radius 3 cm is placed 0.5 m directly below a water faucet. The flow of water from the faucet is two liters per minute. How much water flows through the sphere each minute?
a) zero liters
b) liters
c) liters
d) 2 liters
e) 6 liters

5. 23. 2. 2. The a solid brass sphere of radius 3 cm is placed 0
The a solid brass sphere of radius 3 cm is placed 0.5 m directly below a water faucet. The flow of water from the faucet is two liters per minute. How much water flows through the sphere each minute?
a) zero liters
b) liters
c) liters
d) 2 liters
e) 6 liters

6. In July, Joe set up his fixed array of solar panels to maximize the amount of electricity output from the array when the Sun was high in the sky. Unfortunately, Joe finds that the array doesn’t operate as well during the winter months, even though there is nothing physical wrong with the array. What is the most likely cause of Joe’s winter problem?
a) Less sunlight reaches the Earth during the winter months.
b) The sun is lower in the sky during the winter, so sunlight strikes the solar panels at an angle.
c) The average temperature is much colder during the winter months.
d) More sunlight is absorbed by the atmosphere during the winter months because the Sun is much lower in the sky.
e) The Sun is not as bright during winter months as it is during the summer months.

7. In July, Joe set up his fixed array of solar panels to maximize the amount of electricity output from the array when the Sun was high in the sky. Unfortunately, Joe finds that the array doesn’t operate as well during the winter months, even though there is nothing physical wrong with the array. What is the most likely cause of Joe’s winter problem?
a) Less sunlight reaches the Earth during the winter months.
b) The sun is lower in the sky during the winter, so sunlight strikes the solar panels at an angle.
c) The average temperature is much colder during the winter months.
d) More sunlight is absorbed by the atmosphere during the winter months because the Sun is much lower in the sky.
e) The Sun is not as bright during winter months as it is during the summer months.

8. When you calculate the electric flux through a Gaussian surface, of what are you determining the flow through the surface?
a) charge
b) electric current
c) electric energy
d) electric field
e) None of the above answers are correct.

9. When you calculate the electric flux through a Gaussian surface, of what are you determining the flow through the surface?
a) charge
b) electric current
c) electric energy
d) electric field
e) None of the above answers are correct.

10. 23. 3. 2. Consider the five situations shown
Consider the five situations shown. Each one contains either a charge q or a charge 2q. A Gaussian surface surrounds the charged particle in each case. Considering the electric flux through each of the Gaussian surfaces, which of the following comparative statements is correct? a) b) c) d) e)

11. 23. 3. 2. Consider the five situations shown
Consider the five situations shown. Each one contains either a charge q or a charge 2q. A Gaussian surface surrounds the charged particle in each case. Considering the electric flux through each of the Gaussian surfaces, which of the following comparative statements is correct? a) b) c) d) e)

12. When a particle with a charge Q is surrounded by a spherical Gaussian surface, the electric flux through the surface is S. Consider what would happen if the particle was surrounded by a cylindrical Gaussian surface or a Gaussian cube. How would the fluxes through the cylindrical Cyl and cubic Cubic surfaces compare to S? a) b) c) d) e)

13. When a particle with a charge Q is surrounded by a spherical Gaussian surface, the electric flux through the surface is S. Consider what would happen if the particle was surrounded by a cylindrical Gaussian surface or a Gaussian cube. How would the fluxes through the cylindrical Cyl and cubic Cubic surfaces compare to S? a) b) c) d) e)

14. A spherical Gaussian surface of radius R is surrounding a particle with a net charge q. If the spherical Gaussian surface is replaced by a cube, under what conditions would the electric flux through the sides of the cube be the same as through the spherical surface?
a) under all conditions
b) if the sides of the cube are of length R
c) if the sides of the cube are of length 2R
d) if the diagonals of the cube are of length 2R
e) under no conditions

15. A spherical Gaussian surface of radius R is surrounding a particle with a net charge q. If the spherical Gaussian surface is replaced by a cube, under what conditions would the electric flux through the sides of the cube be the same as through the spherical surface?
a) under all conditions
b) if the sides of the cube are of length R
c) if the sides of the cube are of length 2R
d) if the diagonals of the cube are of length 2R
e) under no conditions

16. Using Gauss’ law, find the approximate magnitude of the electric field at the surface of a cube that has 0.10-m sides and a uniform volume charge density  = 2.0 × 109 C/m3.
a) N/C
b) 7.1 N/C
c) 23 N/C
d) 44 N/C
e) 116 N/C

17. Using Gauss’ law, find the approximate magnitude of the electric field at the surface of a cube that has 0.10-m sides and a uniform volume charge density  = 2.0 × 109 C/m3.
a) N/C
b) 7.1 N/C
c) 23 N/C
d) 44 N/C
e) 116 N/C

18. 23.4.3. Gauss’ law may be written: . Which of
the following statements concerning the charge q is true?
a) The charge q is the sum of all charges.
b) The charge q is the sum of all charges on the Gaussian surface.
c) The charge q is the sum of all charges inside the Gaussian surface.
d) The electric field due to q is zero inside the Gaussian surface.
e) The charge q is the amount of charge present whenever the electric field is constant.

19. 23.4.3. Gauss’ law may be written: . Which of
the following statements concerning the charge q is true?
a) The charge q is the sum of all charges.
b) The charge q is the sum of all charges on the Gaussian surface.
c) The charge q is the sum of all charges inside the Gaussian surface.
d) The electric field due to q is zero inside the Gaussian surface.
e) The charge q is the amount of charge present whenever the electric field is constant.

20. 23. 6. 1. A conducting shell with an outer radius of 2
A conducting shell with an outer radius of 2.5 cm and an inner radius of 1.5 cm has an excess charge of 1.5 × 107 C. What is the surface charge density on the inner wall of the shell?
a) 1.5 × 109 C/m2
b) 2.9 × 1010 C/m2
c) 4.8 × 1010 C/m2
d) 8.5 × 109 C/m2
e) None of the above answers is correct.

21. 23. 6. 1. A conducting shell with an outer radius of 2
A conducting shell with an outer radius of 2.5 cm and an inner radius of 1.5 cm has an excess charge of 1.5 × 107 C. What is the surface charge density on the inner wall of the shell?
a) 1.5 × 109 C/m2
b) 2.9 × 1010 C/m2
c) 4.8 × 1010 C/m2
d) 8.5 × 109 C/m2
e) None of the above answers is correct.

22. A metal sphere with a net charge Q is at the center of an insulating sphere of radius R. What is the magnitude of the electric field at a point located at r > R? a) b) c) d) e)

23. A metal sphere with a net charge Q is at the center of an insulating sphere of radius R. What is the magnitude of the electric field at a point located at r > R? a) b) c) d) e)

24. Using Gauss’ law, find the approximate magnitude of the electric field at the center of a circular face of a solid cylinder that has a length of m, a radius of m, and a uniform volume charge density  = 2.0 × 109 C/m3.
a) N/C
b) 11 N/C
c) 23 N/C
d) 33 N/C
e) 76 N/C

25. Using Gauss’ law, find the approximate magnitude of the electric field at the center of a circular face of a solid cylinder that has a length of m, a radius of m, and a uniform volume charge density  = 2.0 × 109 C/m3.
a) N/C
b) 11 N/C
c) 23 N/C
d) 33 N/C
e) 76 N/C

26. 23. 7. 2. A straight, copper wire has a length of 0
A straight, copper wire has a length of 0.50 m and an excess charge of –1.0 × 105 C distributed uniformly along its length. Find the magnitude of the electric field at a point located 7.5 × 10–3 m from the midpoint of the wire.
a) 1.9 × 1010 N/C
b) 7.3 × 108 N/C
c) 6.1 × 1013 N/C
d) 1.5 × 106 N/C
e) 4.8 × 107 N/C

27. 23. 7. 2. A straight, copper wire has a length of 0
A straight, copper wire has a length of 0.50 m and an excess charge of –1.0 × 105 C distributed uniformly along its length. Find the magnitude of the electric field at a point located 7.5 × 10–3 m from the midpoint of the wire.
a) 1.9 × 1010 N/C
b) 7.3 × 108 N/C
c) 6.1 × 1013 N/C
d) 1.5 × 106 N/C
e) 4.8 × 107 N/C

28. An infinite slab of electrically insulating material has a thickness t. The slab has a uniform volume charge density . Which one of the following expressions gives the electric field at a point P at a depth t  d relative to the surface? a) b) c) d) e)

29. An infinite slab of electrically insulating material has a thickness t. The slab has a uniform volume charge density . Which one of the following expressions gives the electric field at a point P at a depth t  d relative to the surface? a) b) c) d) e)

30. A large sheet of electrically insulating material has a uniform charge density . Let’s compare the electric field produced by the insulating sheet with that produced by a thin metal (electrically conducting) slab with /2 charge density distributed on one large surface of the slab and /2 distributed over the surface on the opposite side. How does the electric field at a distance d from each surface compare?
a) The electric field near the insulating sheet is four times that near the conducting slab.
b) The electric field near the insulating sheet is twice that near the conducting slab.
c) The electric field near the insulating sheet is the same as that near the conducting slab.
d) The electric field near the insulating sheet is one half that near the conducting slab.
e) The electric field near the insulating sheet is one fourth that near the conducting slab.

31. A large sheet of electrically insulating material has a uniform charge density . Let’s compare the electric field produced by the insulating sheet with that produced by a thin metal (electrically conducting) slab with /2 charge density distributed on one large surface of the slab and /2 distributed over the surface on the opposite side. How does the electric field at a distance d from each surface compare?
a) The electric field near the insulating sheet is four times that near the conducting slab.
b) The electric field near the insulating sheet is twice that near the conducting slab.
c) The electric field near the insulating sheet is the same as that near the conducting slab.
d) The electric field near the insulating sheet is one half that near the conducting slab.
e) The electric field near the insulating sheet is one fourth that near the conducting slab.

32. 23. 9. 1. A spherical shell has an outer radius of 0
A spherical shell has an outer radius of 0.10 m and an inner radius of cm. Within the shell is a charge q = 2.0 × 109 C. What is the surface charge density on the outer surface of the shell?
a) 2.0 × 109 C/m2
b) 9.9 × 109 C/m2
c) 1.6 × 108 C/m2
d) 3.8 × 1010 C/m2
e) 8.0 × 108 C/m2

33. 23. 9. 1. A spherical shell has an outer radius of 0
A spherical shell has an outer radius of 0.10 m and an inner radius of cm. Within the shell is a charge q = 2.0 × 109 C. What is the surface charge density on the outer surface of the shell?
a) 2.0 × 109 C/m2
b) 9.9 × 109 C/m2
c) 1.6 × 108 C/m2
d) 3.8 × 1010 C/m2
e) 8.0 × 108 C/m2

34. A total charge of –6.50 µC is uniformly distributed within a sphere that has a radius of m. What is the magnitude and direction of the electric field at m from the surface of the sphere?
a)  105 N/C, radially inward
b)  105 N/C, radially outward
c)  106 N/C, radially inward
d)  105 N/C, radially outward
e)  105 N/C, radially inward

35. A total charge of –6.50 µC is uniformly distributed within a sphere that has a radius of m. What is the magnitude and direction of the electric field at m from the surface of the sphere?
a)  105 N/C, radially inward
b)  105 N/C, radially outward
c)  106 N/C, radially inward
d)  105 N/C, radially outward
e)  105 N/C, radially inward