# Gauss' Law - Chapter No 21

Right Answers have been shown below in red color.

1. A total charge of 6.3×10−8 C is distributed uniformly throughout a 2.7-cm radius sphere. The volume charge density is:

A. 3.7 × 10−7 C/m3
B. 6.9 × 10−6 C/m3
C. 6.9 × 10−6 C/m2
D. 2.5 × 10−4 C/m3
E. 7.6 × 10−4 C/m3

2. Charge is placed on the surface of a 2.7-cm radius isolated conducting sphere. The surface charge density is uniform and has the value 6.9 × 10−6 C/m2. The total charge on the sphere is:

A. 5.6 × 10−10 C
B. 2.1 × 10−8 C
C. 4.7 × 10−8 C
D. 6.3 × 10−8 C
E. 9.5 × 10−3 C

3. A spherical shell has an inner radius of 3.7 cm and an outer radius of 4.5 cm. If the charge is distributed uniformly throughout the shell with a volume density of 6.1 × 10−4 C/m3 the total charge is:

A. 1.0 × 10−7 C
B. 1.3 × 10−7 C
C. 2.0 × 10−7 C
D. 2.3 × 10−7 C
E. 4.0 × 10−7 C

4. A cylinder has a radius of 2.1 cm and a length of 8.8 cm. The total charge 6.1×10−7 C is distributed uniformly throughout. The volume charge density is:

A. 5.3 × 10−5 C/m3
B. 5.3 × 10−5 C/m2
C. 8.5 × 10−4 C/m3
D. 5.0 × 10−3 C/m3
E. 6.3 × 10−2 C/m3

5. When a piece of paper is held with one face perpendicular to a uniform electric field the flux through it is 25 N · m2 /C. When the paper is turned 25◦ with respect to the field the flux through it is:

A. 0
B. 12 N · m2/C
C. 21 N · m2/C
D. 23 N · m2/C
E. 25 N · m2/C

6. The flux of the electric field (24 N/C)i + (30 N/C)j + (16 N/C)k through a 2.0 m2 portion of the yz plane is:

A. 32 N · m2 /C
B. 34 N · m2 /C
C. 42 N · m2 /C
D. 48 N · m2 /C
E. 60 N · m2 /C

7. Consider Gauss’s law:  ∫E · dA = q/ϵo. Which of the following is true?

A. E must be the electric field due to the enclosed charge
B. If q = 0, then E = 0 everywhere on the Gaussian surface
C. If the three particles inside have charges of +q, +q, and −2q, then the integral is zero
D. on the surface E is everywhere parallel to dAn
E. If a charge is placed outside the surface, then it cannot affect E at any point on the surface

8. A charged point particle is placed at the center of a spherical Gaussian surface. The electric flux ΦE is changed if:
A. the sphere is replaced by a cube of the same volume B. the sphere is replaced by a cube of one-tenth the volume C. the point charge is moved off center (but still inside the original sphere) D. the point charge is moved to just outside the sphere E. a second point charge is placed just outside the sphere

9. Choose the INCORRECT statement:

A. Gauss’ law can be derived from Coulomb’s law
B. Gauss’ law states that the net number of lines crossing any closed surface in an outward direction is proportional to the net charge enclosed within the surface
C. Coulomb’s law can be derived from Gauss’ law and symmetry
D. Gauss’ law applies to a closed surface of any shape
E. According to Gauss’ law, if a closed surface encloses no charge, then the electric field must vanish everywhere on the surface

10. The outer surface of the cardboard center of a paper towel roll:

A. is a possible Gaussian surface
B. cannot be a Gaussian surface because it encloses no charge
C. cannot be a Gaussian surface since it is an insulator
D. cannot be a Gaussian surface because it is not a closed surface
E. none of the above

11. A physics instructor in an anteroom charges an electrostatic generator to 25 µC, then carries it into the lecture hall. The net electric flux in N · m2/C through the lecture hall walls is:

A. 0
B. 25 × 10−6
C. 2.2 × 10-6
D. 2.8 × 106
E. can not tell unless the lecture hall dimensions are given

12. A point particle with charge q is placed inside the cube but not at its center. The electric flux through any one side of the cube:

A. is zero
B. is q/60
C. is q/460
D. is q/660
E. cannot be computed using Gauss’ law

13. A particle with charge 5.0-µC is placed at the corner of a cube. The total electric flux in N · m2 / C through all sides of the cube is:

A. 0
B. 7.1 × 104
C. 9.4 × 104
D. 1.4 × 105
E. 5.6 × 105

14. A point particle with charge q is at the center of a Gaussian surface in the form of a cube. The electric flux through any one face of the cube is:

A. q/ϵo
B. q/4πϵo
C. q/3ϵo
D. q/6ϵo
E. q/12ϵo

15. The table below gives the electric flux in N · m2/C through the ends and round surfaces of four Gaussian surfaces in the form of cylinders. Rank the cylinders according to the charge inside, from the most negative to the most positive.

A. 1, 2, 3, 4
B. 4, 3, 2, 1
C. 3, 4, 2, 1
D. 3, 1, 4, 2
E. 4, 3, 1, 2

16. A conducting sphere of radius 0.01 m has a charge of 1.0 × 10−9 C deposited on it. The magnitude of the electric field in N/C just outside the surface of the sphere is:

A. 0
B. 450
C. 900
D. 4500
E. 90, 000

17. A round wastepaper basket with a 0.15-m radius opening is in a uniform electric field of 300 N/C, perpendicular to the opening. The total flux through the sides and bottom, in N · m2 C is:

A. 0
B. 4.2
C. 21
D. 280
E. can not tell without knowing the areas of the sides and bottom

18. 10 C of charge is placed on a spherical conducting shell. A particle with a charge of −3 C is placed at the center of the cavity. The net charge on the inner surface of the shell is:

A. −7 C
B. −3 C
C. 0 C
D. +3 C
E. +7 C

19. 10 C of charge are placed on a spherical conducting shell. A particle with a charge of −3 C is placed at the center of the cavity. The net charge on the outer surface of the shell is:

A. −7 C
B. −3 C
C. 0 C
D. +3 C
E. +7 C

20. A 30-N/C uniform electric field points perpendicularly toward the left face of a large neutral conducting sheet. The surface charge density in C/m2 on the left and right faces, respectively, are:

A. −2.7 × 10-9 C/m2 ; +2.7 × 10-9 C/m2
B. +2.7 × 10-9 C/m2 ; −2.7 × 10-9 C/m2
C. −5.3 × 10–9 C/m2 ; +5.3 × 10-9 C/m2
D. +5.3 × 10-9 C/m2 ; −5.3 × 10-9 C/m2
E. 0 ; 0