Deck 23: Gauss Law

Question 1

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

A) -2.7 * 10^-9 C/m²; +2.7 * 10^-9 C/m ²
B) +2.7 * 10^-9 C/m²; -2.7 * 10^-9 C/m ²
C) -5.3 *10^-9 C/m²; +5.3 * 10^-9 C/m ²
D) +5.3 * 10^-9 C/m²; -5.3 *10^-9 C/m ²
E) 0; 0

Answer 1

-2.7 * 10^-9 C/m²; +2.7 * 10^-9 C/m ²

Question 2

A hollow conductor is positively charged. A small uncharged metal ball is lowered by a silk thread through a small opening in the top of the conductor and allowed to touch its inner surface. After the ball is removed, it will have:

A) a positive charge
B) a negative charge
C) no appreciable charge
D) a charge whose sign depends on what part of the inner surface it touched
E) a charge whose sign depends on where the small hole is located in the conductor

Answer 2

no appreciable charge

Question 3

A point charge is placed at the center of a spherical Gaussian surface. The electric flux $\phi$ _E 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

Answer 3

the point charge is moved to just outside the sphere

Question 4

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't tell without knowing the areas of the sides and bottom

Question 5

A particle with charge 5.0- $\mu$ C 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

Question 6

A 3.5-cm radius hemisphere contains a total charge of 6.6 * 10^-7 C. The flux through the rounded portion of the surface is 9.8 *10⁴ N .m²/C. The flux through the flat base is:

A) 0
B) +2.3* 10⁴ N .m²/C
C) -2.3 * 10⁴ N .m²/C
D) -9.8 * 10⁴ N .m²/C
E) +9.8 * 10⁴ N .m²/C

Question 7

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 not an insulator
D) cannot be a Gaussian surface since it is an insulator
E) none of the above

Question 8

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

A) is zero
B) is q/ $\varepsilon$ ₀
C) is q/4 $\varepsilon$ ₀
D) is q/6 $\varepsilon$ ₀
E) cannot be computed using Gauss' law

Question 9

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) zero
B) 450
C) 900
D) 4500
E) 90,000

Question 10

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/ $\varepsilon$ ₀
B) q/4 $\pi$$\varepsilon$ ₀
C) q/4 $\varepsilon$ ₀
D) q/8 $\varepsilon$ ₀
E) q/16 $\varepsilon$ ₀

Question 11

A long line of charge with charge per unit length runs along the cylindrical axis of a cylindrical shell which carries a charge per unit length of $\lambda$ _c. The charge per unit length on the inner and outer surfaces of the shell, respectively are:

A) and $\lambda$ _c
B) and $\lambda$ _c +
C) and $\lambda$ _c - $\lambda$ _c
D) + $\lambda$ _c and $\lambda$ _c -
E) - $\lambda$ _c and $\lambda$ _c +

Question 12

The flux of the electric field 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

Question 13

10 C of charge are placed on a spherical conducting shell. A particle with a charge of -3-C point charge is placed at the center of the cavity. The net charge in coulombs on the inner surface of the shell is:

A) -7
B) -3
C) 0
D) +3
E) +7

Question 14

Charge is distributed uniformly along a long straight wire. The electric field 2 cm from the wire is 20 N/C. The electric field 4 cm from the wire is:

A) 120 N/C
B) 80 N/C
C) 40 N/C
D) 10 N/C
E) 5 N/C

Question 15

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

Question 16

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 $\degree$ 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

Question 17

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

Question 18

A physics instructor in an anteroom charges an electrostatic generator to 25 $\mu$ C, 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 * 10⁵
D) 2.8 *10⁶
E) can't tell unless the lecture hall dimensions are given

Question 19

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

A) -7
B) -3
C) 0
D) +3
E) +7

Question 20

Consider Gauss law: Which of the following is true?

A) must be the electric field due to the enclosed charge
B) If q = 0 then 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 is everywhere parallel to
E) If a charge is placed outside the surface, then it cannot affect on the at any point on the surface

Question 21

Charge Q is distributed uniformly throughout a spherical insulating shell. The net electric flux in N . m²/C through the outer surface of the shell is:

A) 0
B) Q/ $\varepsilon$ ₀
C) 2Q/ $\varepsilon$ ₀
D) Q/4 $\varepsilon$ ₀
E) Q/2 $\pi$$\varepsilon$ ₀

Question 22

Positive charge Q is placed on a conducting spherical shell with inner radius R₁ and outer radius R₂. A point charge q is placed at the center of the cavity. The magnitude of the electric field produced by the charge on the inner surface at a point in the interior of the conductor a distance r from the center, is:

A) 0
B)
C)
D) q/4 $\pi$$\varepsilon$ ₀r²
E) Q/4 $\pi$$\varepsilon$ ₀r²

Question 23

Positive charge Q is placed on a conducting spherical shell with inner radius R₁ and outer radius R₂. A particle with charge q is placed at the center of the cavity. The magnitude of the electric field at a point in the cavity, a distance r from the center, is:

A)
B)
C) q/4 $\pi$$\varepsilon$ ₀r²
D) (q + Q)/4 $\pi$$\varepsilon$ ₀r²
E)

Question 24

Charge Q is distributed uniformly throughout a spherical insulating shell. The net electric flux in N . m²/C through the inner surface of the shell is:

A) 0
B) Q/ $\varepsilon$ ₀
C) 2Q/ $\varepsilon$ ₀
D) Q/4 $\pi$$\varepsilon$ ₀
E) Q/2 $\pi$$\varepsilon$ ₀

Question 25

A particle with charge Q is placed outside a large neutral conducting sheet. At any point in the interior of the sheet the electric field produced by charges on the surface is directed:

A) toward the surface
B) away from the surface
C) toward Q
D) away from Q
E) none of the above

Question 26

Charge is distributed uniformly on the surface of a large flat plate. The electric field 2 cm from the plate is 30 N/C. The electric field 4 cm from the plate is:

A) 120 N/C
B) 80 N/C
C) 30 N/C
D) 15 N/C
E) 7.5 N/C

Question 27

A solid insulating sphere of radius R contains a positive charge that is distrubuted with a volume charge density that does not depend on angle but does increase with distance from the sphere center. Which of the graphs below correctly gives the magnitude E of the electric field as a function of the distance r from the center of the sphere?

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

Question 28

Which of the following graphs represents the magnitude of the electric field as a function of the distance from the center of a solid charged conducting sphere of radius R?

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

Question 29

Positive charge Q is placed on a conducting spherical shell with inner radius R₁ and outer radius R₂. A point charge q is placed at the center of the cavity. The magnitude of the electric field at a point outside the shell, a distance r from the center, is:

A)
B)
C) q/4 $\pi$$\varepsilon$ ₀r²
D) (q + Q)/4 $\pi$$\varepsilon$ ₀r²
E)

Question 30

Two large insulating parallel plates carry charge of equal magnitude, one positive and the other negative, that is distributed uniformly over their inner surfaces. Rank the points 1 through 5 according to the magnitude of the electric field at the points, least to greatest.

A) 1, 2, 3, 4, 5
B) 5, 4, 3, 2, 1
C) 1, 4, and 5 tie, then 2 and 3 tie
D) 2 and 3 tie, then 1 and 4 tie, then 5
E) 2 and 3 tie, then 1, 4, and 5 tie

Question 31

Two large parallel plates carry positive charge of equal magnitude that is distributed uniformly over their inner surfaces. Rank the points 1 through 5 according to the magnitude of the electric field at the points, least to greatest.

A) 1, 2, 3, 4, 5
B) 5, 4, 3, 2, 1
C) 1, 4, and 5 tie, then 2 and 3 tie
D) 2 and 3 tie, then 1 and 4 tie, then 5
E) 2 and 3 tie, then 1, 4, and 5 tie

Question 32

Charge Q is distributed uniformly throughout an insulating sphere of radius R. The magnitude of the electric field at a point R/2 from the center is:

A) Q/4 $\pi$$\varepsilon$ ₀R²
B) Q/ $\pi$$\varepsilon$ ₀R²
C) 3Q/4 $\pi$$\varepsilon$ ₀R²
D) Q/8 $\pi$$\varepsilon$ ₀R²
E) none of these

Question 33

Positive charge Q is distributed uniformly throughout an insulating sphere of radius R, centered at the origin. A particle with a positive charge Q is placed at x = 2R on the x axis. The magnitude of the electric field at x = R/2 on the x axis is:

A) Q/4 $\pi$$\varepsilon$ ₀R²
B) Q/8 $\pi$$\varepsilon$ ₀R²
C) 7Q/18 $\pi$$\varepsilon$ ₀/R²
D) 11Q/18 $\pi$$\varepsilon$ ₀R²
E) none of these

Question 34

A spherical conducting shell has charge Q. A particle with charge q is placed at the center of the cavity. The charge on the inner surface of the shell and the charge on the outer surface of the shell, respectively, are:

A) 0, Q
B) q, Q - q
C) Q, 0
D) -q, Q + q
E) -q, 0