Deck 23: Gauss Law

Question 1

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 at any point on the surface

Answer 1

If the three particles inside have charges of +q, +q and -2q, then the integral is zero

Question 2

The flux of the electric field (24 N/C) + (30 N/C) + (16 N/C) 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

Answer 2

48 N . m²/C

Question 3

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 through the lecture hall walls is:

A) 0 N.m²/C
B) 25 *10^-6 N.m²/C
C) 2.2 * 10⁵ N.m²/C
D) 2.8 *10⁶ N.m²/C
E) can't tell unless the lecture hall dimensions are given

Answer 3

2.8 *10⁶ N.m²/C

Question 4

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 N.m²/C
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 5

The table below gives the electric flux 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 6

Charge Q is distributed uniformly throughout a spherical insulating shell. The net electric flux 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 7

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 N.m²/C
B) 11 N.m²/C
C) 12 N.m²/C
D) 23 N.m²/C
E) 25 N.m²/C

Question 8

Charge Q is distributed uniformly throughout a spherical insulating shell. The net electric flux 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 9

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/6 $\varepsilon$ ₀
E) q/16 $\varepsilon$ ₀

Question 10

To calculate the flux through a curved surface,

A) the area vector has to be perpendicular to the surface somewhere
B) you must divide the surface into pieces that are tiny enough to be almost flat
C) the surface must be spherical
D) the surface cannot be curved very much; then you can treat it as though it were flat
E) actually the flux through a curved surface cannot be calculated.

Question 11

The electric flux Φ through a surface:

A) is the amount of electric field piercing the surface.
B) is the electric field multiplied by the area.
C) does not depend on the area involved.
D) is the line integral of the electric field around the edge of the surface.
E) is the amount of electric field skimming along the surface.

Question 12

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

Question 13

Which statement is correct?

A) The flux through a closed surface is always positive.
B) The flux through a closed surface is always negative.
C) The sign of the flux through a closed surface depends on an arbitrary choice of sign for the surface vector.
D) Inward flux through a closed surface is negative and outward flux is positive.
E) Inward flux through a closed surface is positive and outward flux is negative.

Question 14

A closed cylinder with a 0.15-m radius ends is in a uniform electric field of 300 N/C, perpendicular to the ends. The total flux through the cylinder is:

A) 0 N.m²/C
B) 4.2 N.m²/C
C) 21 N.m²/C
D) 280 N.m²/C
E) can't tell without knowing the length of the cylinder

Question 15

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 16

A cylindrical 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 is:

A) 0 N.m²/C
B) 4.2 N.m²/C
C) 21 N.m²/C
D) 280 N.m²/C
E) can't tell without knowing the areas of the sides and bottom

Question 17

A particle with charge 5.0 $\mu$ C is placed at the corner of a cube. The total electric flux through all sides of the cube is:

A) 0 N.m²/C
B) 7.1 *10⁴ N.m²/C
C) 9.4 * 10⁴ N.m²/C
D) 1.4 *10⁵ N.m²/C
E) 5.6 * 10⁵ N.m²/C

Question 18

Gauss's law:

A) can always be used to calculate the electric field.
B) relates the electric field throughout space to the charges distributed through that space.
C) only applies to point charges.
D) relates the electric field at points on a closed surface to the net charge enclosed by that surface.
E) relates the surface charge density to the electric field.

Question 19

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 20

The area vector for a flat surface:

A) is parallel to the surface and has a magnitude equal to the length of a side of the surface.
B) is perpendicular to the surface and has a magnitude equal to the length of a side of the surface.
C) is parallel to the surface and has a magnitude equal to the area of the surface.
D) is perpendicular to the surface and has a magnitude equal to the area of the surface.
E) none of the above.

Question 21

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 22

A conducting sphere of radius 5.0 cm carries a net charge of 7.5 µC. What is the surface charge density on the sphere?

A) 2.4 x 10^-2 C/m²
B) 1.4 x 10^-2 C/m²
C) 9.5 x 10^-4 C/m²
D) 2.4 x 10^-4 C/m²
E) 6.0 x 10^-5 C/m²

Question 23

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 inner surface of the shell is:

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

Question 24

Two large insulating 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 and 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 and 4 and 5 tie

Question 25

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) 60 N/C
C) 30 N/C
D) 15 N/C
E) 7.5 N/C

Question 26

A 300-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 C/m²; 0 C/m²

Question 27

A long line of charge with λ_ℓ charge per unit length runs along the cylindrical axis of a cylindrical conducting 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) λ_ℓ and $\lambda$ _c
B) −λ_ℓ and $\lambda$ _c + λ_ℓ
C) −λ_ℓ and $\lambda$ _c - λ_ℓ
D) λ_ℓ + $\lambda$ _c and $\lambda$ _c - λ_ℓ
E) λ_ℓ - $\lambda$ _c and $\lambda$ _c + λ_ℓ

Question 28

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 since it is not closed
E) none of the above

Question 29

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

Question 30

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 just outside the surface of the sphere is:

A) 0 N/C
B) 450 N/C
C) 900 N/C
D) 4500 N/C
E) 90,000 N/C

Question 31

A solid insulating sphere of radius R contains a positive charge that is distributed with a volume charge density that does not depend on angle but does increase linearly 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 32

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 33

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 and 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 and 4 and 5 tie

Question 34

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 35

Two large conducting 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 and 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 and 4 and 5 tie

Question 36

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 37

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 on the outer surface of the shell is:

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

Question 38

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