Deck 22: Gausss Law

Question 1

An advantage in evaluating surface integrals related to Gauss's law for symmetric charge distributions is

A)the flux is outward.
B)the flux is inward.
C)the electric field is of constant magnitude on certain surfaces.
D)the charge is always on the surface.
E)the electric field is a constant on any surface.

Answer 1

the electric field is of constant magnitude on certain surfaces.

Question 2

Gauss's law may be applied only to charge distributions that are symmetric.

Answer 2

False

Question 3

If the net flux through a closed surface is positive, then the net charge enclosed must be positive.

Answer 3

True

Question 4

Gauss's law can be applied using any surface.

Question 5

Gaussian surfaces A and B enclose the same positive charge +Q. The area of Gaussian surface A is three times larger than that of Gaussian surface B. The flux of electric field through Gaussian surface A is

A)nine times larger than the flux of electric field through Gaussian surface B.
B)three times larger than the flux of electric field through Gaussian surface B.
C)equal to the flux of electric field through Gaussian surface B.
D)three times smaller than the flux of electric field through Gaussian surface B.
E)unrelated to the flux of electric field through Gaussian surface B.

Question 6

Outside a spherically symmetric charge distribution of net charge Q, Gauss's law can be used to show that the electric field at a given distance

A)must be zero.
B)must be directed outward.
C)acts like it originated in a point charge Q at the center of the distribution.
D)must be directed inward.
E)must be greater than zero.

Question 7

Consider a spherical Gaussian surface of radius R centered at the origin. A charge Q is placed inside the sphere. Where should the charge be located to maximize the magnitude of the flux of the electric field through the Gaussian surface?

A)at x = 0, y = 0, z = R/2
B)at the origin
C)at x = R/2, y = 0, z = 0
D)at x = 0, y = R/2, z = 0
E)The flux does not depend on the position of the charge as long as it is inside the sphere

Question 8

A region of space contains a uniform electric field oriented along the y-axis. A frame of surface area A is placed perpendicular to the y-axis in the xz-plane. The magnitude of the electric flux through this frame is Φ₀. A second frame is placed in the same electric field in such a way that the magnitude of the electric flux through it is Φ₀/2. How is the plane of second frame oriented with respect to the plane of the first one?

A)at a 90° angle
B)at a 60° angle
C)parallel to the first frame
D)perpendicular to the first frame
E)at a 30° angle

Question 9

If the electric flux through a rectangular area is 5.0 N m²/C, and the electric field is then doubled, what is the resulting flux through the area?

A)5.0 N m²/C
B)10 N m²/C
C)2.5 N m²/C
D)1 N m²/C
E)20 N m²/C

Question 10

If a closed surface surrounds a dipole, the net flux through the surface is zero.

Question 11

FIGURE 22-1
Fig. 22-1 shows four Gaussian surfaces surrounding a distribution of charges. Which Gaussian surfaces have no electric flux through them?

A)a.
B)b.
C)c.
D)b and d.
E)b and c.

Question 12

State Gauss's law.

Question 13

FIGURE 22-1
Fig. 22-1 shows four Gaussian surfaces surrounding a distribution of charges. Which Gaussian surfaces have an electric flux of +q/ ε_O through them?

A)a.
B)b.
C)b and d.
D)b and c.
E)c.

Question 14

A charge Q is positioned at the center of a sphere of radius R. The flux of the electric field through the sphere is equal to Φ. If the charge Q is now placed at the center of a cube the flux of the electric field through the surface of the cube is equal to

A)Φ/2.
B)Φ.
C)2Φ.
D)0.
E)The value of the flux depends on the dimensions of the cube.

Question 15

A uniform electric field = E₀ is set-up in a region of space. A frame is placed in that region in such a way that its plane is perpendicular to the y-axis. Which of the following changes would decrease the magnitude of the electric flux through the frame?

A)Sliding the frame sideways parallel to the z-axis within the xz-plane
B)moving the frame vertically along the y-axis keeping parallel to the xz-plane
C)rotating the frame in the xz-plane with respect to the y-axis
D)sliding the frame sideways parallel to the x-axis within the xz-plane
E)tilting the frame so that its plane is now in the yz-plane

Question 16

If a rectangular area is rotated in a uniform electric field from the position where the maximum electric flux goes through it to an orientation where only half the flux goes through it, what has been the angle of rotation?

A)45°
B)26.6°
C)90°
D)30°
E)60°

Question 17

If a charge is located at the center of a spherical volume and the electric flux through the surface of the sphere is Φ₀, what is the flux through the surface if the radius of the sphere doubles?

A)0.125 Φ₀
B)Φ₀
C)5 Φ₀
D)8 Φ₀
E)0.500 Φ₀

Question 18

The electric field in a region of space is oriented along the positive y axis. A circle of radius R is placed in the xz-plane. The flux of the electric field through this circle is Φ. The same electric field passing through a second circle of radius 2R parallel to xz-plane would result in a flux equal to

A)Φ.
B)0.
C)4Φ.
D)2Φ.
E)3Φ.

Question 19

If the net flux through a closed surface is zero, then there can be no charge or charges within that surface.

Question 20

A positive charge Q is located at the center of an imaginary Gaussian cube of sides a. The flux of the electric field through the surface of the cube is Φ. A second, negative charge -Q is placed next to Q inside the cube. Which of the following statements will be true in this case?

A)The net electric field on the surface of the cube is equal to zero
B)The electric field on the surface of the cube is perpendicular to the surface
C)The magnitude of the net electric field is constant on the entire surface of the cube
D)The net flux through the surface of the cube is equal to zero
E)The net flux through the surface is equal to 2Φ

Question 21

Two long straight parallel lines of charge, #1 and #2, carry positive charge per unit lengths of λ1 and λ2 respectively. λ1 > λ2. The electric field halfway between the lines, which are separated by a distance a, has magnitude

Question 22

A charge q = 2 μC is placed at the origin in a region where there is already a uniform electric field = (100 N/C) . Calculate the flux of the net electric field through a Gaussian sphere of radius R = 10 cm centered at the origin.

A)5.52 × 10⁵ Nm²/C
B)1.13 × 10⁵ Nm²/C
C)2.26 × 10⁵ Nm²/C
D)0.565 × 10⁵ Nm²/C
E)0

Question 23

A solid non-conducting sphere of radius R carries a charge Q₁ distributed uniformly. The sphere is surrounded by a concentric spherical shell of inner radius R_a and outer radius R_b. The shell carries a total charge Q₂ distributed uniformly in its volume. What is the net electric field at a radial distance r such that R < r < R_a?

Question 24

Consider two oppositely charged, parallel metal plates. The plates are square with sides L and carry charges Q and -Q. What is the magnitude of the electric field in the region between the plates?

A)E =
B)E =
C)E=0
D)E =
E)E=

Question 25

A long straight line of charge has a uniform positive charge per unit length λ. The line is partially enclosed in a long rectangular box of length L and ends of area A, the line running through the center of each end. The electric flux through the surface of the box is

Question 26

If the electric flux through a circular area is 5.0 Nm²/C, what is the electric flux through a circle of double the diameter assuming the orientations of the circles are the same and the electric field is uniform?

A)5.0 Nm²/C
B)20 Nm²/C
C)2.5 Nm²/C
D)1.0 Nm²/C
E)10.0 Nm²/C

Question 27

Three parallel flat planes of charge are separated by a distance d between each of the planes. The charge density on each of the planes is σ. The maximum magnitude of the electric field in the vicinity of the planes is

Question 28

Consider an electric field = 2x - 3y . The coordinates x and y are measured in meters and the electric field is in N/C. What is the magnitude of the flux of this field through a square whose corners are located at (x, y, z) = (0, 2, 0), (2, 2, 0), (0, 2, 2)?

A)6 Nm²/C
B)0
C)24 Nm²/C
D)12 Nm²/C
E)48 Nm²/C

Question 29

A solid non-conducting sphere of radius R carries a uniform charge density. At a radial distance r₁ = R/4 the electric field has a magnitude E0. What is the magnitude of the electric field at a radial distance r₂ = 2R?

A)E₀/4
B)0
C)E₀/2
D)E₀
E)2E₀

Question 30

A point charge q = +1 μC is located at the origin. What is the flux of the electric field of this charge through a square whose corners are (x, y, z) = (1, 1, 1), (-1, 1, 1), (-1, 1, -1), and (1, 1, -1)?

A)11.3 × 10⁴ Nm²/C
B)0.5 × 10⁴ Nm²/C
C)0
D)1.0 × 10⁴ Nm²/C
E)1.9 × 10⁴ Nm²/C

Question 31

A charge Q is uniformly distributed throughout a nonconducting sphere of radius R. The charge density in the sphere is

Question 32

A region of space contains an electric field = E₁ + E₂ where E₁ and E₂ are positive constants. A frame whose corners are located at (x, y, z) = (a/2, 0, a/2), (-a/2, 0,-a/2), (a/2, 0,-a/2), and (-a/2, 0, a/2). What is the magnitude of the electric flux through the frame?

Question 33

A charge Q is uniformly distributed throughout a nonconducting sphere of radius R.
(a) What is the magnitude of the electric field at a distance R/2 from the center of the sphere?
(b) What is the magnitude of the electric field at a distance 2R from the center of the sphere?

Question 34

FIGURE 22-2
A uniform electric field with a magnitude of 6 × 10⁶ N/C is applied to a cube of edge length 0.1 m as shown in Fig. 22-2. If the direction of the E-field is along the +x-axis, what is the electric flux passing through the shaded face of the cube?

A)0.6 × 10⁴ Nm²/C
B)6 × 10⁴ Nm²/C
C)60 × 10⁴ Nm²/C
D)600 × 10⁴ Nm²/C
E)6000 × 10⁴ Nm²/C

Question 35

If a point charge is located at the center of a cylinder and the electric flux leaving one end of the cylinder is 20% of the total flux leaving the cylinder, what portion of the flux leaves the curved surface of the cylinder?

A)20%
B)100%
C)80%
D)40%
E)60%

Question 36

If a point charge is located at the center of a cube and the electric flux through one face of the cube is 5.0 Nm²/C, what is the total flux leaving the cube?

A)20 Nm²/C
B)30 Nm²/C
C)5.0 Nm²/C
D)25 Nm²/C
E)1 Nm²/C

Question 37

Three parallel flat planes of charge are separated by a distance d between each of the planes. The charge density on each of the planes is σ. The field in the regions between the planes has magnitude

Question 38

Two parallel flat planes of positive charge are separated by a distance d. Plane #1 has charge density σ₁ and plane #2 has a charge density σ2. σ1> σ2.
(a) In the region between the planes, the magnitude of the electric field is
(b) In the region outside the planes the magnitude of the electric field is

Question 39

FIGURE 22-2
An uniform electric field of magnitude E = 100 N/C is oriented along the positive y-axis. What is the magnitude of the flux of this field through a square of surface area A = 2 m² oriented parallel to the yz-plane?

A)200 Nm²/C
B)100 Nm²/C
C)0
D)400 Nm²/C
E)600 Nm²/C

Question 40

Two long straight parallel lines of charge, #1 and #2, carry positive charge per unit lengths of λ1 and λ2, respectively. λ1 > λ2. The locus of points where the electric field is zero in this case is

A)along a line between the lines closer to line #2 than line #1.
B)at a point halfway between the lines.
C)along line #1.
D)along a line between the lines closer to line #1 than line #2.
E)cannot be determined

Question 41

An infinitely long cylinder of radius R = 2 cm carries a uniform charge density ρ = 18 μC/ m³. Calculate the electric field at distance r = 1 cm from the axis of the cylinder.

A)2.5 × 10³ N/C
B)5.1 × 10³ N/C
C)0
D)2.0 × 10³ N/C
E)10.2 × 10³ N/C

Question 42

A non-conducting sphere of radius R = 7 cm carries a charge Q = 4 mC distributed uniformly throughout its volume. At what distance, measured from the center of the sphere does the electric field reach a value equal to half its maximum value?

A)3.5 cm only
B)4.9 cm only
C)3.5 cm and 9.9 cm
D)3.5 cm and 4.9 cm
E)9.9 cm only

Question 43

A solid non-conducting sphere of radius R carries a charge Q distributed uniformly throughout its volume. At a radius r (r < R) from the center of the sphere the electric field has a value E. If the same charge Q were distributed uniformly throughout a sphere of radius 2R the magnitude of the electric field at a radius r would be equal to

A)E/8.
B)E/2.
C)2E.
D)8E.
E)E.

Question 44

A spherical, non-conducting shell of inner radius r₁= 10 cm and outer radius r₂= 15 cm carries a total charge Q = 15 μC distributed uniformly throughout its volume. What is the electric field at a distance r= 12 cm from the center of the shell?

A)5.75 × 10³ N/C
B)0
C)2.87 × 10⁶ N/C
D)5.75 × 10⁶ N/C
E)2.87 × 10³ N/C