Deck 24: Gauss Law

Question 1

A solid sphere with a radius of one unit has a uniform charge distribution. The graph of the electric field as a function of radius has the form of

A)
B)
C)
D)

Answer 1

Question 2

A cubic box with sides of length a is located with its center at the origin. A constant electric field is in the + x direction. The side of the cube, which has a zero flux is

A) parallel to the y-z plane located at x = -a/2.
B) parallel to the y-z plane located at x = a/2.
C) parallel to the x-z plane located at y = a/2.
D) Hold on. All of the above have a nonzero flux.

Answer 2

parallel to the x-z plane located at y = a/2.

Question 3

Charge is placed on a conductor and allowed to reach an equilibrium state. The following statements are correct except

A) the electric field lines are normal to the surface.
B) the charge resides on the surface of the conductor.
C) the net electric field in the conductor is zero.
D) Hold on. All of the above statements are correct.

Answer 3

Hold on. All of the above statements are correct.

Question 4

A solid sphere with a radius of one unit has a charge on its surface. The graph of the electric field as a function of the sphere's radius has the form of

A)
B)
C)
D)

Question 5

Six equal charges, Q, are represented by circles and are arranged as illustrated here. The contributions to the net flux through the rectangle boundary include

A) none of the charges.
B) all six charges.
C) the two charges enclosed by the boundary.
D) the four charges outside the boundary.

Question 6

An infinitely long wire with a radius of one unit has a charge on its surface. The graph of the electric field as a function of the radius has the form of

A)
B)
C)
D)

Question 7

An electron and a proton are enclosed inside a Gaussian surface. The net flux produced by the pair is

A) zero.
B) positive.
C) negative.
D) none of the above.

Question 8

Two oppositely charged conducting plates have surface charge densities of + $\sigma$ and - $\sigma$ respectively. If the two plates are located at x = +1 and -1 unit, the graph of the resulting electric field is best represented by

A)
B)
C)
D)

Question 9

The electric flux due to a constant electric field is

A) a vector.
B) a scalar.
C) always zero.
D) none of the above.

Question 10

The electric flux in metric units is

A) [newton]/[meter]²/[coulomb].
B) [newton]·[meter]/[coulomb]².
C) [newton]·[meter]/[coulomb].
D) [newton]·[meter]²/[coulomb].

Question 11

The units [coulomb]/[meter] are associated with the

A) linear charge density.
B) surface charge density.
C) volume charge density.
D) none of the above.

Question 12

The units [coulomb]/[meter]² are associated with the

A) linear charge density.
B) surface charge density.
C) volume charge density.
D) none of the above.

Question 13

An infinite, insulating slab of thickness d = 1 unit has a uniform volume charge density $\rho$ with x = 0 at the center of the slab. The graph of the electric field as a function of distance from the origin can be best represented by

A)
B)
C)
D)

Question 14

A single electron enclosed inside a Gaussian surface produces

A) no net flux.
B) a net positive flux.
C) a net negative flux.
D) none of the above.

Question 15

A single electron located outside a Gaussian surface produces

A) no net flux.
B) a net positive flux.
C) a net negative flux.
D) none of the above.

Question 16

A charge is initially surrounded by a cubic Gaussian surface whose volume is d³. The cubic surface is replaced by a spherical surface of radius d/2. The net flux of the spherical surface is

A) greater than the net flux through the cube.
B) less than the net flux through the cube.
C) equal to the net flux through the cube.
D) none of the above.

Question 17

A uniform electric field is directed along the positive y axis. A net flux of 5.00 $\times$ 10⁴ N.m²/C passes through a surface whose area is 400.0 cm² and is aligned along the x-z plane. The magnitude of the electric field is

A) zero.
B) 1.25 $\times$ 10⁶ N/C.
C) 2.50 $\times$ 10⁵ N/C.
D) 1.25 $\times$ 10² N/C.

Question 18

A uniform electric field is directed along the positive y axis. If the magnitude of the electric field is 5.00 $\times$ 10⁶ N/C, the electric flux through a 400.0-cm² surface aligned along the x-z plane is

A) zero.
B) 2.00 $\times$ 10⁵ N.m²/C.
C) 2.00 $\times$ 10⁴ N.m²/C.
D) 1.20 $\times$ 10⁵ N.m²/C.

Question 19

A uniform electric field is directed along the positive y axis. If the magnitude of the electric field is 5.00 $\times$ 10⁶ N/C, the electric flux through a 400.0 cm² surface aligned along the y-z plane is

A) zero.
B) 2.00 $\times$ 10⁵ N.m²/C.
C) 2.00 $\times$ 10⁴ N.m²/C.
D) 1.20 $\times$ 10⁵ N.m²/C.

Question 20

A uniform electric field is directed along the positive y axis. The magnitude of the electric field is 5.0 $\times$ 10⁶ N/C. The electric flux through a surface whose area is 400.0 cm² and intersects the x-z plane at a 60° angle is

A) zero.
B) 1.0 $\times$ 10⁵ N.m²/C.
C) 1.7 $\times$ 10⁵ N.m²/C.
D) 1.7 $\times$ 10⁶ N.m²/C.

Question 21

Two point charges, +12 $\mu$ C and -6.0 $\mu$ C, are placed inside a cube whose volume is 2.0 cm³. The net electric flux through the surface of the cube due to these charges is

A) 6.8 * 10⁵ N·m²/C.
B) 6.8 *10⁶ N·m²/C.
C) 6.8 * 10⁷ N·m²/C.
D) zero.

Question 22

A net flux of 1.7 *10⁶ N.m²/C is produced by a set of point charges inside a cube whose side length is 0.10 m. The set of charges that can produce this flux is .

A) -20 $\mu$ C, +8 $\mu$ C, -3 $\mu$ C.
B) 20 $\mu$ C, -8 $\mu$ C, +3 $\mu$ C.
C) 10 $\mu$ C, -5 $\mu$ C, -4 $\mu$ C.
D) -10 $\mu$ C, -8 $\mu$ C, -3 $\mu$ C.

Question 23

A solid metal cylinder is placed in a uniform electric field that is directed along the axis of the cylinder. The electric field in the cylinder

A) is directed parallel to the axis of the cylinder.
B) is directed along the radius of the cylinder.
C) will vary along the length of the cylinder.
D) is zero.

Question 24

A +10.0- $\mu$ C charge is placed on the surface of a metal shell whose radius is 5.0 cm. The electric field at the center of the shell is

A) zero.
B) 9.0 $\times$ 10⁶ N/C.
C) -9.0 $\times$ 10⁶ N/C.
D) 1.4 $\times$ 10⁵ N/C.

Question 25

A +10.0- $\mu$ C charge is placed on the surface of a metal shell whose radius is 5.0 cm. The electric field at a point 5.0 cm from the surface of the shell is

A) zero.
B) 9.0 $\times$ 10⁶ N/C.
C) -9.0 $\times$ 10⁶ N/C.
D) 1.4 $\times$ 10⁵ N/C.

Question 26

The vector normal to the plane defined by the points (1, 0, 0), (0, 2, 0) and parallel to the z axis is

A) $\frac { 2 } { \sqrt { 5 } } i + \frac { 1 } { \sqrt { 5 } } j$
B) $\frac { 2 } { \sqrt { 5 } } i - \frac { 1 } { \sqrt { 5 } } j$
C) $\frac { 1 } { \sqrt { 5 } } i - \frac { 2 } { \sqrt { 5 } } j$
D) $\frac { 1 } { \sqrt { 5 } } i + \frac { 2 } { \sqrt { 5 } } j$
E) k.

Question 27

The vector that is normal to the plane defined by the points (3, 0, 0), (0, 1, 0), and (0, 0, 4) is

A) $\frac { 4 } { 13 } i - \frac { 12 } { 13 } j + \frac { 3 } { 13 } k$
B) $\frac { 4 } { 13 } i + \frac { 12 } { 13 } j - \frac { 3 } { 13 } k$
C) $\frac { 4 } { 13 } i - \frac { 12 } { 13 } j - \frac { 3 } { 13 } k$
D) $\frac { - 4 } { 13 } i + \frac { 12 } { 13 } j + \frac { 3 } { 13 }$

Question 28

The unit-normal vector to the plane defined by the points (0, 1, 1), (1, 1, 0), and (1, 3, 1) is

A) $\frac { 2 } { 3 } i + \frac { 1 } { 3 } j + \frac { 2 } { 3 }$
B) $\frac { - 1 } { 3 } \boldsymbol { i } + \frac { 2 } { 3 } \boldsymbol { j } + \frac { 2 } { 3 } \boldsymbol { k }$
C) $\frac { 2 } { 3 } i + \frac { 1 } { 3 } j - \frac { 2 } { 3 }$
D) $\frac { 2 } { 3 } \boldsymbol { i } + \frac { - 1 } { 3 } \boldsymbol { j } + \frac { 2 } { 3 } \boldsymbol { k }$

Question 29

The unit-normal vector to the plane defined by the points (-2, 0, 0), (0, 1, 0), and (0, 0, 3) is

A) $\frac { - 3 } { 7 } i - \frac { 6 } { 7 } j + \frac { 2 } { 7 } k$
B) $\frac { - 3 } { 7 } i + \frac { 6 } { 7 } j - \frac { 2 } { 7 } k$
C) $\frac { - 3 } { 7 } i + \frac { 6 } { 7 } j + \frac { 2 } { 7 } k$
D) $\frac { 3 } { 7 } i - \frac { 6 } { 7 } j + \frac { 2 } { 7 } k$

Question 30

A surface, whose area is 0.10 m² and normal, is given by $\left( \frac { 1 } { \sqrt { 2 } } i + \frac { 1 } { \sqrt { 2 } } j \right)$ ; it intersects with an electric field given by E= $1.4 \times 10 ^ { 6 } ( i + j + k )$ N/C. The electric flux through this surface is

A) zero.
B) 0.50 $\times$ 10⁵ N.m²/C.
C) 1.0 $\times$ 10⁵ N.m²/C.
D) 2.0 $\times$ 10⁵ N.m²/C.
E) 4.0 $\times$ 10⁵ N.m²/C.

Question 31

A surface, whose area is 0.10 m² and normal, is given by $\left( \frac { 1 } { \sqrt { 3 } } i + \frac { 1 } { \sqrt { 3 } } j + \frac { 1 } { \sqrt { 3 } } k \right)$ ; it intersects an electric field given by E = $1.7 \times 10 ^ { 6 } ( i + j - k )$ N/C. The electric flux through this surface is

A) zero.
B) 0.50 N·m²/C.
C) 1.0 N·m²/C.
D) 2.0 N·m²/C.
E) 4.0 N·m²/C.

Question 32

A surface, whose area is 0.10 m² and normal, is given by $\left( \frac { 1 } { \sqrt { 2 } } i + \frac { 1 } { \sqrt { 2 } } j \right)$ ; it intersects an electric field given by E = $2.0 \times 10 ^ { 6 } ( i - j )$ N/C. The electric flux through this surface is

A) zero.
B) 0.50 N.m²/C.
C) 1.0 N.m²/C.
D) 2.0 N.m²/C.
E) 4.0 N.m²/C.

Question 33

A charge of 10.0 $\mu$ C is placed on a corner of a cube. The flux through one of the sides opposite to the corner where the charge is placed is

A) 1.0 $\times$ 10⁴ N.m²/C.
B) 2.3 $\times$ 10⁴ N.m²/C.
C) 4.7 $\times$ 10⁴ N.m²/C.
D) 5.5 $\times$ 10⁴ N.m²/C.

Question 34

A surface that has an area of 0.20 m² lies on a plane whose normal is perpendicular to the plane defined by the points (3, 0, 0), (0, 1, 0), and (0, 0, 3). The surface intersects with an electric field given by 8.5 $\times$ 10⁵ $( 4 \boldsymbol { i } + 12 \boldsymbol { j } - 3 \boldsymbol { k } )$ N/C. The magnitude of the electric flux through the surface is

A) zero.
B) 9.0 $\times$ 10⁵ N.m²/C.
C) 1.9 $\times$ 10⁶ N.m²/C.
D) 4.0 $\times$ 10⁶ N.m²/C.

Question 35

A surface that has an area of 0.20 m² lies on a plane whose normal is perpendicular to the plane defined by the points (2, 1, 0), (0, 1, -1), and (1, 0, 2). The surface intersects with an electric field given by 4.5 * 10⁵ $( 3 \boldsymbol { i } + 12 \boldsymbol { j } + 3 \boldsymbol { k } )$ N/C. The electric flux through the surface is

A) zero.
B) 1.0 * 10⁶ N.m²/C.
C) 2.0* 10⁶ N.m²/C.
D) 4.0 *10⁶ N.m²/C.

Question 36

The magnitude of the electric field 10.0 cm from an infinitely long charged wire that has a linear charge density of 1.1 $\mu$ C/m is

A) 1.0 $\times$ 10⁵ N/C.
B) 2.0 $\times$ 10⁵ N/C.
C) 3.0 $\times$ 10⁵ N/C.
D) 4.0 $\times$ 10⁵ N/C.

Question 37

A cylindrical wire of radius 1.0 cm has charge distributed throughout its volume with a uniform charge density of 10 $\mu$ C/m³. The electric field at a point 0.50 cm from the central axis of the wire is

A) zero.
B) 2.8 $\times$ 10³ N/C.
C) 5.6 $\times$ 10³ N/C.
D) 8.4 $\times$ 10³ N/C.

Question 38

A cylindrical wire of radius 1.0 cm has charge distributed throughout its volume with a uniform charge density of 10.0 $\mu$ C/m³. The electric field at a point 0.50 cm from the surface of the wire is

A) zero.
B) 3.8 $\times$ 10³ N/C.
C) 7.6 $\times$ 10³ N/C.
D) 11 $\times$ 10³ N/C.

Question 39

An infinitely long cylinder with a radius of 1.0 cm has a charge density that is proportional to the distance from the axis of symmetry, $\rho$ = ar, where a = 10.0 C/m⁴. The charge per unit length within the cylinder is

A) 12 $\mu$ C/m.
B) 21 $\mu$ C/m.
C) 35 $\mu$ C/m.
D) 5.0 $\mu$ C/m.

Question 40

An infinitely long cylinder with a radius of 1.0 cm has a charge density that is proportional to the distance from the axis of symmetry, $\rho$ = ar, where a = 10.0 C/m⁴. The electric field 1.0 cm from the surface of the cylinder is

A) 1.5 $\times$ 10⁶ N/C.
B) 1.0 $\times$ 10⁷ N/C.
C) 1.5 $\times$ 10⁷ N/C.
D) 1.9 $\times$ 10⁷ N/C.

Question 41

An infinitely long cylinder with a radius of 1.0 cm has a charge density that is proportional to the distance from the axis of symmetry, $\rho$ = ar, where a = 10.0 C/m⁴. The electric field 0.50 cm from the central axis of the cylinder is

A) 1.4 $\times$ 10⁶ N/C.
B) 5.4 $\times$ 10⁶ N/C.
C) 9.4 $\times$ 10⁶ N/C.
D) 1.4 $\times$ 10⁷ N/C.

Question 42

A solid sphere of radius 10.0 cm has a total charge of 10.0 $\mu$ C on its surface. The electric field 10.0 cm from the surface of the sphere is

A) 9.00 $\times$ 10⁶ N/C.
B) 2.25 $\times$ 10⁶ N/C.
C) 4.50 $\times$ 10⁶ N/C.
D) 4.50 $\times$ 10⁵ N/C.

Question 43

The net electrical flux through a spherical Gaussian surface of radius 1.0 cm is 24 N.m²/C. If the radius of the surface is doubled to 2.0 cm, the electric flux will become

A) 24 N.m²/C.
B) 12 N.m²/C.
C) 6.0 N.m²/C.
D) 3.0 N.m²/C.

Question 44

The electric field produced by a sheet of charge varies according to the distance d from the surface by the relationship

A) E proportional to d.
B) E proportional to 1/d.
C) E proportional to 1/d².
D) Hold on! E is a constant.

Question 45

A flat conducting surface with a charge density of 10.0 $\mu$ C/m² produces an electric field. The magnitude of the electric field 15 cm from the surface is

A) zero.
B) 0.55 * 10⁶ N/C.
C) 1.1 * 10⁶ N/C.
D) 2.2 *10⁶ N/C.

Question 46

A flat conducting slab with a charge density of 10.0 $\mu$ C/m² produces an electric field. The magnitude of the electric field 15 cm from the surface is

A) zero.
B) 0.55 * 10⁶ N/C.
C) 1.1 * 10⁶ N/C.
D) 2.2 * 10⁶ N/C.

Question 47

The electric field at the surface of a charged conductor

A) is parallel to the surface.
B) is perpendicular to the surface.
C) is parallel and perpendicular to the surface.
D) depends on the curvature of the surface.

Question 48

The charge on a conductor

A) is distributed throughout the material.
B) produces a nonzero electric field in the conductor.
C) is on the surface of the conductor.
D) is not in an equilibrium state.

Question 49

A cubic box with sides of length a is located with its center at the origin. A constant electric field is in the + x direction. The side of the cube that has a negative flux is

A) parallel to the y-z plane located at x = -a/2.
B) parallel to the y-z plane located at x = a/2.
C) parallel to the x-z plane located at y = a/2.
D) parallel to the x-z plane located at y = -a/2.