Deck 24: Gausss Law

Question 1

A point charge +Q is located on the x axis at x = a,and a second point charge −Q is located on the x axis at x = −a.A Gaussian surface with radius r = 2a is centered at the origin.The flux through this Gaussian surface is

A)zero because the negative flux over one hemisphere is equal to the positive flux over the other.
B)greater than zero.
C)zero because at every point on the surface the electric field has no component perpendicular to the surface.
D)zero because the electric field is zero at every point on the surface.
E)none of the above.

Answer 1

zero because the negative flux over one hemisphere is equal to the positive flux over the other.

Question 2

Charge of a uniform density (8.0 nC/m²)is distributed over the entire xy plane.A charge of uniform density (3.0 nC/m²)is distributed over the parallel plane defined by z = 2.0 m.Determine the magnitude of the electric field for any point with z = 3.0 m.

A)0.79 kN/C
B)0.17 kN/C
C)0.62 kN/C
D)0.34 kN/C
E)0.28 kN/C

Answer 2

0.62 kN/C

Question 3

Charge of uniform surface density (4.0 nC/m²)is distributed on a spherical surface (radius = 2.0 cm).What is the total electric flux through a concentric spherical surface with a radius of 4.0 cm?

A)2.8 N ⋅ m²/C
B)1.7 N ⋅ m²/C
C)2.3 N ⋅ m²/C
D)4.0 N ⋅ m²/C
E)9.1 N ⋅ m²/C

Answer 3

2.3 N ⋅ m²/C

Question 4

Charge of uniform density (0.30 nC/m²)is distributed over the xy plane,and charge of uniform density (−0.40 nC/m²)is distributed over the yz plane.What is the magnitude of the resulting electric field at any point not in either of the two charged planes?

A)40 N/C
B)34 N/C
C)28 N/C
D)46 N/C
E)6.0 N/C

Question 5

The total electric flux through a closed cylindrical (length = 1.2 m,diameter = 0.20 m)surface is equal to −5.0 N ⋅ m²/C.Determine the net charge within the cylinder.

A)−62 pC
B)−53 pC
C)−44 pC
D)−71 pC
E)−16 pC

Question 6

Two charges of 15 pC and −40 pC are inside a cube with sides that are of 0.40-m length.Determine the net electric flux through the surface of the cube.

A)+2.8 N ⋅ m²/C
B)−1.1 N ⋅ m²/C
C)+1.1 N ⋅ m²/C
D)−2.8 N ⋅ m²/C
E)−0.47 N ⋅ m²/C

Question 7

Two infinite parallel surfaces carry uniform charge densities of 0.20 nC/m² and −0.60 nC/m².What is the magnitude of the electric field at a point between the two surfaces?

A)34 N/C
B)23 N/C
C)45 N/C
D)17 N/C
E)90 N/C

Question 8

Two infinite,uniformly charged,flat surfaces are mutually perpendicular.One of the sheets has a charge density of +60 pC/m²,and the other carries a charge density of −80 pC/m².What is the magnitude of the electric field at any point not on either surface?

A)1.1 N/C
B)5.6 N/C
C)7.9 N/C
D)3.8 N/C
E)4.0 N/C

Question 9

A uniform linear charge density of 4.0 nC/m is distributed along the entire x axis.Consider a spherical (radius = 5.0 cm)surface centered on the origin.Determine the electric flux through this surface.

A)68 N ⋅ m²/C
B)62 N ⋅ m²/C
C)45 N ⋅ m²/C
D)79 N ⋅ m²/C
E)23 N ⋅ m²/C

Question 10

The xy plane is "painted" with a uniform surface charge density which is equal to 40 nC/m².Consider a spherical surface with a 4.0-cm radius that has a point in the xy plane as its center.What is the electric flux through that part of the spherical surface for which z > 0?

A)14 N ⋅ m²/C
B)11 N ⋅ m²/C
C)17 N ⋅ m²/C
D)20 N ⋅ m²/C
E)23 N ⋅ m²/C

Question 11

Charge of a uniform density (8.0 nC/m²)is distributed over the entire xy plane.A charge of uniform density (5.0 nC/m²)is distributed over the parallel plane defined by z = 2.0 m.Determine the magnitude of the electric field for any point with z = 1.0 m.

A)0.45 kN/C
B)0.17 kN/C
C)0.28 kN/C
D)0.73 kN/C
E)0.62 kN/C

Question 12

The electric field in the region of space shown is given by
N/C where y is in m.What is the magnitude of the electric flux through the top face of the cube shown?

A)90 N ⋅ m²/C
B)6.0 N ⋅ m²/C
C)54 N ⋅ m²/C
D)12 N ⋅ m²/C
E)126 N ⋅ m²/C

Question 13

A charge of uniform volume density (40 nC/m³)fills a cube with 8.0-cm edges.What is the total electric flux through the surface of this cube?

A)2.9 N ⋅ m²/C
B)2.0 N ⋅ m²/C
C)2.6 N ⋅ m²/C
D)2.3 N ⋅ m²/C
E)1.8 N ⋅ m²/C

Question 14

Charges q and Q are placed on the x axis at x = 0 and x = 2.0 m,respectively.If q = −40 pC and Q = +30 pC,determine the net flux through a spherical surface (radius = 1.0 m)centered on the origin.

A)−9.6 N ⋅ m²/C
B)−6.8 N ⋅ m²/C
C)−8.5 N ⋅ m²/C
D)−4.5 N ⋅ m²/C
E)−1.1 N ⋅ m²/C

Question 15

A charge of 0.80 nC is placed at the center of a cube that measures 4.0 m along each edge.What is the electric flux through one face of the cube?

A)90 N ⋅ m²/C
B)15 N ⋅ m²/C
C)45 N ⋅ m²/C
D)23 N ⋅ m²/C
E)64 N ⋅ m²/C

Question 16

A hemispherical surface (half of a spherical surface)of radius R is located in a uniform electric field of magnitude E that is parallel to the axis of the hemisphere.What is the magnitude of the electric flux through the hemisphere surface?

A)πR²E
B)4πR²E/3
C)2πR²E/3
D)πR²E/2
E)πR²E/3

Question 17

A uniform charge density of 500 nC/m³ is distributed throughout a spherical volume (radius = 16 cm).Consider a cubical (4.0 cm along the edge)surface completely inside the sphere.Determine the electric flux through this surface.

A)7.1 N ⋅ m²/C
B)3.6 N ⋅ m²/C
C)12 N ⋅ m²/C
D)19 N ⋅ m²/C
E)970 N ⋅ m²/C

Question 18

Charge of uniform surface density (0.20 nC/m²)is distributed over the entire xy plane.Determine the magnitude of the electric field at any point having z = 2.0 m.

A)17 N/C
B)11 N/C
C)23 N/C
D)28 N/C
E)40 N/C

Question 19

A long cylinder (radius = 3.0 cm)is filled with a nonconducting material which carries a uniform charge density of 1.3 μC/m³.Determine the electric flux through a spherical surface (radius = 2.0 cm)which has a point on the axis of the cylinder as its center.

A)5.7 N ⋅ m²/C
B)4.9 N ⋅ m²/C
C)6.4 N ⋅ m²/C
D)7.2 N ⋅ m²/C
E)15 N ⋅ m²/C

Question 20

A long nonconducting cylinder (radius = 12 cm)has a charge of uniform density (5.0 nC/m³)distributed throughout its column.Determine the magnitude of the electric field 5.0 cm from the axis of the cylinder.

A)25 N/C
B)20 N/C
C)14 N/C
D)31 N/C
E)34 N/C

Question 21

A point charge (5.0 pC)is located at the center of a spherical surface (radius = 2.0 cm),and a charge of 3.0 pC is spread uniformly upon this surface.Determine the magnitude of the electric field 1.0 cm from the point charge.

A)0.72 kN/C
B)0.45 kN/C
C)0.63 kN/C
D)0.90 kN/C
E)0.18 kN/C

Question 22

Charge of uniform density (40 pC/m²)is distributed on a spherical surface (radius = 1.0 cm),and a second concentric spherical surface (radius = 3.0 cm)carries a uniform charge density of 60 pC/m².What is the magnitude of the electric field at a point 2.0 cm from the center of the two surfaces?

A)1.1 N/C
B)4.5 N/C
C)1.4 N/C
D)5.6 N/C
E)0.50 N/C

Question 23

A solid nonconducting sphere (radius = 12 cm)has a charge of uniform density (30 nC/m³)distributed throughout its volume.Determine the magnitude of the electric field 15 cm from the center of the sphere.

A)22 N/C
B)49 N/C
C)31 N/C
D)87 N/C
E)26 N/C

Question 24

Charge of uniform density (80 nC/m³)is distributed throughout a hollow cylindrical region formed by two coaxial cylindrical surfaces of radii 1.0 mm and 3.0 mm.Determine the magnitude of the electric field at a point which is 4.0 mm from the symmetry axis.

A)7.9 N/C
B)10 N/C
C)9.0 N/C
D)8.9 N/C
E)17 N/C

Question 25

A charge of 8.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm),and a second charge of −3.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm).Determine the magnitude of the electric field 5.0 cm from the center of the two surfaces.

A)14 N/C
B)11 N/C
C)22 N/C
D)18 N/C
E)40 N/C

Question 26

A long cylindrical shell (radius = 2.0 cm)has a charge uniformly distributed on its surface.If the magnitude of the electric field at a point 8.0 cm radially outward from the axis of the shell is 85 N/C,how much charge is distributed on a 2.0-m length of the charged cylindrical surface?

A)0.38 nC
B)0.76 nC
C)0.19 nC
D)0.57 nC
E)0.98 nC

Question 27

Charge of uniform density (40 pC/m²)is distributed on a spherical surface (radius = 1.0 cm),and a second concentric spherical surface (radius = 3.0 cm)carries a uniform charge density of 60 pC/m².What is the magnitude of the electric field at a point 4.0 cm from the center of the two surfaces?

A)3.8 N/C
B)4.1 N/C
C)3.5 N/C
D)3.2 N/C
E)0.28 N/C

Question 28

Charge of uniform density (80 nC/m³)is distributed throughout a hollow cylindrical region formed by two coaxial cylindrical surfaces of radii 1.0 mm and 3.0 mm.Determine the magnitude of the electric field at a point which is 2.0 mm from the symmetry axis.

A)7.9 N/C
B)9.0 N/C
C)5.9 N/C
D)6.8 N/C
E)18 N/C

Question 29

A 4.0-pC point charge is placed at the center of a hollow (inner radius = 2.0 cm,outer radius = 4.0 cm)conducting sphere which has a net charge of 4.0 pC.Determine the magnitude of the electric field at a point which is 6.0 cm from the point charge.

A)35 N/C
B)25 N/C
C)30 N/C
D)20 N/C
E)10 N/C

Question 30

A long nonconducting cylinder (radius = 12 cm)has a charge of uniform density (5.0 nC/m³)distributed throughout its volume.Determine the magnitude of the electric field 15 cm from the axis of the cylinder.

A)20 N/C
B)27 N/C
C)16 N/C
D)12 N/C
E)54 N/C

Question 31

A long straight metal rod has a radius of 2.0 mm and a surface charge of density 0.40 nC/m².Determine the magnitude of the electric field 3.0 mm from the axis.

A)18 N/C
B)23 N/C
C)30 N/C
D)15 N/C
E)60 N/C

Question 32

A 5.0-nC point charge is embedded at the center of a nonconducting sphere (radius = 2.0 cm)which has a charge of −8.0 nC distributed uniformly throughout its volume.What is the magnitude of the electric field at a point that is 1.0 cm from the center of the sphere?

A)1.8 × 10⁵ N/C
B)9.0 × 10⁴ N/C
C)3.6 × 10⁵ N/C
D)2.7 × 10⁵ N/C
E)7.2 × 10⁵ N/C

Question 33

The axis of a long hollow metallic cylinder (inner radius = 1.0 cm,outer radius = 2.0 cm)coincides with a long wire.The wire has a linear charge density of −8.0 pC/m,and the cylinder has a net charge per unit length of −4.0 pC/m.Determine the magnitude of the electric field 3.0 cm from the axis.

A)5.4 N/C
B)7.2 N/C
C)4.3 N/C
D)3.6 N/C
E)2.4 N/C

Question 34

Charge of uniform linear density (4.0 nC/m)is distributed along the entire x axis.Determine the magnitude of the electric field on the y axis at y = 2.5 m.

A)36 N/C
B)29 N/C
C)43 N/C
D)50 N/C
E)58 N/C

Question 35

A charge of 5.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm),and a second charge of −2.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm).Determine the magnitude of the electric field 3.0 cm from the center of the two surfaces.

A)30 N/C
B)50 N/C
C)40 N/C
D)20 N/C
E)70 N/C

Question 36

If the electric field just outside a thin conducting sheet is equal to 1.5 N/C,determine the surface charge density on the conductor.

A)53 pC/m²
B)27 pC/m²
C)35 pC/m²
D)13 pC/m²
E)6.6 pC/m²

Question 37

Charge of uniform density (20 nC/m²)is distributed over a cylindrical surface (radius = 1.0 cm),and a second coaxial surface (radius = 3.0 cm)carries a uniform charge density of −12 nC/m².Determine the magnitude of the electric field at a point 4.0 cm from the symmetry axis of the two surfaces.

A)0.45 kN/C
B)1.0 kN/C
C)0.73 kN/C
D)0.56 kN/C
E)2.3 kN/C

Question 38

A long nonconducting cylinder (radius = 6.0 mm)has a nonuniform volume charge density given by αr²,where α = 6.2 mC/m⁵ and r is the distance from the axis of the cylinder.What is the magnitude of the electric field at a point 2.0 mm from the axis?

A)1.4 N/C
B)1.6 N/C
C)1.8 N/C
D)2.0 N/C
E)5.4 N/C

Question 39

Charge of uniform density (20 nC/m²)is distributed over a cylindrical surface (radius = 1.0 cm),and a second coaxial surface (radius = 3.0 cm)carries a uniform charge density of −12 nC/m².Determine the magnitude of the electric field at a point 2.0 cm from the symmetry axis of the two surfaces.

A)2.3 kN/C
B)1.1 kN/C
C)1.7 kN/C
D)3.4 kN/C
E)4.5 kN/C

Question 40

Each 2.0-m length of a long cylinder (radius = 4.0 mm)has a charge of 4.0 nC distributed uniformly throughout its volume.What is the magnitude of the electric field at a point 5.0 mm from the axis of the cylinder?

A)9.9 kN/C
B)8.1 kN/C
C)9.0 kN/C
D)7.2 kN/C
E)18 kN/C

Question 41

Which one of the following cannot be a statement of Gauss's Law for some physical situation?

A)4πr²ε₀E = Q.
B)2πrLε₀E = Q.
C) .
D) .
E) .

Question 42

A constant electric field
Is present throughout a region of space that includes the plane bounded by the x and y axes and the lines x = 30 cm and y = 50 cm.The electric flux through the plane's surface,in N ⋅ m²/C,is

A)0.
B)0.25.
C)25.
D)50.
E)100.

Question 43

Two concentric imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge Q located at the center of the surfaces.When compared to the electric flux Φ₁ through the surface of radius R,the electric flux Φ₂ through the surface of radius 2R is

A) .
B) .
C)Φ₂ = Φ₁.
D)Φ₂ = 2Φ₁.
E)Φ₂ = 4Φ₁.

Question 44

A long cylindrical conductor (radius = 1.0 mm)carries a charge density of 4.0 pC/m and is inside a coaxial,hollow,cylindrical conductor (inner radius = 3.0 mm,outer radius = 4.0 mm)that has a total charge of −8.0 pC/m.What is the magnitude of the electric field 2.0 mm from the axis of these conductors?

A)24 N/C
B)18 N/C
C)zero
D)36 N/C
E)226 N/C

Question 45

When a cube is inscribed in a sphere of radius r,the length L of a side of the cube is
)If a positive point charge Q is placed at the center of the spherical surface,the ratio of the electric flux Φ_sphere at the spherical surface to the flux Φ_cube at the surface of the cube is

A) .
B) .
C)1.
D) .
E) .

Question 46

A point charge of 6.0 nC is placed at the center of a hollow spherical conductor (inner radius = 1.0 cm,outer radius = 2.0 cm)which has a net charge of −4.0 nC.Determine the resulting charge density on the inner surface of the conducting sphere.

A)+4.8 μC/m²
B)−4.8 μC/m²
C)−9.5 μC/m²
D)+9.5 μC/m²
E)−8.0 μC/m²

Question 47

Three originally uncharged infinite parallel planes are arranged as shown.Then the upper plate has surface charge density σ placed on it while the lower plate receives surface charge density −σ.The net charge induced on the center plate is

A)0.
B)−σ/2.
C)+σ/2.
D)−σ.
E)+σ.

Question 48

An uncharged spherical conducting shell surrounds a charge −q at the center of the shell.Then charge +3q is placed on the outside of the shell.When static equilibrium is reached,the charges on the inner and outer surfaces of the shell are respectively

A)+q,−q.
B)−q,+q.
C)+q,+2q.
D)+2q,+q.
E)+3q,0.

Question 49

The field just outside the surface of a long conducting cylinder which has a 2.0-cm radius points radially outward and has a magnitude of 200 N/C.What is the charge density on the surface of the cylinder?

A)2.7 nC/m²
B)1.8 nC/m²
C)3.5 nC/m²
D)4.4 nC/m²
E)0.90 nC/m²

Question 50

An astronaut is in an all-metal chamber outside the space station when a solar storm results in the deposit of a large positive charge on the station.Which statement is correct?

A)The astronaut must abandon the chamber immediately to avoid being electrocuted.
B)The astronaut will be safe only if she is wearing a spacesuit made of non-conducting materials.
C)The astronaut does not need to worry: the charge will remain on the outside surface.
D)The astronaut must abandon the chamber if the electric field on the outside surface becomes greater than the breakdown field of air.
E)The astronaut must abandon the chamber immediately because the electric field inside the chamber is non-uniform.

Question 51

An uncharged metal sphere is placed on an insulating puck on a frictionless table.While being held parallel to the table,a rod with a charge q is brought close to the sphere,but does not touch it.As the rod is brought in,the sphere

A)remains at rest.
B)moves toward the rod.
C)moves away from the rod.
D)moves perpendicular to the velocity vector of the rod.
E)moves upward off the puck.

Question 52

A small metal sphere is suspended from the conducting cover of a conducting metal ice bucket by a non-conducting thread.The sphere is given a negative charge before the cover is placed on the bucket.The bucket is tilted by means of a non-conducting material so that the charged sphere touches the inside of the bucket.Which statement is correct?

A)The negative charge remains on the metal sphere.
B)The negative charge spreads over the outside surface of the bucket and cover.
C)The negative charge spreads over the inside surface of the bucket and cover.
D)The negative charge spreads equally over the inside and outside surfaces of the bucket and cover.
E)The negative charge spreads equally over the sphere and the inside and outside surfaces of the bucket and cover.

Question 53

A spherical conductor (radius = 1.0 cm)with a charge of 2.0 pC is within a concentric hollow spherical conductor (inner radius = 3.0 cm,outer radius = 4.0 cm)which has a total charge of −3.0 pC.What is the magnitude of the electric field 2.0 cm from the center of these conductors?

A)23 N/C
B)zero
C)45 N/C
D)90 N/C
E)110 N/C

Question 54

The electric field just outside the surface of a hollow conducting sphere of radius 20 cm has a magnitude of 500 N/C and is directed outward.An unknown charge Q is introduced into the center of the sphere and it is noted that the electric field is still directed outward but has decreased to 100 N/C.What is the magnitude of the charge Q?

A)1.5 nC
B)1.8 nC
C)1.3 nC
D)1.1 nC
E)2.7 nC

Question 55

Which one of the following is not an expression for electric charge?

A)
B)
C)
D)
E)

Question 56

An uncharged spherical conducting shell surrounds a charge −q at the center of the shell.The charges on the inner and outer surfaces of the shell are respectively

A)−q,−q.
B)−q,+q.
C)+q,−q.
D)+q,+q.
E)+q,0.

Question 57

The electric flux through the two adjacent spherical surfaces shown below is known to be the same.
It is also known that there is no charge inside either spherical surface.We can conclude that

A)there is no electric field present in this region of space.
B)there is a constant E field present in this region of space.
C)the electric flux has a constant value of zero.
D)any of the above may be correct.
E)only (a)and (b)above may be correct.

Question 58

A positive point charge q is placed at the center of an uncharged metal sphere insulated from the ground.The outside of the sphere is then grounded as shown.Then the ground wire is removed.A is the inner surface and B is the outer surface.Which statement is correct?

A)The charge on A is −q;that on B is +q.
B)The charge on B is −q;that on A is +q.
C)The charge is on A and on B.
D)There is no charge on either A or B.
E)The charge on A is −q;there is no charge on B.

Question 59

Two concentric imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge −Q located at the center of the surfaces.When compared to the electric flux Φ₁ through the surface of radius R,the electric flux Φ₂ through the surface of radius 2R is

A) .
B) .
C)Φ₂ = Φ₁.
D)Φ₂ = 2Φ₁.
E)Φ₂ = 4Φ₁.

Question 60

A positive point charge q is placed off center inside an uncharged metal sphere insulated from the ground as shown.Where is the induced charge density greatest in magnitude and what is its sign?

A)A;negative.
B)A;positive.
C)B;negative.
D)B;positive.
E)C;negative.

Question 61

A uniform electric field
Is present in the region between infinite parallel plane plates A and B and a uniform electric field
Is present in the region between infinite parallel plane plates B and C.When the plates are vertical,
Is directed to the right and
To the left.The signs of the charges on plates A,B and C may be

A)−,−,−.
B)+,−,−.
C)+,−,+.
D)+,+,+.
E)any one of the above.

Question 62

Two planes of charge with no thickness,A and B,are parallel and vertical.The electric field in region I to the left of plane A has magnitude
And points to the left.The electric field in the region to the right of B has magnitude
And points to the right.The electric field in the region between the two planes has magnitude
And points to the right.The surface charge density on planes A and B respectively is

A) ,σ.
B) ,σ.
C)σ, .
D)σ, .
E)2σ,σ.

Question 63

At the point of fission,a nucleus of U-238,with 92 protons is divided into two smaller spheres each with 46 protons and a radius of 5.9 × 10−¹⁵ m.What is the repulsive force pushing the two spheres apart when they are just touching one another? (The mass of the U-238 nucleus is 3.98 × 10−²⁵ kg. )

Question 64

A constant electric field
Is present throughout a region of space that includes the plane bounded by the y and z axes and the lines y = 50 cm and z = 50 cm.The electric flux through the plane's surface,in N ⋅ m²/C,is

A)0.
B)0.25.
C)25.
D)50.
E)100.

Question 65

A student has made the statement that the electric flux through one half of a Gaussian surface is always equal and opposite to the flux through the other half of the Gaussian surface.This is

A)never true.
B)never false.
C)true whenever enclosed charge is symmetrically located at a center point,or on a center line or centrally placed plane.
D)true whenever no charge is enclosed within the Gaussian surface.
E)true only when no charge is enclosed within the Gaussian surface.

Question 66

The nucleus of a hydrogen atom,a proton,sets up an electric field.The distance between the proton and electron is about 5.1 × 10−¹¹ m.What is the magnitude of the electric field at this distance from the proton? [The charge on the proton is +1.6 × 10−¹⁹ C.]

Question 67

Two planes of charge with no thickness,A and B,are parallel and vertical.The electric field in the region between the two planes has magnitude
)The electric field in the region to the left of A and the electric field in the region to the right of B may have the magnitudes

A)0,0.
B) , .
C) , .
D)given in any answer above.
E)given only in answer (a)or (b)above.

Question 68

Whitney says that Gauss's Law can be used to find the electric field of a sufficiently symmetrical distribution of charge as long as
Over the whole Gaussian surface.Algie says that the electric field must be a constant vector over the entire Gaussian surface.Which one,if either,is correct?

A)Whitney,because that means no charge is enclosed within the Gaussian surface.
B)Algie,because a constant electric field means that .
C)Both,because the conditions in (a)and (b)are equivalent.
D)Neither,because the electric field can be found from Gauss's law only if holds only over a portion of the Gaussian surface.
E)Neither,because the charge distribution must be symmetric if anywhere on the surface.

Question 69

An constant electric field,
N/C,goes through a surface with area
M².(This surface can also be expressed as an area of 10 m² with the direction of the unit vector (
))What is the magnitude of the electric flux through this area?

A)24 N ⋅ m²/C
B)48 N ⋅ m²/C
C)0.24 N ⋅ m²/C
D)0.48 N ⋅ m²/C
E)0

Question 70

A point charge is located at the origin.Centered along the x axis is a cylindrical closed surface of radius 10 cm with one end surface located at x = 2 m and the other end surface located at x = 4 m.If the magnitude of the electric flux through the surface at x = 2 m is 4 N ⋅ m²/C,what is the magnitude of the electric flux through the surface at x = 4 m?

A)1 N ⋅ m²/C
B)2 N ⋅ m²/C
C)4 N ⋅ m²/C
D)16 N ⋅ m²/C
E)The correct value is not given.

Question 71

A Geiger counter is like an electroscope that discharges whenever ions formed by a radioactive particle produce a conducting path.A typical Geiger counter consists of a thin conducting wire of radius 0.002 cm stretched along the axis of a conducting cylinder of radius 2.0 cm.The wire and the cylinder carry equal and opposites charges of 8.0 × 10−¹⁰ C all along their length of 10.0 cm.What is the magnitude of the electric field at the surface of the wire?

Question 72

If we define the gravitational field
,where
Is a unit radial vector,then Gauss's Law for gravity is

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

Question 73

Three infinite planes of charge,A,B and C,are vertical and parallel to one another.There is a uniform electric field
To the left of plane A and a uniform electric field
To the right of plane C.The field
Points to the left and the field
Points to the right.The signs of the charges on plates A,B and C may be

A)−,−,−.
B)+,−,−.
C)+,−,+.
D)+,+,+.
E)any one of the above.

Question 74

You are told that
Summed over both the surface areas of sphere A and sphere B below totals to
)You can conclude that

A)Sphere A contains charge q_in = −Q.
B)Sphere B contains charge q_in = −Q.
C)Sphere B contains charge q_in = +Q.
D)Each sphere contains charge .
E)The sum of the charges contained in both spheres is −Q.

Question 75

A uniform electric field
Is present in the region between the infinite parallel planes of charge A and B,and a uniform electric field
Is present in the region between the infinite parallel planes of charge B and C.When the planes are vertical and the fields are both non-zero,

A) and are both directed to the right.
B) and are both directed to the left.
C) points to the right and to the left.
D) points to the left and to the right.
E)Any one of the above is possible.

Question 76

The nucleus of lead-208,
,has 82 protons within a sphere of radius 6.34 × 10−¹⁵.Each electric charge has a value of 1.60 × 10−¹⁹ C.Assuming that the protons create a spherically symmetric distribution of charge,calculate the electric field at the surface of the nucleus.

Question 77

A spaceship encounters a single plane of charged particles,with the charge per unit area equal to σ.The electric field a short distance above the plane has magnitude ____ and is directed ____ to the plane.

A) ,parallel
B) ,perpendicular
C) ,parallel
D) ,perpendicular
E) ,parallel

Question 78

A student has made the statement that the electric flux through one half of a Gaussian surface is always equal to the flux through the other half of the Gaussian surface.This is

A)never true.
B)never false.
C)true whenever enclosed charge is symmetrically located at a center point,on a center line,or on a centrally placed plane.
D)true whenever no charge is enclosed within the Gaussian surface.
E)true only when no charge is enclosed within the Gaussian surface.

Question 79

A beam of electrons moves at velocity
)The number of particles per unit volume in the beam of area A is ρ.If we imagine a cylindrical Gaussian surface of radius r and length
Centered on the beam,the electron flux through the surface is

A)0.
B)ρv_fA.
C)2ρv_fA.
D)ρv_f(A+2πr ).
E)2ρv_f(A+πr ).

Question 80

Gino says that the analog of Gauss's law for the flow of an incompressible fluid of density ρ at constant velocity
Is
For an imaginary surface within the fluid.Lorenzo says that it is true only if the area where the fluid enters the surface and the area where it leaves the surface are both perpendicular to the velocity of the fluid.Which one,if either,is correct?

A)Gino,because as much fluid leaves as enters.
B)Lorenzo,because is not equal to zero if the fluid enters or exits at angles other than 90°.
C)Lorenzo,because this is true only when the fluid executes rotational motion.
D)Gino,because it is true only when the fluid is enclosed on all sides,not when it is flowing.
E)Lorenzo,because it is true only when the fluid is enclosed on all sides,not when it is flowing.