Question 1

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

Accepted Answer

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

Question 2

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.

Accepted Answer

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

Question 3

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.

Accepted Answer

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

Question 4

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,

Accepted Answer

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. 
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 5

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?

Accepted Answer

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

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.

Accepted Answer

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 
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

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?

Accepted Answer

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 
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 8

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?

Accepted Answer

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 
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 9

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

Accepted Answer

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

Question 10

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?

Accepted Answer

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. 
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 11

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?

Accepted Answer

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 
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 12

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

Accepted Answer

A) 0. 
B) −σ/2. 
C) +σ/2. 
D) −σ. 
E) +σ. 
A) 0. 
B) −σ/2. 
C) +σ/2. 
D) −σ. 
E) +σ.

Question 13

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?

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

A) 0. 
B) ρvfA. 
C) 2ρvfA. 
D) ρvf(A+2πr   ). 
E) 2ρvf(A+πr   ). 
A) 0. 
B) ρvfA. 
C) 2ρvfA. 
D) ρvf(A+2πr   ). 
E) 2ρvf(A+πr   ).

Question 16

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

Accepted Answer

A)    ,σ. 
B)    ,σ. 
C) σ,   . 
D) σ,   . 
E) 2σ,σ. 
A)    ,σ. 
B)    ,σ. 
C) σ,   . 
D) σ,   . 
E) 2σ,σ.

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

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?

Accepted Answer

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. 
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 20

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?

Accepted Answer

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

Exam 24: Gausss Law

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 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.

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 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,

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?

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.

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 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 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 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?

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

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 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 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

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

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

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?

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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.

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?

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 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?

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 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

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