Question 1

As shown in the figure,a square insulating slab 5.0 mm thick measuring 2.0 m × 2.0 m has a charge of 8.0 × 10-11 C distributed uniformly throughout its volume.Use Gauss's law to determine the electric field at point P,which is located within the slab beneath its center,1.0 mm from one of the faces.
(ε0 = 8.85 × 10-12 C2/N • m2)

Accepted Answer

A)  0.68 N/C 
B)  14 N/C 
C)  23 N/C 
D)  34 N/C 
E)  57 N/C

Question 2

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 the volume of the shell.What is the magnitude of the electric field at a distance r = 12 cm from the center of the shell? (k = 1/4πε0 = 8.99 × 109 N • m2/C2)

Accepted Answer

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

Question 3

Two concentric conducting spherical shells produce a radially outward electric field of magnitude 49,000 N/C at a point 4.10 m from the center of the shells.The outer surface of the larger shell has a radius of 3.75 m.If the inner shell contains an excess charge of -5.30 μC,find the amount of charge on the outer surface of the larger shell.(k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Accepted Answer

The answer of Two concentric conducting spherical shells produce a...

Question 4

A nonconducting spherical shell of inner radius R₁ and outer radius R₂ contains a uniform volume charge density ρ throughout the shell.Use Gauss's law to derive an equation for the magnitude of the electric field at the following radial distances r from the center of the sphere.Your answers should be in terms of ρ,R₁,R₂,r,ε₀,and π. (a)r < R₁ (b)R₁ < r < R₂ (c)r > R₂

Accepted Answer

The answer of A nonconducting spherical shell of inner radius...

Question 5

Charge is distributed uniformly throughout a large insulating cylinder of radius R.The charge per unit length in the cylindrical volume is λ. (a)Use Gauss's law to find the magnitude of the electric field at a distance r from the central axis of the cylinder for r < R.Your answer should be in terms of r,R,λ,ε₀,and π. (b)Check the reasonableness of your answer by evaluating it at the surface of the cylinder.

Accepted Answer

The answer of Charge is distributed uniformly throughout a large...

Question 6

Two very large parallel sheets a distance d apart have their centers directly opposite each other.The sheets carry equal but opposite uniform surface charge densities.A point charge that is placed near the middle of the sheets a distance d/2 from each of them feels an electrical force F due to the sheets.If this charge is now moved closer to one of the sheets so that it is a distance d/4 from that sheet,what force will feel?

Accepted Answer

A)  4F 
B)  2F 
C)  F 
D)  F/2 
E)  F/4

Question 7

Which of the following statements about Gauss's law are correct? (There may be more than one correct choice.)

Accepted Answer

A)  Gauss's law is valid only for symmetric charge distributions, such as spheres and cylinders. 
B)  If there is no charge inside of a Gaussian surface, the electric field must be zero at points of that surface. 
C)  Only charge enclosed within a Gaussian surface can produce an electric field at points on that surface. 
D)  If a Gaussian surface is completely inside an electrostatic conductor, the electric field must always be zero at all points on that surface. 
E)  The electric flux passing through a Gaussian surface depends only on the amount of charge inside that surface, not on its size or shape.

Question 8

An uncharged conductor has a hollow cavity inside of it.Within this cavity there is a charge of +10 µC that does not touch the conductor.There are no other charges in the vicinity.Which statement about this conductor is true? (There may be more than one correct choice.)

Accepted Answer

A)  The inner surface of the conductor carries a charge of -10 µC and its outer surface carries no excess charge. 
B)  The inner and outer surfaces of the conductor each contain charges of -5 µC. 
C)  The net electric field within the material of the conductor points away from the +10 µC charge. 
D)  The outer surface of the conductor contains +10 µC of charge and the inner surface contains -10 µC. 
E)  Both surfaces of the conductor carry no excess charge because the conductor is uncharged.

Question 9

A huge (essentially infinite)horizontal nonconducting sheet 10.0 cm thick has charge uniformly spread over both faces.The upper face carries +95.0 nC/m2 while the lower face carries -25.0 nC/ m2.What is the magnitude of the electric field at a point within the sheet 2.00 cm below the upper face?
(ε0 = 8.85 × 10-12 C2/N • m2)

Accepted Answer

A)  0.00 N/C 
B)  3.95 × 103 N/C 
C)  6.78 × 103 N/C 
D)  7.91 × 103 N/C 
E)  1.36 × 104 N/C

Question 10

A charge Q is uniformly spread over one surface of a very large nonconducting square elastic sheet having sides of length d.At a point P that is 1.25 cm outside the sheet,the magnitude of the electric field due to the sheet is E.If the sheet is now stretched so that its sides have length 2d,what is the magnitude of the electric field at P?

Accepted Answer

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

Question 11

An electric field is set up between two parallel plates,each of area 2.0 m2,by putting 1.0 μC of charge on one plate and -1.0 μC of charge on the other.The plates are separated by 4.0 mm with their centers opposite each other,and the charges are distributed uniformly over the surface of the plates.What is the magnitude of the electric field between the plates at a distance of 1.0 mm from the positive plate,but not near the edges of the plates? (ε0 = 8.85 × 10-12 C2/N • m2)

Accepted Answer

A)  4.2 × 104 N/C 
B)  1.4 × 104 N/C 
C)  3.1 × 104 N/C 
D)  0.00 N/C 
E)  5.6 × 104 N/C

Question 12

An infinitely long nonconducting cylinder of radius R = 2.00 cm carries a uniform volume charge density of 18.0 µC/m3. Calculate the electric field at distance r = 1.00 cm from the axis of the cylinder. (ε0 = 8.85 × 10-12 C2/N • m2)

Accepted Answer

A)  2.50 × 103 N/C 
B)  5.10 × 103 N/C 
C)  zero 
D)  2.00 × 103 N/C 
E)  10.2 × 103 N/C

Question 13

Two concentric spheres are shown in the figure.The inner sphere is a solid nonconductor and carries a charge of +5.00 µC uniformly distributed over its outer surface.The outer sphere is a conducting shell that carries a net charge of -8.00 µC.No other charges are present.The radii shown in the figure have the values R₁ = 10.0 cm,R₂ = 20.0 cm,and R₃ = 30.0 cm.(k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²) (a)Find the total excess charge on the inner and outer surfaces of the conducting sphere. (b)Find the magnitude and direction of the electric field at the following distances r from the center of the inner sphere: (i)r = 9.5 cm,(ii)r = 15.0 cm,(iii)r = 27.0 cm,(iv)r = 35.0 cm.

Accepted Answer

The answer of Two concentric spheres are shown in the...

Question 14

Two flat 4.0 cm × 4.0 cm electrodes carrying equal but opposite charges are spaced 2.0 mm apart with their midpoints opposite each other.Between the electrodes but not near their edges,the electric field strength is 2.5 × 106 N/C.What is the magnitude of the charge on each electrode?
(ε0 = 8.85 × 10-12 C2/N • m2)

Accepted Answer

A)  35 nC 
B)  18 nC 
C)  16 nC 
D)  30 nC

Question 15

The electric field strength in the space between two closely spaced parallel disks is 1.0 × 105 N/C.This field is the result of transferring 3.9 × 109 electrons from one disk to the other.What is the diameter of the disks? (e = 1.60 × 10-19 C,ε0 = 8.85 × 10-12 C2/N • m2)

Accepted Answer

A)  3.0 cm 
B)  1.5 cm 
C)  4.5 cm 
D)  6.0 cm

Question 16

The figure shows four Gaussian surfaces surrounding a distribution of charges. (a)Which Gaussian surfaces have an electric flux of +q/ε₀ through them? (b)Which Gaussian surfaces have no electric flux through them?

Accepted Answer

The answer of The figure shows four Gaussian surfaces surrounding...

Question 17

A non-conducting sphere of radius R = 7.0 cm carries a charge Q = 4.0 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?

Accepted Answer

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 18

A solid nonconducting sphere of radius R carries a uniform charge density throughout its volume.At a radial distance r1 = R/4 from the center,the electric field has a magnitude E0. What is the magnitude of the electric field at a radial distance r2 = 2R?

Accepted Answer

A)  E0/4 
B)  zero 
C)  E0/2 
D)  E0 
E)  2E0

Question 19

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

Accepted Answer

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 charge can be located anywhere, since flux does not depend on the position of the charge as long as it is inside the sphere.

Question 20

Electric charge is uniformly distributed inside a nonconducting sphere of radius 0.30 m.The electric field at a point P,which is 0.50 m from the center of the sphere,is 15,000 N/C and is directed radially outward.At what distance from the center of the sphere does the electric field have the same magnitude as it has at P?

Accepted Answer

A)  0.11 m 
B)  0.13 m 
C)  0.15 m 
D)  0.17 m 
E)  at no other point

Exam 24: Gausss Law

Which of the following statements about Gauss's law are correct? (There may be more than one correct choice.)

An uncharged conductor has a hollow cavity inside of it.Within this cavity there is a charge of +10 µC that does not touch the conductor.There are no other charges in the vicinity.Which statement about this conductor is true? (There may be more than one correct choice.)

An infinitely long nonconducting cylinder of radius R = 2.00 cm carries a uniform volume charge density of 18.0 µC/m³. Calculate the electric field at distance r = 1.00 cm from the axis of the cylinder. (ε₀ = 8.85 × 10^-12 C²/N • m²)

The electric field strength in the space between two closely spaced parallel disks is 1.0 × 10⁵ N/C.This field is the result of transferring 3.9 × 10⁹ electrons from one disk to the other.What is the diameter of the disks? (e= 1.60 × 10^-19C,ε₀ = 8.85 × 10^-12 C²/N • m²)

The figure shows four Gaussian surfaces surrounding a distribution of charges. (a)Which Gaussian surfaces have an electric flux of +q/ε₀ through them? (b)Which Gaussian surfaces have no electric flux through them?

A non-conducting sphere of radius R = 7.0 cm carries a charge Q = 4.0 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 solid nonconducting sphere of radius R carries a uniform charge density throughout its volume.At a radial distance r₁ = R/4 from the center,the electric field has a magnitude E₀. What is the magnitude of the electric field at a radial distance r₂ = 2R?

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

Exam 24: Gausss Law

Which of the following statements about Gauss's law are correct? (There may be more than one correct choice.)

An uncharged conductor has a hollow cavity inside of it.Within this cavity there is a charge of +10 µC that does not touch the conductor.There are no other charges in the vicinity.Which statement about this conductor is true? (There may be more than one correct choice.)

An infinitely long nonconducting cylinder of radius R = 2.00 cm carries a uniform volume charge density of 18.0 µC/m3. Calculate the electric field at distance r = 1.00 cm from the axis of the cylinder. (ε0 = 8.85 × 10-12 C2/N • m2)

The electric field strength in the space between two closely spaced parallel disks is 1.0 × 105 N/C.This field is the result of transferring 3.9 × 109 electrons from one disk to the other.What is the diameter of the disks? (e = 1.60 × 10-19 C,ε0 = 8.85 × 10-12 C2/N • m2)

The figure shows four Gaussian surfaces surrounding a distribution of charges. (a)Which Gaussian surfaces have an electric flux of +q/ε0 through them? (b)Which Gaussian surfaces have no electric flux through them?

A non-conducting sphere of radius R = 7.0 cm carries a charge Q = 4.0 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 solid nonconducting sphere of radius R carries a uniform charge density throughout its volume.At a radial distance r1 = R/4 from the center,the electric field has a magnitude E0. What is the magnitude of the electric field at a radial distance r2 = 2R?

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

An infinitely long nonconducting cylinder of radius R = 2.00 cm carries a uniform volume charge density of 18.0 µC/m³. Calculate the electric field at distance r = 1.00 cm from the axis of the cylinder. (ε₀ = 8.85 × 10^-12 C²/N • m²)

The electric field strength in the space between two closely spaced parallel disks is 1.0 × 10⁵ N/C.This field is the result of transferring 3.9 × 10⁹ electrons from one disk to the other.What is the diameter of the disks? (e= 1.60 × 10^-19C,ε₀ = 8.85 × 10^-12 C²/N • m²)

The figure shows four Gaussian surfaces surrounding a distribution of charges. (a)Which Gaussian surfaces have an electric flux of +q/ε₀ through them? (b)Which Gaussian surfaces have no electric flux through them?

A solid nonconducting sphere of radius R carries a uniform charge density throughout its volume.At a radial distance r₁ = R/4 from the center,the electric field has a magnitude E₀. What is the magnitude of the electric field at a radial distance r₂ = 2R?