Question 1

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

(a)b 
(b)c

Question 2

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)

Accepted Answer

The electric field between parallel plates is given by E = σ/ε₀, where σ is the surface charge density. The charge transferred is q = n * e, where n is the number of electrons. The area A of the disks is related to σ by σ = q/A. Solving for A and using the relation A = π(d/2)², we find the diameter d.

Question 3

The graph in the figure shows the electric field strength (not the field lines)as a function of distance from the center for a pair of concentric uniformly charged spheres.Which of the following situations could the graph plausibly represent? (There may be more than one correct choice.)

Accepted Answer

,D

Question 4

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

Accepted Answer

,E

Question 5

If the electric flux through a closed surface is zero,the electric field at points on that surface must be zero.

Accepted Answer

The electric flux through a closed surface being zero does not necessarily mean that the electric field at points on the surface is zero. It may be possible that the electric field is non-zero inside the closed surface, but the flux due to the field lines entering the surface is equal to the flux due to the field lines leaving the surface. This leads to net zero flux but not necessarily zero electric field.

Question 6

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

The answer of An electric field is set up between...

Question 7

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?

Accepted Answer

The angle of rotation is 60° because when the flux is halved, it implies that the cosine of the angle between the field direction and the normal to the area is 0.5 (since flux = EAcosθ, where E is the electric field strength, A is the area, and θ is the angle). Cosine of 60° is 0.5, indicating the area has been rotated by 60° from its initial position to reach this state.

Question 8

The cube of insulating material shown in the figure has one corner at the origin.Each side of the cube has length 0.080 m so the top face of the cube is parallel to the xz-plane and is at y = 0.080 m.It is observed that there is an electric field that is in the +y direction and whose magnitude depends only on y.Use Gauss's law to calculate the net charge enclosed by the cube. (ε₀ = 8.85 × 10^-12 C²/N • m²)

Accepted Answer

The answer of The cube of insulating material shown in...

Question 9

At a distance D from a very long (essentially infinite)uniform line of charge,the electric field strength is 1000 N/C.At what distance from the line will the field strength to be 2000 N/C?

Accepted Answer

The answer of At a distance D from a very...

Question 10

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

The electric field between two parallel plates with equal but opposite charge is uniform. This means the force experienced by a point charge in this field does not depend on its position between the plates. Therefore, even when the charge is moved closer to one of the sheets, the force it feels remains F.

Question 11

A nonuniform electric field is directed along the x-axis at all points in space.This magnitude of the field varies with x,but not with respect to y or z.The axis of a cylindrical surface,0.80 m long and 0.20 m in diameter,is aligned parallel to the x-axis,as shown in the figure.The electric fields E₁ and E₂,at the ends of the cylindrical surface,have magnitudes of 6000 N/C and 1000 N/C respectively,and are directed as shown.What is the net electric flux passing through the cylindrical surface?

Accepted Answer

The answer of A nonuniform electric field is directed along...

Question 12

Two long straight parallel lines,#1 and #2,carry uniform positive linear charge densities.The charge density on line #2 is twice as great as the charge density on line #1.The locus of points where the electric field due to these lines is zero is

Accepted Answer

The electric field is zero at a point where the electric fields due to both lines cancel each other out. Since line #2 has a greater charge density, the point where the electric fields cancel out must be closer to line #1, as the electric field strength is inversely proportional to the distance from the charge source.

Question 13

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

The answer of A charge Q is uniformly spread over...

Question 14

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

When an external charge is placed inside an uncharged hollow conductor, the charges in the conductor will move and redistribute in such a way that the electric field inside the conductor is zero everywhere. This means that the charges on the inner surface of the conductor will rearrange themselves in such a way that they cancel out the electric field of the +10 µC charge inside. The charges on the outer surface of the conductor will then distribute themselves in such a way as to maintain a zero electric field everywhere outside the conductor. This can only happen if the outer surface of the conductor contains +10 µC of charge and the inner surface contains -10 µC of charge. Therefore, the correct statement is D.

Question 15

Two very large,flat plates are parallel to each other. Plate A,located at y = 1.0 cm,is along the xz-plane and carries a uniform surface charge density -1.00 μC/m². Plate B is located at y = -1.0 cm and carries a uniform surface charge density +2.00 μC/m².What is the electric field vector at the point having x,y,z coordinates (-0.50 cm,0.00 cm,0.00 cm)? (ε₀ = 8.85 × 10^-12 C²/N • m²)

Accepted Answer

The answer of Two very large,flat plates are parallel to...

Question 16

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

Using the formula for electric field strength between parallel plates, 
E = (Q/εA), 
where Q is the charge on each electrode, ε is the permittivity of free space, and A is the area of each electrode. 
Rearranging the equation, 
Q = EεA 
The area is given by (4.0 cm x 4.0 cm)/2 = 8.0 cm^2 = 8.0 x 10^(-4) m^2 
Plugging in the values, 
Q = (2.5 x 10^16 N/C)(8.85 x 10^-12 C^2/N m^2)(8.0 x 10^(-4) m^2) = 35 x 10^(-9) C = 35 nC 
Therefore, the magnitude of the charge on each electrode is 35 nC.

Question 17

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

The flux through a Gaussian surface depends only on the total charge enclosed by the surface, not on the charge's location within the surface. This is a direct consequence of Gauss's law.

Question 18

Two large,flat,horizontally oriented plates are parallel to each other,a distance d apart.Half way between the two plates the electric field has magnitude E.If the separation of the plates is reduced to d/2 what is the magnitude of the electric field half way between the plates?

Accepted Answer

The electric field between two parallel plates is given by $E = \frac{\sigma}{\varepsilon_0}$, where $\sigma$ is the surface charge density and $\varepsilon_0$ is the permittivity of free space. This formula shows that the electric field is independent of the distance between the plates, so halving the distance does not change the magnitude of the electric field.

Question 19

A cone is resting on a tabletop as shown in the figure with its face horizontal.A uniform electric field of magnitude 4550 N/C points vertically upward.How much electric flux passes through the sloping side surface area of the cone?

Accepted Answer

The answer of A cone is resting on a tabletop...

Question 20

Under electrostatic conditions,the electric field just outside the surface of any charged conductor

Accepted Answer

The electric field just outside the surface of any charged conductor is always perpendicular to the surface of the conductor. This is because if it were not perpendicular, there would be a component of the field that is tangent to the surface, and this would result in a continual flow of charge along the surface until the tangential component of the field became zero. However, in electrostatic conditions, there is no flow of charge, so the electric field must be perpendicular to the surface to avoid this scenario.

Quiz 24: Gausss Law

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?

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 graph in the figure shows the electric field strength (not the field lines) as a function of distance from the center for a pair of concentric uniformly charged spheres.Which of the following situations could the graph plausibly represent? (There may be more than one correct choice.)

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

If the electric flux through a closed surface is zero,the electric field at points on that surface must be zero.

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?

At a distance D from a very long (essentially infinite) uniform line of charge,the electric field strength is 1000 N/C.At what distance from the line will the field strength to be 2000 N/C?

Two long straight parallel lines,#1 and #2,carry uniform positive linear charge densities.The charge density on line #2 is twice as great as the charge density on line #1.The locus of points where the electric field due to these lines is zero is

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.)

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

Two large,flat,horizontally oriented plates are parallel to each other,a distance d apart.Half way between the two plates the electric field has magnitude E.If the separation of the plates is reduced to d/2 what is the magnitude of the electric field half way between the plates?

A cone is resting on a tabletop as shown in the figure with its face horizontal.A uniform electric field of magnitude 4550 N/C points vertically upward.How much electric flux passes through the sloping side surface area of the cone?

Under electrostatic conditions,the electric field just outside the surface of any charged conductor

Quiz 24: Gausss Law

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?

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 graph in the figure shows the electric field strength (not the field lines) as a function of distance from the center for a pair of concentric uniformly charged spheres.Which of the following situations could the graph plausibly represent? (There may be more than one correct choice.)

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

If the electric flux through a closed surface is zero,the electric field at points on that surface must be zero.

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?

At a distance D from a very long (essentially infinite) uniform line of charge,the electric field strength is 1000 N/C.At what distance from the line will the field strength to be 2000 N/C?

Two long straight parallel lines,#1 and #2,carry uniform positive linear charge densities.The charge density on line #2 is twice as great as the charge density on line #1.The locus of points where the electric field due to these lines is zero is

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.)

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

Two large,flat,horizontally oriented plates are parallel to each other,a distance d apart.Half way between the two plates the electric field has magnitude E.If the separation of the plates is reduced to d/2 what is the magnitude of the electric field half way between the plates?

A cone is resting on a tabletop as shown in the figure with its face horizontal.A uniform electric field of magnitude 4550 N/C points vertically upward.How much electric flux passes through the sloping side surface area of the cone?

Under electrostatic conditions,the electric field just outside the surface of any charged conductor

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?

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)