Question 1

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.)
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.

Accepted Answer

According to the principle of electrostatics, charges on a conductor always reside on its surface. Since the inner charge of +10 µC does not touch the conductor, it cannot influence the charge distribution on the inner or outer surface of the conductor. Thus, the outer surface of the conductor will have to carry charges that are equal and opposite to the inner charge to maintain electrical neutrality. Therefore, the outer surface of the conductor must have a charge of +10 µC and the inner surface must have an equal and opposite charge of -10 µC. This also means that the net electric field within the material of the conductor is zero, as charges only reside on its surface. Hence, the correct answer is D.

Question 2

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

Accepted Answer

The magnitude of the charge on each electrode can be found using the formula for the electric field between two parallel plates: $E = \frac{\sigma}{\epsilon_0}$, where $E$ is the electric field strength, $\sigma$ is the surface charge density ($\frac{Q}{A}$), and $\epsilon_0$ is the permittivity of free space. Rearranging for $Q$, we get $Q = E \cdot A \cdot \epsilon_0$. Substituting the given values, $E = 2.5 \times 10^6 \, \text{N/C}$, $A = 4.0 \, \text{cm} \times 4.0 \, \text{cm} = 16 \, \text{cm}^2 = 16 \times 10^{-4} \, \text{m}^2$, and $\epsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2/\text{N} \cdot \text{m}^2$, we find $Q = 2.5 \times 10^6 \times 16 \times 10^{-4} \times 8.85 \times 10^{-12} = 35.4 \times 10^{-9} \, \text{C} = 35 \, \text{nC}$.

Question 3

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) A) (+1.13 × 10⁵ N/C) B) (-2.83 × 10⁵ N/C) C) (+1.19 × 10⁵ N/C) D) (+1.69 × 10⁵ N/C) E) (-1.19 × 10⁵ N/C)

Accepted Answer

Using Gauss's law, we know that the electric field between two large parallel plates is given by: 
E = σ/ε0 
where σ is the surface charge density and ε0 is the vacuum permittivity. 
The electric field due to plate A is: 
EA = -σ/ε0 = (1.00 μC/m^2)/(8.85 × 10^-12 C^2/N·m^2) = -1.13 × 10^5 N/C 
The electric field due to plate B is: 
EB = σ/ε0 = (2.00 μC/m^2)/(8.85 × 10^-12 C^2/N·m^2) = 2.26 × 10^5 N/C 
The net electric field at the point (-0.50 cm,0.00 cm,0.00 cm) is the sum of EA and EB in the x-direction since the two plates are parallel to the xz-plane. 
ENet = EA + EB = (2.26 - 1.13) × 10^5 N/C = 1.13 × 10^5 N/C 
Therefore, the correct answer is A.

Question 4

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

Accepted Answer

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

Question 5

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 9000 N/C and 5000 N/C respectively,and are directed as shown.(ε₀ = 8.85 × 10^-12 C²/N • m²)The charge enclosed by the cylindrical surface is closest to A) -1.1 nC. B) 1.1 nC. C) -2.4 nC. D) -4.8 nC. E) 4.8 nC.

Accepted Answer

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

Question 6

A charge of 1.0 × 10^-6 μC is located inside a sphere,1.25 cm from its center.What is the electric flux through the sphere due to this charge? (ε₀ = 8.85 × 10^-12 C²/N • m²) A) 0.11 N • m²/C B) 8.9 N • m²/C C) 0.028π N • m²/C D) It cannot be determined without knowing the radius of the sphere.

Accepted Answer

The answer of A charge of 1.0 × 10^-6 μC...

Question 7

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
A) along a line between the lines closer to line #2 than line #1.
B) at a point midway between the lines.
C) along a line perpendicular to lines #1 and #2.
D) along a line between the lines closer to line #1 than line #2.

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 8

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) 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

Accepted Answer

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

Question 9

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 10

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

Accepted Answer

The answer of A solid nonconducting sphere of radius R...

Question 11

A charge q = 2.00 μC is placed at the origin in a region where there is already a uniform electric Field = (100 N/C) )Calculate the flux of the net electric field through a Gaussian sphere of radius R = 10.0 cm centered at the origin.(ε₀ = 8.85 × 10^-12 C²/N • m²) A) 5.52 × 10⁵ N • m²/C B) 1.13 × 10⁵N • m²/C C) 2.26 × 10⁵ N • m²/C D) zero

Accepted Answer

The answer of A charge q = 2.00 μC is...

Question 12

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

Accepted Answer

The answer of The electric field strength in the space...

Question 13

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 14

Four dipoles,each consisting of a +10-µC charge and a -10-µC charge,are located in the xy-plane with their centers 1.0 mm from the origin,as shown.A sphere passes through the dipoles,as shown in the figure.What is the electric flux through the sphere due to these dipoles? (ε₀ = 8.85 × 10^-12 C²/N • m²) A) 4.5 × 10⁶ N • m²/C B) 0.00 N • m²/C C) 9.0 × 10⁶ N • m²/C D) 11 × 10⁵ N • m²/C

Accepted Answer

The answer of Four dipoles,each consisting of a +10-µC charge...

Question 15

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

Accepted Answer

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

Question 16

Under electrostatic conditions,the electric field just outside the surface of any charged conductor
A) is always parallel to the surface.
B) is always zero because the electric field is zero inside conductors.
C) is always perpendicular to the surface of the conductor.
D) is perpendicular to the surface of the conductor only if it is a sphere, a cylinder, or a flat sheet.
E) can have nonzero components perpendicular to and parallel to the surface of the conductor.

Accepted Answer

Under electrostatic conditions, the electric field just outside the surface of any charged conductor is always perpendicular to the surface of the conductor. This is known as the "normal component" of the electric field. This is because any tangential component of the electric field would cause charges to move along the surface, which would not be in electrostatic equilibrium. Additionally, the electric field inside a conductor is always zero in electrostatic conditions, but that does not mean the electric field just outside the surface is also zero.

Question 17

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?
A) 45°
B) 26.6°
C) 90°
D) 30°
E) 60°

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 18

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 19

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? A) -160 N • m²/C B) -350 N • m²/C C) 0.00 N • m²/C D) +350 N • m²/C E) +160 N • m²/C

Accepted Answer

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

Question 20

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...

Quiz 1: A: Foundations

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.)

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?

A charge of 1.0 × 10^-6 μC is located inside a sphere,1.25 cm from its center.What is the electric flux through the sphere due to this charge? (ε₀ = 8.85 × 10^-12 C²/N • m²)

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

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?

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?

A charge q = 2.00 μC is placed at the origin in a region where there is already a uniform electric Field = (100 N/C) ) Calculate the flux of the net electric field through a Gaussian sphere of radius R = 10.0 cm centered at the origin.(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)

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

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?

Quiz 1: A: Foundations

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.)

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?

A charge of 1.0 × 10-6 μC is located inside a sphere,1.25 cm from its center.What is the electric flux through the sphere due to this charge? (ε0 = 8.85 × 10-12 C2/N • m2)

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

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?

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?

A charge q = 2.00 μC is placed at the origin in a region where there is already a uniform electric Field = (100 N/C) ) Calculate the flux of the net electric field through a Gaussian sphere of radius R = 10.0 cm centered at the origin.(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)

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

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?

A charge of 1.0 × 10^-6 μC is located inside a sphere,1.25 cm from its center.What is the electric flux through the sphere due to this charge? (ε₀ = 8.85 × 10^-12 C²/N • m²)

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?

A charge q = 2.00 μC is placed at the origin in a region where there is already a uniform electric Field = (100 N/C) ) Calculate the flux of the net electric field through a Gaussian sphere of radius R = 10.0 cm centered at the origin.(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)