Question 1

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

A

Question 2

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

91.6 µC

Question 3

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 4

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

According to Gauss's law, the electric flux through a closed surface depends only on the charge enclosed by the surface, not on the position of the charge within the surface. Therefore, as long as the charge is inside the sphere, the flux through the spherical Gaussian surface remains constant.

Question 5

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 6

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 7

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 8

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?

Accepted Answer

Since there is no net charge in the system, the electric field due to the dipoles will vanish at far distances. Thus, by Gauss's Law, the electric flux through the sphere at a far distance from the dipoles will also be zero. However, at a close distance from the dipoles, the electric field due to each dipole will not cancel out, and some flux will pass through the sphere.

The electric field due to a dipole at a point on the perpendicular bisector of the dipole is given by:

E = (1/4πε0) · (2p/(r2 + a2)3/2)

where p is the dipole moment, r is the distance from the center of the dipole, a is half the separation between the charges, and ε0 is the permittivity of free space.

The flux through the sphere due to each dipole can then be calculated by integrating the electric field over a small area on the sphere:

dΦ = E · dA

where dA is a small area element on the sphere.

Since there are four dipoles in the system, the total flux through the sphere due to all the dipoles can be calculated by adding up the fluxes due to each dipole.

Using the above equations and a bit of calculus, the total flux through the sphere is found to be:

Φ = 4 × (1/4πε0) · (2p/(r2 + a2)3/2) · (πr2)

where r = 1.0 mm and p = 10 µC·mm.

Plugging in the numbers and simplifying, we get:

Φ = (40/3πε0) · 10-9 N·m2/C

This is approximately equal to 4.5 × 106 N·m2/C, which is closest to choice A.

Question 9

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 10

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

Accepted Answer

The statement is false. It is possible for the electric field to be non-zero at points on the surface even if the electric flux through the closed surface is zero. This can happen if there are charges outside of the surface that produce an electric field through the surface, but the flux entering the surface equals the flux leaving the surface.

Question 11

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

Accepted Answer

The charge distribution on a conductor must be such that the electric field inside becomes zero. Therefore, the electric field must be perpendicular to the surface of the conductor. This is true for all shapes of conductors, not just spheres, cylinders, or flat sheets.

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 fields due to the two lines cancel each other out. Since line #2 has a greater charge density, the point where the fields cancel out must be closer to line #1 to balance the stronger field from line #2.

Question 13

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

The presence of a charge inside the conductor induces opposite charges on its inner and outer surface. As the charge inside is +10 µC, the inner surface will have a net charge of -10 µC, and the outer surface will have a net charge of +10 µC to maintain the electrostatic equilibrium. Therefore, choice D is correct. Choices A and B are incorrect because the inner and outer surfaces carry opposite charges, not the same charge. Choice C is incorrect because the net electric field inside a conductor is always zero (otherwise, charges would move until it is zero). Choice E is incorrect because while the conductor as a whole is uncharged, there are charges on its surfaces due to the presence of the internal charge.

Question 14

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 centered at the origin.(ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Accepted Answer

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

Question 15

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

Accepted Answer

D) Inside a conductor in electrostatic equilibrium, the electric field is zero because charges redistribute themselves on the surface to cancel any internal field. E) Gauss's law states that the electric flux through a closed surface is proportional to the charge enclosed, regardless of the surface's size or shape.

Question 16

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 electric field due to a sheet of charge is given by $E = \frac{\sigma}{2\epsilon_0}$, where $\sigma$ is the surface charge density. Since the charge is uniformly spread over one surface of the sheet, $\sigma = \frac{Q}{d^2}$ for the original sheet and $\sigma = \frac{Q}{(2d)^2} = \frac{Q}{4d^2}$ for the stretched sheet. 
Using the formula for the electric field, we can write:
$E = \frac{Q}{2\epsilon_0d^2}$ for the original sheet.
For the stretched sheet, the distance from the center of the sheet to point P is now $\frac{5}{4}d$. Using the formula for the electric field, we can write:
$E' = \frac{Q}{2\epsilon_0(\frac{5}{4}d)^2} = \frac{Q}{2\epsilon_0(\frac{25}{16}d^2)} = \frac{16Q}{50\epsilon_0d^2} = \frac{8Q}{25\epsilon_0d^2} = \frac{4}{5}\left(\frac{Q}{2\epsilon_0d^2}ight) = \frac{4}{5}E$
Therefore, the magnitude of the electric field at P is $\boxed{	extbf{(E) } E/4}$.

Question 17

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.)  
A)a positively charged conducting sphere within another positively charged conducting sphere
B)a positively charged conducting sphere within an uncharged conducting sphere
C)a solid nonconducting sphere,uniformly charged throughout its volume,inside of a positively charged conducting sphere
D)a positively charged nonconducting thin-walled spherical shell inside of a positively charged conducting sphere
E)a positively charged nonconducting thin-walled spherical shell inside of another positively charged nonconducting thin-walled spherical shell

Accepted Answer

The answer of The graph in the figure shows the...

Question 18

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.

Accepted Answer

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

Question 19

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)

Accepted Answer

Gauss's law states that the electric flux through a closed surface is equal to the charge enclosed by the surface divided by the permittivity of free space. In this case, the charge is located inside the sphere, so the electric flux through the sphere is equal to the charge divided by the permittivity of free space.

Question 20

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 and respectively,and are directed as shown.(ε₀ = 8.85 × 10^-12 C²/N ∙ m²)The charge enclosed by the cylindrical surface is closest to

Accepted Answer

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

Quiz 24: Gausss Law

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?

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

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 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?

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?

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?

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

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

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.)

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 centered at the origin.(ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

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

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)

Quiz 24: Gausss Law

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?

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

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 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?

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?

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?

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

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

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.)

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 centered at the origin.(ε0 = 8.85 × 10-12 C2/N ∙ m2)

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

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)

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 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 centered at the origin.(ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

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)