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 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

A

Question 2

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

Since the conductor is uncharged, it must have an equal but opposite amount of charge on both its inner and outer surfaces to neutralize the +10 µC charge within the cavity. Therefore, the inner surface of the conductor must carry a charge of -10 µC and the outer surface must carry +10 µC of charge. Choices A and E are incorrect because the outer surface must carry a charge to neutralize the charge within the cavity. Choice B is incorrect because the charges on the inner and outer surfaces would have to be equal if they were to be distributed uniformly, which is not necessarily the case. Choice C is incorrect because the net electric field within a conductor is always zero.

Question 3

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

Accepted Answer

Under electrostatic conditions, the electric field inside a conductor is zero. However, just outside the surface of the conductor, the electric field is perpendicular to the surface. This is because if the electric field were not perpendicular to the surface, there would be a component of the field parallel to the surface that would drive free charges in the conductor to move, which would result in a non-zero net electric field inside the conductor. Therefore, the electric field just outside the surface of any charged conductor is always perpendicular to the surface.

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?

Accepted Answer

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

Question 5

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 6

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 7

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

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

Question 8

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 9

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 10

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 11

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

Accepted Answer

The answer of Which of the following statements about Gauss's...

Question 12

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 13

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

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

Question 14

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 means that the net charge enclosed by the surface is zero. However, the electric field at points on the surface can still be non-zero due to external charges or fields.

Question 15

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 16

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

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

Question 17

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 18

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 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?

Accepted Answer

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

Question 20

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...

Quiz 24: Gausss Law