Exam 27: Gausss Law

28) A hollow conducting spherical shell has radii of 0.80 m and 1.20 m, as shown in the figure. The sphere carries an excess charge of -500 nC. A point charge of +300 nC is present at the center. The surface charge density on the inner spherical surface is closest to

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 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 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?

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)

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.)

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.

A hollow conducting spherical shell has radii of 0.80 m and 1.20 m, as shown in the figure. The sphere carries a net excess charge of -500 nC. A point charge of +300 nC is present at the center. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C) The radial component of the electric field at a point that is 1.50 m from the center is closest to

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 figure shows four Gaussian surfaces surrounding a distribtuion 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 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)

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 hollow conducting spherical shell has radii of 0.80 m and 1.20 m, as shown in the figure. The sphere carries a net excess charge of -500 nC. A point charge of +300 nC is present at the center. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C) The radial component of the electric field at a point that is 0.60 m from the center is closest to

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?

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?

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)

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)

A neutral hollow spherical conducting shell of inner radius 1.00 cm and outer radius 3.00 cm has a +2.00-µC point charge placed at its center. Find the surface charge density (a) on the inner surface of the shell. (b) on the outer surface of the shell.

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