Exam 18: Thermal Properties of Matter

Lines of charge: The cross section of a long coaxial cable is shown in the figure, with radii as given. The linear charge density on the inner conductor is and the linear charge density on the outer conductor is The inner and outer cylindrical surfaces are respectively denoted by A, B, C, and D, as shown. The magnitude of the electric field at a point that is from the axis is closest to

Lines of charge: An infinitely long nonconducting cylinder of radius R = 2.00 cm carries a uniform volume charge density of 180 μC/m³. Calculate the electric field at distance r = 1.00 cm from the axis of the cylinder. (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Gauss's law: 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)

Gauss's law: 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

Spheres of charge: 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?

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

Flux: 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?

Spheres of charge: A non-conducting sphere of radius R = 7.0 cm carries a charge Q = 4.0 mC distributed uniformly throughout its volume. At what distance, measured from the center of the sphere, does the electric field reach a value equal to half its maximum value?

Charge on conductors: 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

Flux: 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?

Sheets of charge: A very large sheet of a conductor carries a uniform charge density of 4.00 pC/mm² on its surfaces. What is the electric field strength 3.00 mm outside the surface of the conductor? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

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

Gauss's law: 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)

Gauss's 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?

Spheres of charge: 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?

Gauss's law: 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

Sheets of charge: 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?

Charge on conductors: 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.

Charge on conductors: 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

Flux: 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?