Exam 27: Gausss 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 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

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 -30 nC/m and the linear charge density on the outer conductor is -70 nC/m. The inner and outer cylindrical surfaces are respectively denoted by A, B, C, and D, as shown. The radial component of the electric field at a point that 34 mm from the axis is closest to

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)

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. What is the maximum magnitude of the electric field due to this sphere?

An irregular conductor carries a surface charge density of -6.75 µC/m² at and in the vicinity of a point P on the surface. An electron is released just above P outside the conductor. What are the magnitude and direction of its acceleration the instant after it is released? (ε₀ = 8.85 × 10^-12 C²/N ∙ m², e = 1.60 × 10^-19 C, ^m_el = 9.11 × 10^-31 kg)

A spherical, non-conducting shell of inner radius r₁= 10 cm and outer radius r₂ = 15 cm carries a total charge Q = 15 μC distributed uniformly throughout the volume of the shell. What is the magnitude of the electric field at a distance r = 12 cm from the center of the shell? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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?

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

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)

Charge is distributed uniformly throughout a large insulating cylinder of radius R. The charge per unit length in the cylindrical volume is λ. (a) Use Gauss's law to find the magnitude of the electric field at a distance r from the central axis of the cylinder for r < R. Your answer should be in terms of r, R, λ, ε₀ , and π. (b) Check the reasonableness of your answer by evaluating it at the surface of the cylinder.

A nonconducting spherical shell of inner radius R₁ and outer radius R₂ contains a uniform volume charge density ρ throughout the shell. Use Gauss's law to derive an equation for the magnitude of the electric field at the following radial distances r from the center of the sphere. Your answers should be in terms of ρ, R₁, R₂, r, ε₀ , and π. (a) r < R₁ (b) R₁ < r < R₂ (c) r > R₂

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

Consider two closely spaced and oppositely charged parallel metal plates. The plates are square with sides of length L and carry charges Q and -Q on their facing surfaces. What is the magnitude of the electric field in the region between the plates?

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

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 -40 nC/m and the linear charge density on the outer conductor is -50 nC/m. 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 94 mm from the axis is closest to

A solid nonconducting sphere of radius R carries a charge Q distributed uniformly throughout its volume. At a certain distance r₁ (r₁ < R) from the center of the sphere, the electric field has magnitude E. If the same charge Q were distributed uniformly throughout a sphere of radius 2R, the magnitude of the electric field at the same distance r₁ from the center would be equal to

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?

Two extremely large nonconducting horizontal sheets each carry uniform charge density on the surfaces facing each other. The upper sheet carries +5.00 µC/m². The electric field midway between the sheets is 4.25 × 10⁵ N/C pointing downward. What is the surface charge density on the lower sheet? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

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)

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