Exam 21: Gausss Law

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?

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

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?

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

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

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) î. 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)

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)

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 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 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.)

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)

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)

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 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

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

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

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.

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 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?

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