Exam 22: Gausss Law

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 radial component of the electric field at a point that 34 mm from the axis is closest to

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

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 . (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 spherical,non-conducting shell of inner radius = 10 cm and outer radius = 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?

A huge (essentially infinite)horizontal nonconducting sheet 10.0 cm thick has charge uniformly spread over both faces.The upper face carries while the lower face carries .What is the magnitude of the electric field at a point within the sheet 2.00 cm below the upper face?

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?

Electric charge is uniformly distributed inside a nonconducting sphere of radius .The electric field at a point P,which is 0.50 m from the center of the sphere,is 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 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?

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.)

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. = The radial component of the electric field at a point that is 0.60 m from the center is closest to

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. = The radial component of the electric field at a point that is 1.50 m from the center is closest to

A neutral hollow spherical conducting shell of inner radius 1.00 cm and outer radius 3.00 cm has a 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.

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

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?

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.)

Electric charge is uniformly distributed inside a nonconducting sphere of radius .The electric field at a point P,which is 0.50 m from the center of the sphere,is and is directed radially outward.What is the maximum magnitude of the electric field due to this sphere?

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 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)

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 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