Exam 24: Gausss 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)

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.

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

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)

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?

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 1.50 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 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

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

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.(ε₀ = 8.85 × 10^-12 C²/N • m²) The magnitude of the electric field at a point that is 94 mm from the axis 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)

Two very large,flat plates are parallel to each other. Plate A,located at y = 1.0 cm,is along the xz-plane and carries a uniform surface charge density -1.00 μC/m². Plate B is located at y = -1.0 cm and carries a uniform surface charge density +2.00 μC/m².What is the electric field vector at the point having x,y,z coordinates (-0.50 cm,0.00 cm,0.00 cm)? (ε₀ = 8.85 × 10^-12 C²/N • m²)

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?

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 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?

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 large,flat,horizontally oriented plates are parallel to each other,a distance d apart.Half way between the two plates the electric field has magnitude E.If the separation of the plates is reduced to d/2 what is the magnitude of the electric field half way between the plates?

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

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)

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?