Exam 24: Gausss Law

As shown in the figure,a square insulating slab 5.0 mm thick measuring 2.0 m × 2.0 m has a charge of 8.0 × 10^-11 C distributed uniformly throughout its volume.Use Gauss's law to determine the electric field at point P,which is located within the slab beneath its center,1.0 mm from one of the faces.

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

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?

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.

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.) A)a positively charged conducting sphere within another positively charged conducting sphere B)a positively charged conducting sphere within an uncharged conducting sphere C)a solid nonconducting sphere,uniformly charged throughout its volume,inside of a positively charged conducting sphere D)a positively charged nonconducting thin-walled spherical shell inside of a positively charged conducting sphere E)a positively charged nonconducting thin-walled spherical shell inside of another positively charged nonconducting thin-walled spherical shell

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 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?

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

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 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 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?

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?

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

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?

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 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?

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

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?

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 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