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The figure shows four Gaussian surfaces surrounding a distribution of charges. The figure shows four Gaussian surfaces surrounding a distribution of charges. (a)Which Gaussian surfaces have an electric flux of +q/ε<sub>0</sub> through them? (b)Which Gaussian surfaces have no electric flux through them? (a)Which Gaussian surfaces have an electric flux of +q/ε0 through them? (b)Which Gaussian surfaces have no electric flux through them?

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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) 3.5 cm only
B) 4.9 cm only
C) 3.5 cm and 9.9 cm
D) 3.5 cm and 4.9 cm
E) 9.9 cm only

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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. 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<sup>-11</sup> 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. A) 0.68 N/C B) 14 N/C C) 23 N/C D) 34 N/C E) 57 N/C 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<sup>-11</sup> 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. A) 0.68 N/C B) 14 N/C C) 23 N/C D) 34 N/C E) 57 N/C


A) 0.68 N/C
B) 14 N/C
C) 23 N/C
D) 34 N/C
E) 57 N/C

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A

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. 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 R<sub>1</sub> = 10.0 cm,R<sub>2</sub> = 20.0 cm,and R<sub>3</sub> = 30.0 cm.(k = 1/4πε<sub>0</sub> = 8.99 × 10<sup>9</sup> N ∙ m<sup>2</sup>/C<sup>2</sup>) (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.

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(a)-5.00 µC (inner surface),-3...

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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?


A) E0/4
B) zero
C) E0/2
D) E0
E) 2E0

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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?


A) 4E
B) 2E
C) E
D) E/2
E) E/4

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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 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 E<sub>1</sub> and E<sub>2</sub>,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) -160 N ∙ m<sup>2</sup>/C B) -350 N ∙ m<sup>2</sup>/C C) 0.00 N ∙ m<sup>2</sup>/C D) +350 N ∙ m<sup>2</sup>/C E) +160 N ∙ m<sup>2</sup>/C


A) -160 N ∙ m2/C
B) -350 N ∙ m2/C
C) 0.00 N ∙ m2/C
D) +350 N ∙ m2/C
E) +160 N ∙ m2/C

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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) 0.11 N ∙ m2/C
B) 8.9 N ∙ m2/C
C) 0.028π N ∙ m2/C
D) It cannot be determined without knowing the radius of the sphere.

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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? 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/m<sup>2</sup> while the lower face carries -25.0 nC/m<sup>2</sup>.What is the magnitude of the electric field at a point within the sheet 2.00 cm below the upper face? A) 0.00 N/C B) 3.95 × 10<sup>3</sup> N/C C) 6.78 × 10<sup>3</sup> N/C D) 7.91 × 10<sup>3</sup> N/C E) 1.36 × 10<sup>4</sup> N/C


A) 0.00 N/C
B) 3.95 × 103 N/C
C) 6.78 × 103 N/C
D) 7.91 × 103 N/C
E) 1.36 × 104 N/C

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C

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)

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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 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 = 1/4πε<sub>0</sub> = 8.99 × 10<sup>9</sup> N ∙ m<sup>2</sup>/C) The radial component of the electric field at a point that is 0.60 m from the center is closest to A) zero. B) +5000 N/C. C) +7500 N/C. D) -5000 N/C. E) -7500 N/C.


A) zero.
B) +5000 N/C.
C) +7500 N/C.
D) -5000 N/C.
E) -7500 N/C.

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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)

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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) at x = 0,y = 0,z = R/2.
B) at the origin.
C) at x = R/2,y = 0,z = 0.
D) at x = 0,y = R/2,z = 0.
E) The charge can be located anywhere,since flux does not depend on the position of the charge as long as it is inside the sphere.

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

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False

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.) 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 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

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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? A very large sheet of a conductor carries a uniform charge density of 4.00 pC/mm<sup>2</sup> on its surfaces.What is the electric field strength 3.00 mm outside the surface of the conductor? A) 4.52 × 10<sup>5</sup> N/C B) 2.26 × 10<sup>5</sup> N/C C) 9.04 × 10<sup>5</sup> N/C D) 0.452 N/C E) 0.226 N/C


A) 4.52 × 105 N/C
B) 2.26 × 105 N/C
C) 9.04 × 105 N/C
D) 0.452 N/C
E) 0.226 N/C

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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 a net excess charge of -500 nC.A point charge of +300 nC is present at the center.(k = 1/4πε<sub>0</sub> = 8.99 × 10<sup>9</sup> N ∙ m<sup>2</sup>/C) The radial component of the electric field at a point that is 1.50 m from the center is closest to A) +1200 N/C. B) +2000 N/C. C) -800 N/C. D) -1600 N/C. E) -2000 N/C.


A) +1200 N/C.
B) +2000 N/C.
C) -800 N/C.
D) -1600 N/C.
E) -2000 N/C.

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


A) Gauss's law is valid only for symmetric charge distributions,such as spheres and cylinders.
B) If there is no charge inside of a Gaussian surface,the electric field must be zero at points of that surface.
C) Only charge enclosed within a Gaussian surface can produce an electric field at points on that surface.
D) If a Gaussian surface is completely inside an electrostatic conductor,the electric field must always be zero at all points on that surface.
E) The electric flux passing through a Gaussian surface depends only on the amount of charge inside that surface,not on its size or shape.

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


A) is always parallel to the surface.
B) is always zero because the electric field is zero inside conductors.
C) is always perpendicular to the surface of the conductor.
D) is perpendicular to the surface of the conductor only if it is a sphere,a cylinder,or a flat sheet.
E) can have nonzero components perpendicular to and parallel to the surface of the conductor.

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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) E = 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) E = B) E = C) E = 0 D) E = E) E =
B) E = 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) E = B) E = C) E = 0 D) E = E) E =
C) E = 0
D) E = 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) E = B) E = C) E = 0 D) E = E) E =
E) E = 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) E = B) E = C) E = 0 D) E = E) E =

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