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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.

A) True
B) False

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An irregular conductor carries a surface charge density of -6.75 µC/m2 at and in the vicinity of a point P on the surface.An electron is released just above P outside the conductor.What are the magnitude and direction of its acceleration the instant after it is released? An irregular conductor carries a surface charge density of -6.75 µC/m<sup>2</sup> at and in the vicinity of a point P on the surface.An electron is released just above P outside the conductor.What are the magnitude and direction of its acceleration the instant after it is released? , ,<sup> </sup> <sup> </sup> , An irregular conductor carries a surface charge density of -6.75 µC/m<sup>2</sup> at and in the vicinity of a point P on the surface.An electron is released just above P outside the conductor.What are the magnitude and direction of its acceleration the instant after it is released? , ,<sup> </sup> <sup> </sup> , An irregular conductor carries a surface charge density of -6.75 µC/m<sup>2</sup> at and in the vicinity of a point P on the surface.An electron is released just above P outside the conductor.What are the magnitude and direction of its acceleration the instant after it is released? , ,<sup> </sup> <sup> </sup>

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1.34 × 1017 ...

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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 an excess charge of 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 .A point charge of is present at the center.The surface charge density on the inner spherical surface is closest to A) zero. B) +4.0 × 10<sup>-8</sup> C/m<sup>2</sup>. C) +6.0 × 10<sup>-8</sup> C/ m<sup>2</sup>. D) -4.0 × 10<sup>-8</sup> C/ m<sup>2</sup>. E) -6.0 × 10<sup>-8</sup> C/ m<sup>2</sup>. .A point charge of 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 .A point charge of is present at the center.The surface charge density on the inner spherical surface is closest to A) zero. B) +4.0 × 10<sup>-8</sup> C/m<sup>2</sup>. C) +6.0 × 10<sup>-8</sup> C/ m<sup>2</sup>. D) -4.0 × 10<sup>-8</sup> C/ m<sup>2</sup>. E) -6.0 × 10<sup>-8</sup> C/ m<sup>2</sup>. is present at the center.The surface charge density on the inner spherical surface 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 .A point charge of is present at the center.The surface charge density on the inner spherical surface is closest to A) zero. B) +4.0 × 10<sup>-8</sup> C/m<sup>2</sup>. C) +6.0 × 10<sup>-8</sup> C/ m<sup>2</sup>. D) -4.0 × 10<sup>-8</sup> C/ m<sup>2</sup>. E) -6.0 × 10<sup>-8</sup> C/ m<sup>2</sup>.


A) zero.
B) +4.0 × 10-8 C/m2.
C) +6.0 × 10-8 C/ m2.
D) -4.0 × 10-8 C/ m2.
E) -6.0 × 10-8 C/ m2.

F) D) and E)
G) C) and D)

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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. 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.

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As shown in the figure,a square insulating slab 5.0 mm thick measuring As shown in the figure,a square insulating slab 5.0 mm thick measuring has a charge of 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 has a charge of As shown in the figure,a square insulating slab 5.0 mm thick measuring has a charge of 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 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 has a charge of 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 has a charge of 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

F) All of the above
G) A) and B)

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A solid nonconducting sphere of radius R carries a uniform charge density throughout its volume.At a radial distance A solid nonconducting sphere of radius R carries a uniform charge density throughout its volume.At a radial distance from the center,the electric field has a magnitude E<sub>0</sub>.What is the magnitude of the electric field at a radial distance ? A) E<sub>0</sub>/4 B) zero C) E<sub>0</sub>/2 D) E<sub>0</sub> E) 2E<sub>0</sub> from the center,the electric field has a magnitude E0.What is the magnitude of the electric field at a radial distance A solid nonconducting sphere of radius R carries a uniform charge density throughout its volume.At a radial distance from the center,the electric field has a magnitude E<sub>0</sub>.What is the magnitude of the electric field at a radial distance ? A) E<sub>0</sub>/4 B) zero C) E<sub>0</sub>/2 D) E<sub>0</sub> E) 2E<sub>0</sub> ?


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

F) A) and B)
G) A) and C)

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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 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 and respectively,and are directed as shown. The charge enclosed by the cylindrical surface is closest to A) -1.1 nC. B) 1.1 nC. C) -2.4 nC. D) -4.8 nC. E) 4.8 nC. and 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 and respectively,and are directed as shown. The charge enclosed by the cylindrical surface is closest to A) -1.1 nC. B) 1.1 nC. C) -2.4 nC. D) -4.8 nC. E) 4.8 nC. respectively,and are directed as shown. 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 and respectively,and are directed as shown. The charge enclosed by the cylindrical surface is closest to A) -1.1 nC. B) 1.1 nC. C) -2.4 nC. D) -4.8 nC. E) 4.8 nC. The charge enclosed by the cylindrical surface 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 E<sub>1</sub> and E<sub>2</sub>,at the ends of the cylindrical surface,have magnitudes of and respectively,and are directed as shown. The charge enclosed by the cylindrical surface is closest to A) -1.1 nC. B) 1.1 nC. C) -2.4 nC. D) -4.8 nC. E) 4.8 nC.


A) -1.1 nC.
B) 1.1 nC.
C) -2.4 nC.
D) -4.8 nC.
E) 4.8 nC.

F) A) and D)
G) B) and C)

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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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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 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 .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. .It is observed that there is an electric field 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 .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. 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. 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 .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. 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 .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.

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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 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 and 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 and 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 and 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 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 and 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

F) C) and E)
G) B) and D)

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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) 45°
B) 26.6°
C) 90°
D) 30°
E) 60°

F) A) and B)
G) B) and E)

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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? 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? A) 4.5 × 10<sup>6</sup> N • m<sup>2</sup>/C B) 0.00 N • m<sup>2</sup>/C C) 9.0 × 10<sup>6</sup> N • m<sup>2</sup>/C D) 11 × 10<sup>5</sup> N • m<sup>2</sup>/C 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? A) 4.5 × 10<sup>6</sup> N • m<sup>2</sup>/C B) 0.00 N • m<sup>2</sup>/C C) 9.0 × 10<sup>6</sup> N • m<sup>2</sup>/C D) 11 × 10<sup>5</sup> N • m<sup>2</sup>/C


A) 4.5 × 106 N • m2/C
B) 0.00 N • m2/C
C) 9.0 × 106 N • m2/C
D) 11 × 105 N • m2/C

E) None of the above
F) All of the above

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A very large sheet of a conductor carries a uniform charge density of A very large sheet of a conductor carries a uniform charge density of 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 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 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

F) All of the above
G) A) and C)

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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.

F) A) and D)
G) B) and D)

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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.

F) B) and C)
G) C) and D)

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

F) All of the above
G) A) and E)

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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 Two extremely large nonconducting horizontal sheets each carry uniform charge density on the surfaces facing each other.The upper sheet carries .The electric field midway between the sheets is pointing downward.What is the surface charge density on the lower sheet? .The electric field midway between the sheets is Two extremely large nonconducting horizontal sheets each carry uniform charge density on the surfaces facing each other.The upper sheet carries .The electric field midway between the sheets is pointing downward.What is the surface charge density on the lower sheet? pointing downward.What is the surface charge density on the lower sheet? Two extremely large nonconducting horizontal sheets each carry uniform charge density on the surfaces facing each other.The upper sheet carries .The electric field midway between the sheets is pointing downward.What is the surface charge density on the lower sheet?

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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

F) A) and E)
G) B) and D)

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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? A charge of 1.0 × 10<sup>-6</sup> μC is located inside a sphere,1.25 cm from its center.What is the electric flux through the sphere due to this charge? A) 0.11 N • m<sup>2</sup>/C B) 8.9 N • m<sup>2</sup>/C C) 0.028π N • m<sup>2</sup>/C D) It cannot be determined without knowing the radius of the sphere.


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.

E) C) and D)
F) B) and D)

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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 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 magnitude of the electric field at a point that is from the axis is closest to A) 17,000 N/C. B) 15,000 N/C. C) 13,000 N/C. D) 11,000 N/C. E) 9600 N/C. and the linear charge density on the outer conductor is 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 magnitude of the electric field at a point that is from the axis is closest to A) 17,000 N/C. B) 15,000 N/C. C) 13,000 N/C. D) 11,000 N/C. E) 9600 N/C. The inner and outer cylindrical surfaces are respectively denoted by A,B,C,and D,as shown. 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 magnitude of the electric field at a point that is from the axis is closest to A) 17,000 N/C. B) 15,000 N/C. C) 13,000 N/C. D) 11,000 N/C. E) 9600 N/C. The magnitude of the electric field at a point that is 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 magnitude of the electric field at a point that is from the axis is closest to A) 17,000 N/C. B) 15,000 N/C. C) 13,000 N/C. D) 11,000 N/C. E) 9600 N/C. from the axis is closest to 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 magnitude of the electric field at a point that is from the axis is closest to A) 17,000 N/C. B) 15,000 N/C. C) 13,000 N/C. D) 11,000 N/C. E) 9600 N/C.


A) 17,000 N/C.
B) 15,000 N/C.
C) 13,000 N/C.
D) 11,000 N/C.
E) 9600 N/C.

F) A) and B)
G) B) and D)

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