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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 -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 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 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) A) and B)
G) A) and E)

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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? 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?

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

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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) D) and E)

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A spherical,non-conducting shell of inner radius A spherical,non-conducting shell of inner radius <sub> </sub>= 10 cm and outer radius <sub> </sub>= 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? (k = 1/4πε<sub>0</sub> = 8.99 × 10<sup>9</sup> N ∙ m<sup>2</sup>/C<sup>2</sup>) A) 5.75 × N/C B) zero C) 2.87 × N/C D) 5.75 × N/C E) 2.87 × N/C = 10 cm and outer radius A spherical,non-conducting shell of inner radius <sub> </sub>= 10 cm and outer radius <sub> </sub>= 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? (k = 1/4πε<sub>0</sub> = 8.99 × 10<sup>9</sup> N ∙ m<sup>2</sup>/C<sup>2</sup>) A) 5.75 × N/C B) zero C) 2.87 × N/C D) 5.75 × N/C E) 2.87 × N/C = 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? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)


A) 5.75 × A spherical,non-conducting shell of inner radius <sub> </sub>= 10 cm and outer radius <sub> </sub>= 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? (k = 1/4πε<sub>0</sub> = 8.99 × 10<sup>9</sup> N ∙ m<sup>2</sup>/C<sup>2</sup>) A) 5.75 × N/C B) zero C) 2.87 × N/C D) 5.75 × N/C E) 2.87 × N/C N/C
B) zero
C) 2.87 × A spherical,non-conducting shell of inner radius <sub> </sub>= 10 cm and outer radius <sub> </sub>= 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? (k = 1/4πε<sub>0</sub> = 8.99 × 10<sup>9</sup> N ∙ m<sup>2</sup>/C<sup>2</sup>) A) 5.75 × N/C B) zero C) 2.87 × N/C D) 5.75 × N/C E) 2.87 × N/C N/C
D) 5.75 × A spherical,non-conducting shell of inner radius <sub> </sub>= 10 cm and outer radius <sub> </sub>= 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? (k = 1/4πε<sub>0</sub> = 8.99 × 10<sup>9</sup> N ∙ m<sup>2</sup>/C<sup>2</sup>) A) 5.75 × N/C B) zero C) 2.87 × N/C D) 5.75 × N/C E) 2.87 × N/C N/C
E) 2.87 × A spherical,non-conducting shell of inner radius <sub> </sub>= 10 cm and outer radius <sub> </sub>= 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? (k = 1/4πε<sub>0</sub> = 8.99 × 10<sup>9</sup> N ∙ m<sup>2</sup>/C<sup>2</sup>) A) 5.75 × N/C B) zero C) 2.87 × N/C D) 5.75 × N/C E) 2.87 × N/C N/C

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

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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.(ε<sub>0</sub> = 8.85 × 10<sup>-12</sup> C<sup>2</sup>/N ∙ m<sup>2</sup>) 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.(ε<sub>0</sub> = 8.85 × 10<sup>-12</sup> C<sup>2</sup>/N ∙ m<sup>2</sup>) 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.(ε0 = 8.85 × 10-12 C2/N ∙ m2) 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.(ε<sub>0</sub> = 8.85 × 10<sup>-12</sup> C<sup>2</sup>/N ∙ m<sup>2</sup>) 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 C)
G) None of the above

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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? (ε0 = 8.85 × 10-12 C2/N ∙ m2,e = 1.60 × 10-19 C, mel = 9.11 × 10-31 kg)

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1.34 × 1017 ...

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A charge q = 2.00 μC is placed at the origin in a region where there is already a uniform electric field 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 centered at the origin.(ε<sub>0</sub> = 8.85 × 10<sup>-12</sup> C<sup>2</sup>/N ∙ m<sup>2</sup>) A) 5.52 × 10<sup>5</sup> N ∙ m<sup>2</sup>/C B) 1.13 × 10<sup>5 </sup>N ∙ m<sup>2</sup>/C C) 2.26 × 10<sup>5</sup> N ∙ m<sup>2</sup>/C D) zero = (100 N/C) 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 centered at the origin.(ε<sub>0</sub> = 8.85 × 10<sup>-12</sup> C<sup>2</sup>/N ∙ m<sup>2</sup>) A) 5.52 × 10<sup>5</sup> N ∙ m<sup>2</sup>/C B) 1.13 × 10<sup>5 </sup>N ∙ m<sup>2</sup>/C C) 2.26 × 10<sup>5</sup> N ∙ m<sup>2</sup>/C D) zero .Calculate the flux of the net electric field through a Gaussian sphere of radius 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 centered at the origin.(ε<sub>0</sub> = 8.85 × 10<sup>-12</sup> C<sup>2</sup>/N ∙ m<sup>2</sup>) A) 5.52 × 10<sup>5</sup> N ∙ m<sup>2</sup>/C B) 1.13 × 10<sup>5 </sup>N ∙ m<sup>2</sup>/C C) 2.26 × 10<sup>5</sup> N ∙ m<sup>2</sup>/C D) zero centered at the origin.(ε0 = 8.85 × 10-12 C2/N ∙ m2)


A) 5.52 × 105 N ∙ m2/C
B) 1.13 × 105 N ∙ m2/C
C) 2.26 × 105 N ∙ m2/C
D) zero

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

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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


A) along a line between the lines closer to line #2 than line #1.
B) at a point midway between the lines.
C) along a line perpendicular to lines #1 and #2.
D) along a line between the lines closer to line #1 than line #2.

E) All of the above
F) B) and C)

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An infinitely long nonconducting cylinder of radius R = 2.00 cm carries a uniform volume charge density of An infinitely long nonconducting cylinder of radius R = 2.00 cm carries a uniform volume charge density of Calculate the electric field at distance r = 1.00 cm from the axis of the cylinder.(ε<sub>0</sub> = 8.85 × 10<sup>-12</sup> C<sup>2</sup>/N ∙ m<sup>2</sup>) A) 2.50 × 10<sup>3</sup> N/C B) 5.10 × 10<sup>3</sup> N/C C) zero D) 2.00 × 10<sup>3</sup> N/C E) 10.2 × 10<sup>3</sup> N/C Calculate the electric field at distance r = 1.00 cm from the axis of the cylinder.(ε0 = 8.85 × 10-12 C2/N ∙ m2)


A) 2.50 × 103 N/C
B) 5.10 × 103 N/C
C) zero
D) 2.00 × 103 N/C
E) 10.2 × 103 N/C

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

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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) The inner surface of the conductor carries a charge of -10 µC and its outer surface carries no excess charge.
B) The inner and outer surfaces of the conductor each contain charges of -5 µC.
C) The net electric field within the material of the conductor points away from the +10 µC charge.
D) The outer surface of the conductor contains +10 µC of charge and the inner surface contains -10 µC.
E) Both surfaces of the conductor carry no excess charge because the conductor is uncharged.

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

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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


A) E/8.
B) E/2.
C) 2E.
D) 8E.
E) E.

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

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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 y = 0.080 m.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 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. 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 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. 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.

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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.At what distance from the center of the sphere does the electric field have the same magnitude as it has at P?


A) 0.11 m
B) 0.13 m
C) 0.15 m
D) 0.17 m
E) at no other point

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

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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 radial component of the electric field at a point that 34 mm from the axis is closest to A) -16,000 N/C. B) +16,000 N/C. C) -37,000 N/C. D) +37,000 N/C. E) zero. 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 radial component of the electric field at a point that 34 mm from the axis is closest to A) -16,000 N/C. B) +16,000 N/C. C) -37,000 N/C. D) +37,000 N/C. E) zero. 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 radial component of the electric field at a point that 34 mm from the axis is closest to A) -16,000 N/C. B) +16,000 N/C. C) -37,000 N/C. D) +37,000 N/C. E) zero. The radial component of the electric field at a point that 34 mm 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 radial component of the electric field at a point that 34 mm from the axis is closest to A) -16,000 N/C. B) +16,000 N/C. C) -37,000 N/C. D) +37,000 N/C. E) zero.


A) -16,000 N/C.
B) +16,000 N/C.
C) -37,000 N/C.
D) +37,000 N/C.
E) zero.

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

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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

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(a)E = 0 (...

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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.

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(a)-1590 µ...

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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) None of the above
G) All of the above

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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?


A) 25,000 N/C
B) 30,000 N/C
C) 36,000 N/C
D) 42,000 N/C
E) 48,000 N/C

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

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