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Sheets of charge: 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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Gauss's law: 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 Gauss's law: 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 = (3280 N/C ∙ m)y 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. (ε<sub>0</sub> = 8.85 × 10<sup>-12</sup> C<sup>2</sup>/N ∙ m<sup>2</sup>) = (3280 N/C ∙ m)y Gauss's law: 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 = (3280 N/C ∙ m)y 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. (ε<sub>0</sub> = 8.85 × 10<sup>-12</sup> C<sup>2</sup>/N ∙ m<sup>2</sup>) 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) Gauss's law: 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 = (3280 N/C ∙ m)y 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. (ε<sub>0</sub> = 8.85 × 10<sup>-12</sup> C<sup>2</sup>/N ∙ m<sup>2</sup>)

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Charge on conductors: 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.

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D

Lines of charge: 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) Lines of charge: 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/ Lines of charge: 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

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Spheres of charge: 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

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Spheres of charge: 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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Gauss's law: A charge q = 2.00 μC is placed at the origin in a region where there is already a uniform electric field Gauss's law: 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. (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) Gauss's law: 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. (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 R = 10.0 cm 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

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Lines of charge: Charge is distributed uniformly throughout a large insulating cylinder of radius R. The charge per unit length in the cylindrical volume is λ. (a) Use Gauss's law to find the magnitude of the electric field at a distance r from the central axis of the cylinder for r < R. Your answer should be in terms of r, R, λ, ε0 , and π. (b) Check the reasonableness of your answer by evaluating it at the surface of the cylinder.

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(a) E = blured image (b) At r = ...

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Charge on conductors: 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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Spheres of charge: 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.

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Spheres of charge: A spherical, non-conducting shell of inner radius Spheres of charge: A spherical, non-conducting shell of inner radius = 10 cm and outer radius = 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 Spheres of charge: A spherical, non-conducting shell of inner radius = 10 cm and outer radius = 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 × Spheres of charge: A spherical, non-conducting shell of inner radius = 10 cm and outer radius = 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 × Spheres of charge: A spherical, non-conducting shell of inner radius = 10 cm and outer radius = 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 × Spheres of charge: A spherical, non-conducting shell of inner radius = 10 cm and outer radius = 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 × Spheres of charge: A spherical, non-conducting shell of inner radius = 10 cm and outer radius = 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

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Charge on conductors: 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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Sheets of charge: 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 = Sheets of charge: 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 = Sheets of charge: 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 = Sheets of charge: 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 = Sheets of charge: 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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Lines of charge: 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.

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Sheets of charge: 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. (ε0 = 8.85 × 10-12 C2/N ∙ m2) Sheets of charge: 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. (ε<sub>0</sub> = 8.85 × 10<sup>-12</sup> C<sup>2</sup>/N ∙ m<sup>2</sup>) 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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Spheres of charge: 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. Spheres of charge: 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>/<sup>C</sup>2) (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), ...

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Lines of charge: 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 Lines of charge: 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 Lines of charge: 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. Lines of charge: 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 Lines of charge: 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.

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Sheets of charge: 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? (ε0 = 8.85 × 10-12 C2/N ∙ m2)


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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Spheres of charge: 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.) Spheres of charge: 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

Charge on conductors: 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 Charge on conductors: 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.

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D

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