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For a uniformly charged spherical sphere of radius R carrying a total charge Q,calculate the electric field at a distance R/2 outside the sphere divided by the electric field at a distance R/2 inside the sphere.


A) 9/8
B) infinity
C) 4/9
D) 8.0
E) 8/9

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The electric field for an infinite plane of charge is discontinuous by the amount _____ at a point where there is a surface charge density σ\sigma .


A) ε\varepsilon 0/ σ\sigma
B) σ\sigma / ε\varepsilon 0
C) ε\varepsilon 0/ σ\sigma 2
D) ε\varepsilon 02/ σ\sigma 2
E) σ\sigma 2/ ε\varepsilon 0

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Consider a uniform electric field Consider a uniform electric field = (5.0 kN/C) .What is the flux of this field through a square of side 20 cm if the normal to its plane makes a 45º angle with the x axis? A) 71 N · m<sup>2</sup>/C B) 0.14 kN · m<sup>2</sup>/C C) 0.28 kN · m<sup>2</sup>/C D) 0.35 kN · m<sup>2</sup>/C E) 0.19 kN · m<sup>2</sup>/C = (5.0 kN/C) Consider a uniform electric field = (5.0 kN/C) .What is the flux of this field through a square of side 20 cm if the normal to its plane makes a 45º angle with the x axis? A) 71 N · m<sup>2</sup>/C B) 0.14 kN · m<sup>2</sup>/C C) 0.28 kN · m<sup>2</sup>/C D) 0.35 kN · m<sup>2</sup>/C E) 0.19 kN · m<sup>2</sup>/C .What is the flux of this field through a square of side 20 cm if the normal to its plane makes a 45º angle with the x axis?


A) 71 N · m2/C
B) 0.14 kN · m2/C
C) 0.28 kN · m2/C
D) 0.35 kN · m2/C
E) 0.19 kN · m2/C

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A solid spherical conductor has a radius of 15 cm.The electric field 30 cm from the center of this sphere has a magnitude of 800 N/C.What is the surface charge density σ\sigma on the sphere?


A) 7.1 ×\times 10-9 C/m2
B) 1.0 ×\times 10-8 C/m2
C) 1.4 ×\times 10-8 C/m2
D) 2.8 ×\times 10-8 C/m2
E) 1.1 ×\times 10-7 C/m2

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An infinitely long cylinder of radius 4.0 cm carries a uniform volume charge density ρ\rho = 200 nC/m3.What is the electric field at r = 2.0 cm?


A) zero
B) 0.11 kN/C
C) 57 N/C
D) 0.44 kN/C
E) 0.23 kN/C

Correct Answer

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An infinitely long cylinder of radius 4.0 cm carries a uniform volume charge density ρ\rho = 200 nC/m3.What is the electric field at r = 4.1 cm?


A) zero
B) 0.11 kN/C
C) 57 N/C
D) 0.44 kN/C
E) 0.23 kN/C

Correct Answer

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Which diagram best represents the electric field along the y-axis? Which diagram best represents the electric field along the y-axis? A) 1 B) 2 C) 3 D) 4 E) none of the diagrams


A) 1
B) 2
C) 3
D) 4
E) none of the diagrams

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A spherical shell of radius 9.0 cm carries a uniform surface charge density σ\sigma = 9.0 nC/m2.The electric field at r = 9.1 cm is approximately


A) zero
B) 1.0 kN/C
C) 0.65 kN/C
D) 0.32 kN/C
E) 0.13 kN/C

Correct Answer

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Use the following figure to answer the next problem: Use the following figure to answer the next problem: -A solid sphere of radius a is concentric with a hollow sphere of radius b,where b > a.If the solid sphere has a charge +Q and the hollow sphere a charge of -Q,the electric field at radius r,where r > b,is which of the following,in terms of k = (4 \pi\varepsilon <sub>0</sub>) <sup>-1</sup>? A) kQ/r<sup>2 </sup> B) 2kQ/r<sup>2 </sup> C) kQ/a<sup>2 </sup> D) kQ/b<sup>2 </sup> E) zero -A solid sphere of radius a is concentric with a hollow sphere of radius b,where b > a.If the solid sphere has a charge +Q and the hollow sphere a charge of -Q,the electric field at radius r,where r > b,is which of the following,in terms of k = (4 πε\pi\varepsilon 0) -1?


A) kQ/r2
B) 2kQ/r2
C) kQ/a2
D) kQ/b2
E) zero

Correct Answer

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Which of the following circumstances about Gauss's law is true?


A) Gauss's law is applicable in highly symmetric cases such as uniformly charged infinite plane,infinite cylinder,or sphere.
B) Gauss's law is applicable for a point charge.
C) Gauss's law is applicable for two or more point charges.
D) Gauss's law is applicable for any objects of any shape.
E) all of the above

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An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density σ\sigma = 12 nC/m2.The electric field at r = 2.0 cm is approximately


A) 12 kN/C
B) 0.56 kN/C
C) 1.3 kN/C
D) 0.81 kN/C
E) zero

Correct Answer

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A uniform circular ring has charge Q = 7.36 μ\mu C,and radius r = 3.33 cm.Calculate the magnitude of the electric field at a distance of 4.20 cm along the axis of the ring.


A) 1.81 ×\times 101 N/C
B) 6.52 N/C
C) 1.44 ×\times 107 N/C
D) 1.44 ×\times 101 N/C
E) 1.81 ×\times 107 N/C

Correct Answer

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Use the following figure to answer the problem: Use the following figure to answer the problem: -An infinite line charge of linear density \lambda = 0.30 µC/m lies along the z axis and a point charge q = 6.0 µC lies on the y axis at y = 2.0 m.The electric field at the point P on the x axis at x = 3.0 m is approximately A) (4.2 kN/C) B) (4.2 kN/C) + (0.64 kN/C) C) (-0.96 kN/C) D) (2.8 kN/C) + (0.64 kN/C) E) (5.2 kN/C) - (2.3 kN/C) -An infinite line charge of linear density λ\lambda = 0.30 µC/m lies along the z axis and a point charge q = 6.0 µC lies on the y axis at y = 2.0 m.The electric field at the point P on the x axis at x = 3.0 m is approximately


A) (4.2 kN/C) Use the following figure to answer the problem: -An infinite line charge of linear density \lambda = 0.30 µC/m lies along the z axis and a point charge q = 6.0 µC lies on the y axis at y = 2.0 m.The electric field at the point P on the x axis at x = 3.0 m is approximately A) (4.2 kN/C) B) (4.2 kN/C) + (0.64 kN/C) C) (-0.96 kN/C) D) (2.8 kN/C) + (0.64 kN/C) E) (5.2 kN/C) - (2.3 kN/C)
B) (4.2 kN/C) Use the following figure to answer the problem: -An infinite line charge of linear density \lambda = 0.30 µC/m lies along the z axis and a point charge q = 6.0 µC lies on the y axis at y = 2.0 m.The electric field at the point P on the x axis at x = 3.0 m is approximately A) (4.2 kN/C) B) (4.2 kN/C) + (0.64 kN/C) C) (-0.96 kN/C) D) (2.8 kN/C) + (0.64 kN/C) E) (5.2 kN/C) - (2.3 kN/C) + (0.64 kN/C) Use the following figure to answer the problem: -An infinite line charge of linear density \lambda = 0.30 µC/m lies along the z axis and a point charge q = 6.0 µC lies on the y axis at y = 2.0 m.The electric field at the point P on the x axis at x = 3.0 m is approximately A) (4.2 kN/C) B) (4.2 kN/C) + (0.64 kN/C) C) (-0.96 kN/C) D) (2.8 kN/C) + (0.64 kN/C) E) (5.2 kN/C) - (2.3 kN/C)
C) (-0.96 kN/C) Use the following figure to answer the problem: -An infinite line charge of linear density \lambda = 0.30 µC/m lies along the z axis and a point charge q = 6.0 µC lies on the y axis at y = 2.0 m.The electric field at the point P on the x axis at x = 3.0 m is approximately A) (4.2 kN/C) B) (4.2 kN/C) + (0.64 kN/C) C) (-0.96 kN/C) D) (2.8 kN/C) + (0.64 kN/C) E) (5.2 kN/C) - (2.3 kN/C)
D) (2.8 kN/C) Use the following figure to answer the problem: -An infinite line charge of linear density \lambda = 0.30 µC/m lies along the z axis and a point charge q = 6.0 µC lies on the y axis at y = 2.0 m.The electric field at the point P on the x axis at x = 3.0 m is approximately A) (4.2 kN/C) B) (4.2 kN/C) + (0.64 kN/C) C) (-0.96 kN/C) D) (2.8 kN/C) + (0.64 kN/C) E) (5.2 kN/C) - (2.3 kN/C) + (0.64 kN/C) Use the following figure to answer the problem: -An infinite line charge of linear density \lambda = 0.30 µC/m lies along the z axis and a point charge q = 6.0 µC lies on the y axis at y = 2.0 m.The electric field at the point P on the x axis at x = 3.0 m is approximately A) (4.2 kN/C) B) (4.2 kN/C) + (0.64 kN/C) C) (-0.96 kN/C) D) (2.8 kN/C) + (0.64 kN/C) E) (5.2 kN/C) - (2.3 kN/C)
E) (5.2 kN/C) Use the following figure to answer the problem: -An infinite line charge of linear density \lambda = 0.30 µC/m lies along the z axis and a point charge q = 6.0 µC lies on the y axis at y = 2.0 m.The electric field at the point P on the x axis at x = 3.0 m is approximately A) (4.2 kN/C) B) (4.2 kN/C) + (0.64 kN/C) C) (-0.96 kN/C) D) (2.8 kN/C) + (0.64 kN/C) E) (5.2 kN/C) - (2.3 kN/C) - (2.3 kN/C) Use the following figure to answer the problem: -An infinite line charge of linear density \lambda = 0.30 µC/m lies along the z axis and a point charge q = 6.0 µC lies on the y axis at y = 2.0 m.The electric field at the point P on the x axis at x = 3.0 m is approximately A) (4.2 kN/C) B) (4.2 kN/C) + (0.64 kN/C) C) (-0.96 kN/C) D) (2.8 kN/C) + (0.64 kN/C) E) (5.2 kN/C) - (2.3 kN/C)

Correct Answer

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Use the following scenario for the next question. Use the following scenario for the next question. A solid conducting sphere of radius ra is placed concentrically inside a conducting spherical shell of inner radius r<sub>b1</sub> and outer radius r<sub>b2</sub>. The inner sphere carries a charge Q while the outer sphere does not carry any net charge. -The electric field for r<sub>b1 </sub>< r < r<sub>b</sub><sub>2</sub> is A) -kQ/r<sup>2</sup> B) kQ/r<sup>2</sup> C) -2kQ/r D) 2kQ/r E) zero A solid conducting sphere of radius ra is placed concentrically inside a conducting spherical shell of inner radius rb1 and outer radius rb2. The inner sphere carries a charge Q while the outer sphere does not carry any net charge. -The electric field for rb1 < r < rb2 is


A) -kQ/r2
B) kQ/r2
C) -2kQ/r
D) 2kQ/r
E) zero

Correct Answer

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A uniform line charge of linear charge density λ\lambda = 5.00 nC/m extends from x = 0 to x = 10 m.The magnitude of the electric field at x = 12 m is


A) 3.86 N/C
B) 9.62 N/C
C) 15.3 N/C
D) 18.8 N/C
E) 37.5 N/C

Correct Answer

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Use the following figure to answer the next problem: Use the following figure to answer the next problem: -A sphere of radius 8.0 cm carries a uniform volume charge density \rho = 500 nC/m<sup>3</sup>.What is the electric field at r = 8.1 cm? A) 0.12 kN/C B) 1.5 kN/C C) 0.74 kN/C D) 2.3 kN/C E) 12 kN/C -A sphere of radius 8.0 cm carries a uniform volume charge density ρ\rho = 500 nC/m3.What is the electric field at r = 8.1 cm?


A) 0.12 kN/C
B) 1.5 kN/C
C) 0.74 kN/C
D) 2.3 kN/C
E) 12 kN/C

Correct Answer

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A non-conducting pipe has a uniform charge density of 50 C/m3.The inner radius of the pipe is 25 cm,while the outer radius is 35 cm.Calculate the magnitude of the electric field at r = 40 cm.


A) 6.8 ×\times 1011 N/C
B) 8.5 ×\times 1011 N/C
C) 4.2 ×\times 1011 N/C
D) 1.3 ×\times 1011 N/C
E) 8.7 ×\times 1010 N/C

Correct Answer

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Use the following figure to answer the problem: Use the following figure to answer the problem: -An infinite line charge of linear density \lambda = 0.30 µC/m lies along the z axis and a point charge q = 6.0 µC lies on the y axis at y = 2.0 m.The y component of the electric field at the point P on the x axis at x = 3.0 m is approximately A) 1.8 kN/C B) 2.3 kN/C C) 0.96 kN/C D) 4.2 kN/C E) 2.8 kN/C -An infinite line charge of linear density λ\lambda = 0.30 µC/m lies along the z axis and a point charge q = 6.0 µC lies on the y axis at y = 2.0 m.The y component of the electric field at the point P on the x axis at x = 3.0 m is approximately


A) 1.8 kN/C
B) 2.3 kN/C
C) 0.96 kN/C
D) 4.2 kN/C
E) 2.8 kN/C

Correct Answer

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Use the following figure to answer the next problem: Use the following figure to answer the next problem: -A solid sphere of radius a is concentric with a hollow sphere of radius b,where b > a.If the solid sphere has a charge +Q and the hollow sphere a charge of -Q,the electric field at radius r,where a < r < b,is which of the following,in terms of k = (4 \pi\varepsilon <sub>0</sub>) <sup>-1</sup>? A) kQ/r<sup>2 </sup> B) 2kQ/r<sup>2 </sup> C) kQ/a<sup>2 </sup> D) kQ/b<sup>2 </sup> E) kQ/(b - a) <sup>2 </sup> -A solid sphere of radius a is concentric with a hollow sphere of radius b,where b > a.If the solid sphere has a charge +Q and the hollow sphere a charge of -Q,the electric field at radius r,where a < r < b,is which of the following,in terms of k = (4 πε\pi\varepsilon 0) -1?


A) kQ/r2
B) 2kQ/r2
C) kQ/a2
D) kQ/b2
E) kQ/(b - a) 2

Correct Answer

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An infinitely long cylinder of radius 4.0 cm carries a uniform volume charge density ρ\rho = 200 nC/m3.What is the electric field at r = 3.9 cm?


A) zero
B) 0.44 kN/C
C) 57 N/C
D) 0.11 kN/C
E) 0.23 kN/C

Correct Answer

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