Deck 2: The Electric Field II: Continuous Charge Distributions

Question 1

A disk of radius 10 cm carries a uniform surface charge density of 6.0 µC/m². The electric field on the axis of the disk at a distance of 5.0 m is approximately

A) 0.34 MN/C
B) 68 kN/C
C) 99 kN/C
D) 0.54 MN/C
E) 18 kN/C

Answer 1

68 kN/C

Question 2

A uniform line charge of linear charge density $\lambda$ = 10.0 nC/m extends from x = 5 m to
X = 8 m. The magnitude of the electric field at x = 10 m is

A) 27.0 N/C
B) 9.62 N/C
C) 15.3 N/C
D) 18.8 N/C
E) 37.5 N/C

Answer 2

27.0 N/C

Question 3

A uniform line charge of linear charge density $\lambda$ = 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

Answer 3

18.8 N/C

Question 4

A uniform circular ring has charge Q and radius r. A uniformly charged disk also has charge Q and radius r. Calculate the electric field at a distance of r along the axis of the ring divided by the electric field at a distance of r along the axis of the disk.

A) 1.0
B) 0.60
C) 1.7
D) 0.50
E) 0.85

Question 5

A uniform line charge of linear charge density $\lambda$ = 10.0 nC/m extends from x = 5 m to
X = 8 m. The magnitude of the electric field at the point y = 5 m on the perpendicular bisector of the finite line of charge is

A) 3.86 N/C
B) 5.79 N/C
C) 8.31 N/C
D) 10.3 N/C
E) 12.6 N/C

Question 6

Use the following 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)

Question 7

A cubical surface with sides 2.0 m long is oriented with right and left faces perpendicular to a uniform electric field of (1.6 *10⁵ N/C) . The net charge enclosed by this surface is approximately

A) 25 * 10⁵ µC
B) 6.4 *10⁵ µC
C) 13 *10⁵ µC
D) zero
E) 38 * 10⁵ µC

Question 8

Consider a uniform electric field = (5.0 kN/C) . What is the flux of this field through a square of side 20 cm in a plane parallel to the yz plane?

A) 0.10 kN · m²/C
B) 0.20 kN · m²/C
C) 0.40 kN · m²/C
D) 0.50 kN · m²/C
E) 0.13 kN · m²/C

Question 9

A disk of radius 10 cm carries a uniform surface charge density of 6.0 µC/m². The electric field on the axis of the disk at a distance of 0.10 cm is approximately

A) 0.34 MN/C
B) 68 kN/C
C) 99 kN/C
D) 0.54 MN/C
E) 18 kN/C

Question 10

A uniform circular ring has charge Q = 7.36 $\mu$ 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 * 10¹ N/C
B) 6.52 N/C
C) 1.44* 10⁷ N/C
D) 1.44 *10¹ N/C
E) 1.81 * 10⁷ N/C

Question 11

A uniform circular ring has charge Q and radius r. The magnitude of the electric field at a distance of r along the axis of the ring is E_o. If the radius were to double, then calculate the new electric field at a distance of r along the axis of the ring in terms of E_o.

A) 0.40 E_o
B) 0.25 E_o
C) 0.50 E_o
D) 0.20 E_o
E) 0.089 E_o

Question 12

A cubical surface with no charge enclosed and with sides 2.0 m long is oriented with right and left faces perpendicular to a uniform electric field E of (1.6 * 10⁵ N/C) . The net electric flux $\phi$ _E through this surface is approximately

A) zero
B) 6.4 *10⁵ N · m²/C
C) 13* 10⁵ N · m²/C
D) 25 * 10⁵ N · m²/C
E) 38 *10⁵ N · m²/C

Question 13

A uniform line charge of linear charge density $\lambda$ = 5.00 nC/m extends from x = 0 to x = 10 m. The magnitude of the electric field at the point y = 12 m on the perpendicular bisector of the finite line of charge is

A) 18.8 N/C
B) 15.3 N/C
C) 9.65 N/C
D) 4.27 N/C
E) 2.88 N/C

Question 14

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 · 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

Question 15

Use the following 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 x 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) 4.2 kN/C
C) 0.96 kN/C
D) 5.2 kN/c
E) 0.64 mN/C

Question 16

Use the following 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

Question 17

An infinite plane lies in the yz-plane and it has a uniform surface charge density. The electric field at a distance x from the plane

A) decreases linearly with x.
B) decreases as 1/x².
C) is constant and does not depend on x.
D) increases linearly with x.
E) is undetermined.

Question 18

A conducting circular disk has a uniform positive surface charge density. Which of the following diagrams best represents the electric field lines from the disk? (The disk is drawn as a cross-section.)

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

Question 19

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

Question 20

A disk of radius 10 cm carries a uniform surface charge density of 6.0 µC/m². The electric field on the axis of the disk at a distance of 10 cm is approximately

A) 0.34 MN/C
B) 68 kN/C
C) 99 kN/C
D) 0.54 MN/C
E) 18 kN/C

Question 21

An electric field is = (400 N/C) for x > 0 and = (-400 N/C) for x < 0. A cylinder of length 30 cm and radius 10 cm has its center at the origin and its axis along the x axis such that one end is at x = +15 cm and the other is at x = -15 cm. What is the net outward flux through the entire cylindrical surface?

A) zero
B) 2.5 kN · m²/C
C) 0.50 kN · m²/C
D) 25 N · m²/C
E) 0.25 MN · m²/C

Question 22

Use the following figure to answer the next problems:

-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$$\isin$ ₀)^-1?

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

Question 23

Use the following figure to answer the next problems:

-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 < a, is which of the following, in terms of k = (4 $\pi$$\isin$ ₀)^-1?

A) kQ/r²
B) kQr/a³
C) kQ/a²
D) kQ/b²
E) zero

Question 24

A hollow spherical shell of radius 5.36 cm has a charge of 1.91 $\mu$ C placed at its center. Calculate the electric flux through an area of 1.20*10^-2 m² on the shell.

A) 6.48 *10⁵ N^.m²/C
B) 2.16 * 10⁵ N^.m²/C
C) 7.20* 10⁴ N^.m²/C
D) 2.16 * 10¹ N^.m²/C
E) none of the above

Question 25

A sphere of radius 8.0 cm carries a uniform volume charge density $\rho$ = 500 nC/m³. What is the electric field at r = 3.0 cm?

A) 36.0 N/C
B) 230 N/C
C) 140 N/C
D) 565 N/C
E) 450 N/C

Question 26

A cube of side 3.56 cm has a charge of 9.11 $\mu$ C placed at its center. Calculate the electric flux through one side of the cube.

A) 1.03*10⁶ N^.m²/C
B) 2.58 *10⁵ N^.m²/C
C) 8.13 * 10⁸ N^.m²/C
D) 1.72 * 10⁵ N^.m²/C
E) 1.35 * 10⁸ N^.m²/C

Question 27

Use the following figure to answer the next problems:

-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$$\isin$ ₀)^-1?

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

Question 28

The figure shows a surface enclosing the charges 2q and -q. The net flux through the surface surrounding the two charges is

A) q/ $\isin$ ₀
B) 2q/F $\isin$ ₀
C) -q/ $\isin$ ₀
D) zero
E) None of these is correct.

Question 29

An electric field is = (400 N/C) for x > 0 and = (-400 N/C) for x < 0. A cylinder of length 30 cm and radius 10 cm has its center at the origin and its axis along the x axis such that one end is at x = +15 cm and the other is at x = -15 cm. What is the net charge inside the cylinder?

A) zero
B) 22 nC
C) 0.22 nC
D) 4.5 nC
E) 2.2 µC

Question 30

A surface is so constructed that, at all points on the surface, the vector points outward. Therefore, it can be said that

A) the surface encloses a net positive charge.
B) the surface encloses a net negative charge.
C) the surface encloses no net charge.
D) the surface vector $\Delta$ S at all points on the surface is necessarily parallel to the electric field vector .
E) the surface vector $\Delta$ S at all points on the surface is necessarily perpendicular to the electric field vector .

Question 31

A rod of infinite length has a charge per unit length of $\lambda$ (= q/l). Gauss's law makes it easy to determine that the electric field strength at a perpendicular distance r from the rod is, in terms of k = (4 $\pi$$\isin$ ₀)^-1,

A) k $\lambda$ /r²
B) k $\lambda$ /r
C) 4 $\pi$ k $\lambda$ /r
D) 2k $\lambda$ /r
E) zero

Question 32

A horizontal surface of area 0.321 m² has an electric flux of 123 N^.m²/C passing through it at an angle of 25° to the horizontal. If the flux is due to a uniform electric field, calculate the magnitude of the latter.

A) 907 N^.m²/C
B) 423 N^.m²/C
C) 1.10 * 10^-3 N^.m²/C
D) 2.36 * 10^-3 N^.m²/C
E) 383 N^.m²/C

Question 33

An electric field is = (400 N/C) for x > 0 and = (-400 N/C) for x < 0. A cylinder of length 30 cm and radius 10 cm has its center at the origin and its axis along the x axis such that one end is at x = +15 cm and the other is at x = -15 cm. What is the flux through the curved surface of the cylinder?

A) zero
B) 1.3 kN · m²/C
C) 0.25 kN · m²/C
D) 1.3 N · m²/C
E) 0.13 MN · m²/C

Question 34

A sphere of radius 8.0 cm carries a uniform volume charge density $\rho$ = 500 nC/m³. What is the electric field at r = 7.9 cm?

A) 16 N/C
B) 3.3 N/C
C) 60 N/C
D) 9.5 N/C
E) 1.5 kN/C

Question 35

The figure shows a surface, S, with two charges q and -2q. The net flux through the surface is

A) q/ $\isin$ ₀
B) -2q/ $\isin$ ₀
C) -q/ $\isin$ ₀
D) zero
E) None of these is correct.

Question 36

A surface is so constructed that, at all points on the surface, the vector points inward. Therefore, it can be said that

A) the surface encloses a net positive charge.
B) the surface encloses a net negative charge.
C) the surface encloses no net charge.
D) the surface vector $\Delta$ S at all points on the surface is necessarily parallel to the electric field vector .
E) the surface vector $\Delta$ S at all points on the surface is necessarily perpendicular to the electric field vector .

Question 37

A hollow metal sphere has a total charge of 100 µC. If the radius of the sphere is
50 cm, the electric field intensity at a distance of 3.0 m from the surface of the sphere is approximately

A) 3.0 *10⁵ N/C
B) 2.6*10⁵ N/C
C) 1.0* 10⁵ N/C
D) 7.4 * 10⁴ N/C
E) 3.6 * 10⁶ N/C

Question 38

An electric field is = (400 N/C) for x > 0 and = (-400 N/C) for x < 0. A cylinder of length 30 cm and radius 10 cm has its center at the origin and its axis along the x axis such that one end is at x = +15 cm and the other is at x = -15 cm. What is the flux through each end of the cylinder?

A) zero
B) 1.3 kN · m²/C
C) 0.25 kN · m²/C
D) 13 N · m²/C
E) 0.13 MN · m²/C

Question 39

The figure shows a surface enclosing the charges q and -q. The net flux through the surface surrounding the two charges is

A) q/ $\isin$ ₀
B) 2q/ $\isin$ ₀
C) -q/ $\isin$ ₀
D) zero
E) None of these is correct.

Question 40

A solid sphere of radius a is concentric with a hollow sphere of radius b, where b > a. If the solid sphere has a uniform charge distribution totaling +Q and the hollow sphere a charge of -Q, the electric field at radius r, where r < a, is which of the following, in terms of k = (4 $\pi$$\isin$ ₀)^-1?

A) kQ/r²
B) kQr/a³
C) kQ/a²
D) kQ/b²
E) zero

Question 41

A spherical shell of radius 9.0 cm carries a uniform surface charge density
$\Sigma$ = 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

Question 42

Use the figure for the next three problems. An infinite slab of thickness 2d lies in the xz-plane. The slab has a uniform volume charge density $\rho$ .

-The electric at y = b where 0 < b < d is

A) 4 $\pi$ k $\rho$ b
B) 2 $\pi$ k $\rho$ b
C) 4 $\pi$ k $\rho$ /b
D) 2 $\pi$ k $\rho$ /b
E) 4 $\pi$ k $\rho$ /b²

Question 43

A spherical shell of radius 9.0 cm carries a uniform surface charge density
$\Sigma$ = 9.0 nC/m². The electric field at r = 8.9 cm is approximately

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

Question 44

Use the figure for the next three problems. An infinite slab of thickness 2d lies in the xz-plane. The slab has a uniform volume charge density $\rho$ .

-The electric at y = b where b > d is

A) 2 $\pi$ k $\rho$ /d
B) 4 $\pi$ k $\rho$ /d²
C) 4 $\pi$ k $\rho$ d
D) 2 $\pi$ k $\rho$ d
E) 4 $\pi$ k $\rho$ /d

Question 45

A sphere of radius 8.0 cm carries a uniform volume charge density $\rho$ = 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

Question 46

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density $\Sigma$ = 12 nC/m². The electric field at r = 5.9 cm is approximately

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

Question 47

An infinitely long cylinder of radius 4.0 cm carries a uniform volume charge density
$\rho$ = 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

Question 48

A sphere of radius 8.0 cm carries a uniform volume charge density $\rho$ = 500 nC/m³. What is the electric field at r = 20 cm?

A) 0.24 kN/C
B) 0.12 kN/C
C) 4.8 N/C
D) 15 N/C
E) 5.4 N/C

Question 49

An infinitely long cylinder of radius 4.0 cm carries a uniform volume charge density
$\rho$ = 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

Question 50

For a solid uniformly charged sphere of radius R, 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) 2.0
D) 8.0
E) 8/9

Question 51

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density $\Sigma$ = 12 nC/m². The electric field at r = 10 cm is approximately

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

Question 52

An infinite plane of surface charge density $\Sigma$ = +8.00 nC/m² lies in the yz plane at the origin, and a second infinite plane of surface charge density $\Sigma$ = -8.00 nC/m² lies in a plane parallel to the yz plane at x = 4.00 m. The electric field at x = 5.00 m is approximately

A) 226 N/C
B) 339 N/C
C) 904 N/C
D) 452 N/C
E) zero

Question 53

An infinitely long cylinder of radius 4.0 cm carries a uniform volume charge density
$\rho$ = 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

Question 54

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density $\Sigma$ = 12 nC/m². The electric field at r = 6.1 cm is approximately

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

Question 55

An infinitely long cylinder of radius 4.0 cm carries a uniform volume charge density
$\rho$ = 200 nC/m³. What is the electric field at r = 8.0 cm?

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

Question 56

A spherical shell of radius 9.0 cm carries a uniform surface charge density
$\Sigma$ = 9.0 nC/m². The electric field at r = 4.0 cm is approximately

A) 0.13 kN/C
B) 1.0 kN/C
C) 0.32 kN/C
D) 0.75 kN/C
E) zero

Question 57

An infinite plane of surface charge density $\Sigma$ = +8.00 nC/m² lies in the yz plane at the origin, and a second infinite plane of surface charge density $\Sigma$ = -8.00 nC/m² lies in a plane parallel to the yz plane at x = 4.00 m. The electric field at x = 3.50 m is approximately

A) 226 N/C
B) 339 N/C
C) 904 N/C
D) 452 N/C
E) zero

Question 58

A spherical shell of radius 9.0 cm carries a uniform surface charge density
$\Sigma$ = 9.0 nC/m². The electric field at r = 16 cm is approximately

A) 0.32 kN/C
B) 1.0 kN/C
C) zero
D) 0.13 kN/C
E) 0.53 kN/C

Question 59

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density $\Sigma$ = 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

Question 60

Which diagram best represents the electric field along the y-axis?

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

Question 61

Use the following scenario for the next question. A solid conducting sphere of radius r_a is placed concentrically inside a conducting spherical shell of inner radius r_b1 and outer radius r_b2. The inner sphere carries a charge Q while the outer sphere does not carry any net charge.

-The electric field for r_b1 $\lt$ r $\lt$ r_b2 is

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

Question 62

Use the following scenario for the next question. A solid conducting sphere of radius r_a is placed concentrically inside a conducting spherical shell of inner radius r_b1 and outer radius r_b2. The inner sphere carries a charge Q while the outer sphere does not carry any net charge.

-The electric field for r $\gt$ r_b1 is

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

Question 63

The electric field at the surface of a conductor

A) is parallel to the surface.
B) depends only on the total charge on the conductor.
C) depends only on the area of the conductor.
D) depends only on the curvature of the surface.
E) depends on the area and curvature of the conductor and on its charge.

Question 64

Electrical conductors contain

A) only free electrons.
B) only bound electrons.
C) both free and bound electrons.
D) neither bound nor free electrons.
E) only protons and neutrons.

Question 65

The charge on an originally uncharged insulated conductor is separated by induction from a positively charged rod brought near the conductor. For which of the various Gaussian surfaces represented by the dashed lines does = 0?

A) S₁
B) S₂
C) S₃
D) S₄
E) S₅

Question 66

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 * 10¹¹ N/C
B) 8.5 * 10¹¹ N/C
C) 4.2 * 10¹¹ N/C
D) 1.3* 10¹¹ N/C
E) 8.7 * 10¹⁰ N/C

Question 67

The electric field for a spherical shell of charge is discontinuous by the amount _____ at a point where there is a surface charge density $\sigma$ .

A) $\isin$ ₀/ $\sigma$
B) $\sigma$ / $\isin$ ₀
C) $\isin$ ₀/ $\sigma$ ²
D) $\isin$ ₀2/ $\sigma$ ²
E) $\sigma$ ²/ $\isin$ ₀

Question 68

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 = 30 cm.

A) 5.2 *10⁹ N/C
B) 2.6 * 10¹¹ N/C
C) 8.2 * 10¹⁰ N/C
D) 4.7 * 10¹¹ N/C
E) 4.9*10¹⁰ N/C

Question 69

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

A) $\isin$ ₀/ $\sigma$
B) $\sigma$ / $\isin$ ₀
C) $\isin$ ₀/ $\sigma$ ²
D) $\isin$ ₀2/ $\sigma$ ²
E) $\sigma$ ²/ $\isin$ ₀

Question 70

A large, flat conducting plate has a surface charge density $\sigma$ = 8.0 * 10^-9 C/m² on one of its surfaces. What is the magnitude of the electric field 10 µm from this plate?

A) 72 N/C
B) 0.23 kN/C
C) 0.90 kN/C
D) 90 MN/C
E) 9.0 * 10¹² N/C

Question 71

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

Question 72

Use the following scenario for the next question. A solid conducting sphere of radius r_a is placed concentrically inside a conducting spherical shell of inner radius r_b1 and outer radius r_b2. The inner sphere carries a charge Q while the outer sphere does not carry any net charge.

-The electric field for r_a $\lt$ r $\lt$ r_b1 is

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

Question 73

A thin conducting plane with surface charge density $\sigma$ is exposed to an external electric E_ext. The difference in the electric field between one surface of the plane to the other surface is

A) $\sigma$ / $\isin$ ₀
B) $\sigma$ / $\isin$ ₀ + E_ext
C) $\sigma$ / $\isin$ ₀ + E_ext.
D) 2 $\sigma$ / $\isin$ ₀ + E_ext
E) $\sigma$ /2 $\isin$ ₀ +E_ext.

Question 74

The surface charge density for r = r_b1 is

A) Q/( $\pi$ r_b1²)
B) - Q/( $\pi$ r_b1²)
C) Q/(4 $\pi$ r_b1²)
D)-Q/(4 $\pi$ r_b1²)
E) zero

Question 75

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 $\sigma$ on the sphere?

A) 7.1* 10^-9 C/m²
B) 1.0 *10^-8 C/m²
C) 1.4 * 10^-8 C/m²
D) 2.8 *10^-8 C/m²
E) 1.1 * 10^-7 C/m²