chapter gauss’ law 23 - kfupm...dr. m. f. al-kuhaili – phys 102 – chapter 23 page 1 phys102...

Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 23

PHYS102 Previous Exam Problems –

CHAPTER

23

Gauss’ Law Electric flux & Gauss law Conductors in electrosratic equilibrium Cylindrical symmetry Planar symmetry Spherical symmetry

1. A spherical conducting shell has charge Q. A particle with charge q is placed at the center of the

spherical shell. What are the charge on the inner surface of the shell and the charge on the outer surface of the

shell, respectively? (Ans: −q, (Q + q)) 2. Figure 1 shows a Gaussian surface in the shape of a cube with edge 2.0 m. This cube lies in a region where

the electric field vector is given by; E = -4.0 i + 8.0 j (N/C). Find the net charge contained in the cube. (Ans: 0)

3. If the constant electric field in figure 2 has a magnitude of E = 25 N/C, calculate the electric flux through

the curved surface of the hemisphere (half a sphere of radius R = 5.0 cm). [Knowing that the electric field is

perpendicular to the flat surface and that the hemisphere encloses no electric charges] (Ans: 0.20 N·m2/C)

4. A charge is distributed uniformly along a long straight wire. If the electric field 4.0 cm from the wire is 40

N/C, what is the magnitude of the electric field 8.0 cm from the wire? (Ans: 20 N/C)

5. Figure 3 shows a 3.0×105 N/C uniform electric field pointing perpendicularly to the left face of a large

neutral vertical conducting plate. What are the surface charge density of the left (σL) and right (σR) faces of the

plate, respectively? (Ans: -2.7×10-6 C/m2 , +2.7×10-6 C/m2)

6. A conducting spherical shell, of inner radius a = 2.0 cm and outer radius b = 4.0 cm, is neutral. A small

charge Q = 4.0 nC is located at the center of the shell. What is the magnitude of the electric field E at r = 1.0 cm

and r = 3.0 cm from the center of the spherical shell, respectively? (Ans: 36×104 N/C, and zero) 7. Figure 5 shows short sections of two very long parallel wires carrying uniform linear charge densities + 6.0

μC/m and - 2.0 μC/m. Find the magnitude and direction of the net electric field at point P.

(Ans: -5.04×106 i N/C)

8. For the electric field: E = (10 i + 20y j ) N/C, what is the electric flux through a 2.0 m2 portion of the xy

plane? (Ans: zero)

9. A solid non-conducting sphere, of radius 4.0 m, has a uniform charge density. What is the ratio of the

magnitude of the electric field at a distance 2.0 m from the center to the magnitude of the electric field at the

surface of the sphere? (Ans: 0.5)

10. When a piece of paper is held with its face perpendicular to a uniform electric field, the flux through it is

30.0 N·m2/C. When the paper is turned at a certain angle with respect to the field, the flux through it is 24.6

N·m2/C. What is the angle? (Ans: 35o)


11. An infinitely long uniformly charged rod is coaxial with an infinitely long uniformly charged cylindrical

shell of radius 5.0 cm. The linear density of the rod is + 15 × 10-9 C/m and that of the cylindrical shell is –

20×10-9 C/m. What is the magnitude of the electric field at a distance of 10 cm from the axis? (Ans: 900 N/C)

12. A particle, of mass 1.0 g and charge 1.0×10-6 C, is held stationary between two parallel non-conducting

sheets that carry equal but opposite surface charge densities. What is the magnitude of the surface charge

density? (Ans: 8.7×10-8 C/m2)

13. An insulating spherical shell of radius 15 cm has a total charge of 10 μC uniformly distributed on its

surface. Calculate the electric field intensity at a distance of 14 cm from the center of the shell. (Ans: 0)

14. A point charge of 12 μC is placed at the center of a spherical shell of radius 12 cm. Find the ratio of the

total electric flux through the entire surface of the shell to that of a concentric spherical surface of radius 6.0 cm.

(Ans: 1)

15. An insulating sphere of radius R = 10 mm has a uniform charge density ρ = 6.00×10-3 C/m3. Calculate the

electric flux through a concentric spherical surface with radius 5.00 mm. (Ans: 355 N.m2/C)

16. The electric field, at a distance of 40 cm, from a very long uniform wire of charge is 840 N/C. How much

charge is contained in a 2.0 cm long of the wire? (Ans: 0.37 nC)

17. A large insulating solid sphere has a charge density of 5.00 nC/m3. Calculate the electric field inside the

sphere at a distance of 10.0 cm from its center. (Ans: 18.8 N/C)

18. A long solid non-conducting cylinder (radius = 12 cm) has a uniform charge density (5.0 nC/m3)

distributed throughout its volume. Determine the magnitude of the electric field 5.0 cm from the axis of the

cylinder. (Ans: 14 N/C)

19. A conducting spherical shell with a net charge qo has an outer radius R. A point charge qo

is placed at a

distance R/3 from the center of the shell. What is the surface charge density on the outer surface of the shell?

(Ans: 2qo / 4π R2)

20. A point charge is at the center (0,0) of a conducting sphere which has a radius of 0.3 m. Another point

charge of 2 µC is located at r = 0.40 m. If the net flux through the surface of the sphere is 360 Nm2/C, calculate

the value of the charge inside the sphere. (Ans: 3.2 nC)

21. A very long uniform line of charge having a linear charge density of 6.8 μC/m lies along the x axis. A

second line of charge has a linear charge density of -3.40 μC/m and is parallel to the x axis at y = 0.5 m. What is

the net electric field at a point where y = 0.25 m on the y axis? (Ans: 7.3×105 N/C along the +y axis)

22. The net electric flux passing through a closed surface is -4.00×102 N.m2/C. What is net electric charge

contained inside the surface if the surface is a cylinder of height 3.52 cm and radius 1.12 cm?

(Ans: -3.54×10-9 C)

23. A charged, isolated, large non-conducting plate is placed on the xy plane. At 1.5 m from the plate, on the z

axis, the measured electric field is 104 N/C, and directed into the plate. What is the surface charge density on the

plate? (Ans: -1.8×10-7 C/m2)

24. In figure 9, the magnitude of the electric field at point A, due to an infinite line charge density of 9.0×10-6

C/m, is 7.2×104 N/C. If point A is at a distance R from the line charge, what is R? (Ans: 2.3 m)


25. A point charge, q1 = -2.0×10-6 C, is placed inside a cube of side 5.0 cm, and another point charge q2 =

3.0×10-6 C is placed outside the cube. Find the net electric flux through the surfaces of the cube.

(Ans: -2.3×105 N.m2/C)

26. Figure 10 shows portions of two large, parallel, non-conducting sheets, A and B. The surface charge

densities are: σ1 = -4.5 μC/m2 and σ2 = -6.5 μC/m2. Find the electric field at any point between the two sheets.

(Ans: 1.1×105 N/C towards B)

27. A hollow metallic sphere, of radius 2.0 cm, is filled with a non-conducting material which carries a charge

of 5.0 pC distributed uniformly throughout its volume. What is the magnitude of the electric field 1.5 cm from

the center of the sphere? (Ans: 84 N/C)

28. A total charge of 5.0×10-6 C is uniformly distributed inside an irregularly shaped insulator. The volume of

the insulator is 3.0 m3. Now, imagine a cube of volume 0.50 m3 inside the insulator. What is the total electric

flux through the surfaces of the cube? (Ans: 9.4×104 N.m2/C)

29. Figure 11 shows cross-sections through two large, parallel non-conducting sheets with identical

distributions of negative charge. The surface charge density for each sheet is 7.00×10-15 C/m2.What is the

electric field at point A? (Ans: 7.91×10-4 N/C, downward)

30. A point charge of +4.0 μC lies at the center of a hollow spherical conducting shell that has a net charge of

-13.0 μC. If the inner radius of the shell is 2.0 cm and the outer radius is 3.0 cm, what is the ratio between the

charge density on the inner surface to the charge density on the outer surface? (Ans: 1: 1)

31. A point charge of 2.0 μC is placed at the center of a cube 50 cm on edge. What is the flux through the

bottom surface? (Ans: 3.8×104 N.m2/C)

32. An electron is shot directly toward the center of a large metal plate that has excess negative charge with

surface charge density 2.0×10-6 C/m2. If the initial kinetic energy of the electron is 200 eV and if the electron is

to stop just as it reaches the plate, how far from the plate must it be shot? [1 eV = 1.60×10-19 J](Ans: 0.9 mm)

33. An isolated conductor of arbitrary shape has a net charge of -15×10-6 C. Inside the conductor is a cavity

within which is a point charge q = -5.0×10-6 C. What is the charge on the cavity-wall, qin , and what is the charge

on the outer surface of the conductor, qout ? (Ans: qin = 5.0×10-6 C, qout = -20×10-6 C)

34. An infinitely long line has a charge density of 7.6 nC/m. Calculate the electric flux through a spherical

surface of radius R = 7.7 cm whose center, C, lies on the line charge as shown in figure 13. (Ans: 132 N.m2/C)

35. Figure 14 shows two parallel plates, infinite and non-conducting, with surface charge densities of 8.9×10-4

C/m2 and –8.9×10-4C/m2. B, a ball with negligible mass, carries a positive charge of 6.0×10-8 C and is attached

to point A with a non-conducting string of length 10 cm. At equilibrium, what is magnitude of the tension in the

string? (Ans: 6.0 N)

36. A solid insulating sphere has a charge of 20 μC uniformly distributed throughout its volume. The

magnitude of the electric fields inside the sphere at r = 2 cm and outside the sphere at r = 10 cm, measured from

the center of the sphere, are equal. Find the volume charge density of the sphere. (Ans: 24 mC/m3)


37. Charge is uniformly distributed over the entire xy plane with a surface charge density of 20 μC/m2. A

sphere has a radius of 1.0 m, and is centered at the origin. What is the net electric flux through the surface of the

sphere? (Ans: 7.1×106 N.m2/C)

38. As shown in figure 16, a small non-conducting ball of mass m = 1.0×10-6 kg and charge q = 2.0×10-8 C,

distributed uniformly through its volume, hangs from an insulating thread that makes an angle θ = 20o with a

vertical, uniformly charged non-conducting sheet (shown in cross section). Considering the weight of the ball

and assuming that the sheet extends far vertically and into and out of the page, calculate the surface charge

density of the sheet. (Ans: 3.2×10-9 C/m2)

39. A cone having a base of radius r = 0.10 m and height h = 0.50 m is located in a uniform electric field E =

25 V/m (see figure 17). Calculate the electric flux through the curved surface of the cone. (Ans: 0.79 V.m)

40. Figure 21 shows the cross sections of four very long rods that extend into and out of the page. The value

below each rod is the uniform linear charge density λ in units of μC/m, and the distance d = 1.0 cm. What is the

net electric field at point P? (Ans: − 7.2 × 106 i N/C)

41. A point charge q = + 4.00 μC is placed at the center of a conducting spherical shell. The net electric flux

outside the shell is – 1.00×106 N.m2/C. What is the net charge of the shell? (Ans: −12.9 μC)

42. Consider a conducting neutral spherical shell having an inner radius of 3.70 cm and an outer radius of

4.50 cm. A positive point charge q is placed at the center of the shell. The magnitude of the electric field a

distance 5.00 cm from the center of the shell is 2500 N/C. Calculate the magnitude of the charge density on the

outer surface of the shell. (Ans: 2.73×10−8 C/m2)

43. Figure 22 shows a Gaussian cube of side 2.0 m. The cube is placed in a non-uniform electric field E =

24 i + 30y j + 16 k (N/C). What is the electric flux through the shaded face? (Ans: 240 N.m2/C)

44. Consider an infinitely large non-conducting flat sheet carrying a uniform charge density σ = +20 nC/m2

and a long thin wire carrying a uniform charge density λ = −2.0 nC/m arranged as shown in figure 23. What is

the magnitude of the net electric field due to these two charge distributions at point P? (Ans: 670 N/C)

45. A closed cylinder whose main axis is along the x axis is shown in figure 24. It is placed in a uniform

electric field of magnitude 200 N/C pointing in the negative x axis. The cylinder has a cross sectional area of

12.5 cm2 and a length of 6.0 cm. What are the fluxes through faces I, II and III, respectively?

(Ans: 0.25, zero , - 0.25 N.m2/C)

46. Figure 25 shows two infinitely long rods carrying uniform linear charge densities λ1 and λ2. If the net

electric field at point A is zero, what is the ratio λ2/λ1? (Ans: 1.4)

47. Figure 26 shows two large, parallel, non-conducting sheets, each with fixed uniform charge density: σ1 =

+ 2.2×10-6 C/m2 and σ2 = - 4.3×10-6 C/m2. What is the ratio of the magnitude of the electric field at point A to

that at point B? (Ans: 3.1)

48. Two long, charged, coaxial cylindrical shells have radii 3.0 and 6.0 cm. The charge per unit length is

-2.00×10-6 C/m on the inner cylinder and +5.00×10-6 C/m on the outer cylinder. Find the electric field at r = 4.0

cm, where r is the radial distance from the common central axis. (Ans: 9.00×105 N/C, radially inward)

49. A point charge q1 = 4.0 nC is located on the x axis at x = 2.0 m, and a second point charge q2 = – 6.0 nC is

located on the y axis at y = 1.0 m. What is the magnitude of the total electric flux due to these two point charges

through a spherical surface centered at the origin and with a radius of 1.5 m? (Ans: 0.68 kNm2/C)


50. A long cylindrical shell (radius = 2.0 cm) has a charge uniformly distributed on its surface. If the

magnitude of the electric field at a point 8.0 cm radially outward from the axis of the shell is 85 N/C, how much

charge is distributed on a 2.0 m length of the charged cylindrical surface? (Ans: 0.76 nC)

51. A ball of radius 20 cm is uniformly charged to 80 nC. What is the magnitude of the electric field at r = 10

cm? (Ans: 9000 N/C)

52. Two large flat non-conducting sheets have equal but opposite surface charge densities. The distance

between them is 2.0 cm. An electron released from rest from the negative plate strikes the positive plate after 15

ns. What is the magnitude of the surface charge density on each sheet? (Ans: 9.0 nC/m2)

53. A charged conducting spherical shell with an outer radius of 2.0 m has a point charge of +3.0 μC at its

center. The electric field at a distance of 3.0 m from the center has a magnitude of 1.2×104 N/C and is radially

outward. What is the charge on the outer surface of the shell? (Ans: +12 μC)

54. A spherical conducting shell has a radius of 20 cm. Point A is a distance of 30 cm from the center of the

sphere. The electric field at point A is 500 N/C, and is directed radially outward. An additional charge Q is

introduced at the center of the shell. The electric field at point A decreases to 100 N/C. What is Q ? (Ans: -4 nC)

55. A small insulating sphere of mass m = 20.0×10-9 kg and charge q = + 1.00 nC is hanging at equilibrium

above a charged insulating sheet. What is the surface charge density of the sheet? (Ans: +3.47 nC/m2)

56. A charge q = 2.00 μC is placed at the origin in a region where there is already a uniform electric field

given by E = 100 i (N/C). Calculate the net flux through a Gaussian sphere of radius R = 10.0 cm centered at the

origin. (Ans: 2.26×105 N·m2/C)

57. A non-conducting sphere of radius R = 7.0 cm carries a charge Q = 5.0 × 10−3 C distributed uniformly

throughout its volume. At what distance within the sphere, measured from the center of the sphere does the

electric field reach a value equal to half its maximum value? (Ans: 3.5 cm)

58. Figure 29 shows a Gaussian cube in region where the electric field is along the y-axis. E = –30.0 j (N/C)

on the top face and +20.0 j (N/C) on the bottom face of the cube. Determine the net charge contained within the

cube. (Ans: –1.77 × 10-9 C)

59. Figure 30 shows short sections of two very long parallel lines of charge, fixed in place and separated by L

= 10 cm. The uniform linear charge densities are +6.0 μC/m for Line 1 and –2.0 μC/m for Line 2. Find the x-

coordinate of the point along the x-axis at which the net electric field due to the two line charges is zero.

(Ans: +10 cm)

60. Figure 31 shows the magnitude of the electric field due to a sphere with a positive charge distributed

uniformly throughout its volume. What is the value of the charge on the sphere? (Ans: 2.2 μC)

61. In figure 32, find the electric flux through surface 1 if the electric field is along the positive x-axis and has

magnitude E = 500 N/C. (Ans: 1000 N.m2/C)

62. Figure 35 shows, in cross section, three infinitely large parallel and flat non-conducting sheets on which

charge is uniformly distributed. The surface charge densities are σ1 = +2.00 μC/m2, σ2 = + 5.00 μC/m2, and σ3 =

–3.00 μC/m2, and distance L = 1.50 cm. What is the net electric field at point P? (Ans: +2.26 × 105 j N/C)

63. Two infinite wires are charged with uniform and opposite linear charge densities +λ and –λ, where λ =

1.00 nC/m, as shown in figure 36. What is the flux of the electric field through the Gaussian cylindrical surface

(S)? (Ans: +2.26 N.m2/C)


64. A cylindrical Gaussian surface has a radius of 0.20 m. The axis of the cylinder is along the x axis, with

one end at x = 0 and the other end at x = 2.0 m (see figure 38). The cylinder lies in a region where the electric

field is E = x i (N/C), where x is in meters. What is the charge enclosed inside the cylinder? (Ans: +2.2 pC)

65. An electric field given by E = 2.0 i + 4.0 (y2 + 2.0) j (N/C) pierces the Gaussian cube shown in figure 29.

What is the electric flux through the top face of the cube? (Ans: 96 N.m2/C)

66. A long, straight wire has fixed negative charge with a linear charge density of magnitude 4.5 nC/m. The

wire is enclosed by a coaxial, thin walled non-conducting cylindrical shell of radius 20 cm. The shell is to have

a positive charge on its outside surface (with a surface charge density σ) that makes the net electric field at

points 30 cm from the center of the shell equal to zero. Calculate σ. (Ans: 3.6 × 10 – 9 C/m2)

67. Figure 40 shows three Gaussian surfaces A, B and C, with corresponding electric flux ΦA = – q/ε0 ,

ΦB = + 3q/ε0 and ΦC = –2q/ε0 through them, respectively. What is the value of the charge q1? (Ans: +2q)

68. The electric field in a certain region of the Earth’s atmosphere is directed vertically downward. At an

altitude of 150 m, the field has a magnitude of 30 N/C. At an altitude of 100 m, the magnitude of the electric

field is 50 N/C. Find the net amount of electric charge contained in a cube 50 m on edge, with horizontal faces

at altitudes of 100 and 150 m. (Ans: 0.44 μC)

69. Figure 41 shows cross sections of two identical charged solid spheres, 1 and 2, of radius R. The charge is

uniformly distributed throughout the volumes of both the spheres. The net electric field is zero at point P, which

is located on a line connecting the centers of the spheres, at radial distance R/2 from the center of sphere 1. If

the charge on sphere 1 is q1 = 7.8 μC, determine the magnitude of the charge q2 on sphere 2. (Ans: 8.8 µC)


A B C D E Conceptual Problems

1. A spherical conducting shell has charge Q. A particle with charge q is placed at the center of the shell.

The charge on the inner surface of the shell and the charge on the outer surface of the shell, respectively, are A. −q, (Q + q)

B. 0, Q

C. q, (Q − q)

D. Q, 0

E. −q, 0 2. A uniform electric field E = a i + b j intersects a surface of area A. The flux through the area is

A. Zero if the surface lies in the xy plane.

B. Zero if the surface lies in the xz plane.

C. Zero if the surface lies in the yz plane.

D. aA if the surface lies in the xz plane

E. bA if the surface lies in the yz plane 3. Charge Q is distributed uniformly throughout a spherical insulating shell. The net electric flux through the

inner surface of the shell is A. 0

B. Q/εo

C. 2Q/εo

D. Q/4πεo

E. Q/2πεo

4. Figure 4 shows two large, parallel, non-conducting sheets with identical negative uniform charge density of

magnitude σ. A negative point charge q is placed between the two sheets. Rank the four numbered points

according to the magnitude of the net electric field there, greatest first. A. 1,2,3 tie, then 4

B. 1,2 tie, 3, 4

C. 1,2,3,4

D. 4,3,2,1

E. 3,1,2,4

5. Two large insulating parallel plates carry uniformly-distributed surface charge densities of equal

magnitude, one positive and the other negative, as shown in figure 6. Rank the points 1 through 5 according to

the magnitude of the electric field at the points, least to greatest. A. 1, 4, and 5 tie, then 2 and 3 tie

B. 1, 2, 3, 4, 5

C. 2, then 1, 3, and 4 tied, then 5

D. 2 and 3 tie, then 1 and 4 tie, then 5

E. 2 and 3 tie, then 1, 4, and 5 tie

6. Three large insulating sheets of charge with the given charge densities are shown in figure 7. The

magnitudes of the electric field at points A and B are respectively A. σo/2εo, σo/2εo B. 3σo/εo, 3σo/εo C. 2σo/εo, 0 D. 3σo/εo, 0 E. σo/εo, 0


7. Which of the following statements is wrong? A. A shell of uniform charge density exerts a constant force on a charge inside it.

B. Electric field can exert a torque on an electric dipole.

C. Electric field lines extend away from a positive charge.

D. A shell of uniform charge density exerts a constant force on a charge outside it.

E. The magnitude of the charge on a positive ion is an integer multiple of the

electron charge.

8. An imaginary closed spherical surface S of radius R is centered on the origin. A positive charge is

originally at the origin, and the flux through the surface is Φ. The positive charge is slowly moved from the

origin to a point 2R away from the origin. In doing so the flux through S A. decreases to zero.

B. increases to 4Φ.

C. increases to 2Φ.

D. decreases to Φ/4.

E. remains the same Φ.

9. Two concentric shells, one with radius R and the other with radius 2R, surround an isolated point charge.

The ratio of the number of field lines through the larger shell to the number of field lines through the smaller is A. 1

B. 1/4

C. 4

D. 1/2

E. 2 10. Figure 8 shows three situations in which a Gaussian cube sits in an electric field. The arrows and the

values indicate the directions (in N.m2/C) of the flux through the six sides of each cube. In which situations does

the cube enclose, a positive net charge, a negative net charges and zero net charge, respectively? A. 2,3 and 1.

B. 1,2 and 3.

C. 3,2 and 1.

D. 2,1 and 3.

E. 1,3 and 2.

11. Three parallel positively-charged non-conducting sheets are separated by a distance d between adjacent

sheets. The surface charge density on each of the sheets is σ. The electric field in the regions between adjacent

sheets has magnitude: A. σ/2εo B. σ/εo C. 3σ/2εo D. 2σ/3εo E. zero


12. A metallic sphere, in electrostatic equilibrium, has a radius R and carries a net charge Q. Which of the

following statements are true for the sphere? i- It is made of a non-conducting material.

ii- The excess charge resides on its surface.

iii- The electric field inside it is zero.

iv- The electric potential inside it is constant.

A. ii, iii, and iv only.

B. i and ii only.

C. i, ii, and iii only.

D. iii, and iv only.

E. i, ii, and iv only.

13. A point charge of -50e lies at the center of a hollow spherical metal shell that has a net charge of -100e, as

seen in figure 12. Calculate the charge on the (a) shell's inner surface, and (b) on its outer surface. [e is the

magnitude of the charge on the electron] A. (a) 50e (b) -150e

B. (a) -50e (b) -100e

C. (a) 50e (b) -100e

D. (a) -50e (b) 150e

E. (a) zero (b) -150e

14. Calculate the electric flux through the curved surface of a cone of base radius R and height h. The electric

field E is uniform and perpendicular to the base of the cone, and the field lines enter through the base. The cone

has no charge enclosed inside it, as seen in figure 15. A. πR2E

B. πRhΕ

C. -2πRE

D. -πR2E

E. 2πRE

15. A cube of side l has one corner at the origin as shown in figure 18. The cube is lying in a region where the

electric field is given by E = (a + bx) i . What is the net charge enclosed by the cube?

16. A non-uniform electric field given by = 3.0 x i + 4.0 j pierces the Gaussian surface that is in the form of a

cylinder of radius 1.0 m (see figure 19). What is the net charge inside the cylinder?

A. 6πεo

B. 12πεo

C. -12πεo

D. -6πεo

E. zero


17. Figure 20 shows a cross section of a neutral spherical metal shell of inner radius R. A point charge q =

5.0 μC is located at a distance 4R/5 from the center of the shell. Points 1, 2, 3, and 4 are all the same distance

from the center of the spherical shell. At which point is the magnitude of the electric field the largest? A. The electric field is the same at points 1, 2, 3 and 4

B. The electric field is zero outside a conductor

C. Point 1

D. Points 2 and 3

E. Point 4

18. Positive charge q is distributed uniformly throughout an insulating sphere of radius R, centered at the

origin. A particle with a positive charge q is placed at x = 2R on the x axis. The magnitude of the electric field at

x = R/2 on the x axis is: A. q/72πεoR2 B. q/9πεoR2 C. q/8πεoR2 D. 17q/72πεoR2 E. zero

19. A point charge particle is placed at the center of a spherical Gaussian surface. The electric flux through the

Gaussian surface can be changed if A. the point charge is moved to just outside the sphere.

B. the sphere is replaced by a cube of half the volume.

C. the point charge is moved off the center but still inside the original sphere.

D. the sphere is replaced by a cube of the same volume.

E. a second point charge is placed just outside the sphere. 20. Two large and thin metal plates A and B are facing each other. The surface charge densities on the facing

surfaces of the plates are +σ and –σ, respectively, and zero on the outer surfaces. Now, plate B is removed very

far from plate A. The charge density on plate A is: A. σ/2

B. σ

C. 2 σ

D. – σ

E. zero

21. Figure 27 shows two solid spheres, each of radius R, with uniformly distributed charge throughout their

volumes. If the net electric field at point P is zero, what is the ratio q2/q1? A. –1/9

B. 1/9

C. 1/4

D. –1/4

E. –1/3

22. A long wire, of linear charge density λl , runs along the cylindrical axis, of a cylindrical conducting shell,

which carries a net linear charge density of λc. What are the charge per unit length on the inner and outer

surfaces of the shell, respectively? [Note: linear charge density = charge per unit length]


23. Consider a long wire of linear charge density λ. Now imagine a closed cylindrical Gaussian surface of

radius r and length L with the wire as the axis. What is the electric flux through the cylinder surface? A. λL/εo

B. 0

C. (λL2/πr2)λ

D. (2πr2+L)λ/εo

E. (2πr2/L + L)λ/εo

24. A positive point charge q sits at the center of a hollow spherical shell. The shell, with radius R and

negligible thickness, has net charge -2q. What is the electric field strength outside the spherical shell (at r > R)? A. kq/r2, radially inwards

B. kq/r2, radially outwards

C. 2kq/r2, radially inwards

D. 2kq/r2, radially outwards

E. 3kq/r2, radially inwards

25. Two uniformly charged, concentric and hollow, spheres have radii r and 1.5r. The charge of the inner

sphere is q/2 and that on the outer sphere is 3q/2. Find the electric field at a distance 2r from the center of the

spheres. A. 0.5kq/(r2)

B. 0.13kq/(r2)

C. 0.25kq/(r2)

D. 0.35kq/(r2)

E. Zero 26. An isolated conducting spherical shell has an inner radius of 4.0 cm and outer radius of 5.0 cm. A

charge 8.0×10-6 C is put on the shell. What is the ratio of the charge on the inner surface of the shell to the

charge on the outer surface? A. zero

B. 1

C. 2

D. 4

E. 1/4 27. Which one of the graphs in figure 28 represents the magnitude of the electric field as a function of the

distance from the center of a solid charged conducting sphere of radius R? A. V

B. II

C. III

D. IV

E. I

28. Two long straight parallel lines of charge, #1 and #2, carry positive charge per unit lengths of λ1 and λ2,

respectively with λ1 > λ2. The electric field is zero: A. At a point between the lines closer to line #2.

B. At a point halfway between the lines.

C. At a point on line #1.

D. At a point between the lines closer to line #1.

E. At a point on line #2


29. Which of the following statements is NOT TRUE? A. If a charged particle is placed inside a spherical shell of uniform charge density,

there is a non-zero electrostatic force on the particle from the shell.

B. The electric field is zero everywhere inside a conductor in electrostatic

equilibrium.

C. Any excess charge placed on an isolated conductor in electrostatic equilibrium

resides on its surface.

D. The electric field just outside a charged conductor in electrostatic equilibrium is

perpendicular to its surface.

E. The net electric flux through any closed surface is proportional to the net charge

inside the surface. 30. A metallic shell of inner radius R1 and outer radius R2 carries a net charge q. A point charge -q is then

placed at the center of the shell. At which of the following positions, measured from the center of the shell, is

the net electric field NOT equal to zero? A. r < R1

B. R1 < r < R2

C. r > R2

D. r = R2

E. E = 0 everywhere

31. Two long straight parallel lines of charge carry positive charge per unit lengths of λ1 and λ2, with λ1 > λ2

(see figure 33). The position of points where the electric field is zero is: A. along a line between the lines closer to Line 2 than Line 1

B. along a line halfway between the lines

C. to the left of Line 1

D. along a line between the lines closer to Line 1 than Line 2

E. to the right of Line 2

32. A solid non-conducting sphere of radius R carries a uniform charge density. At a radial distance r1 = R/4,

the electric field has a magnitude of Eo. What is the magnitude of the electric field at a radial distance r2 = 2 R? A. Eo

B. Eo/2

C. Eo/4

D. 2Eo

E. 4Eo

33. Three parallel flat non-conducting sheets of charge are separated by a distance d between each of the

sheets. The surface charge density on each of the sheets is shown in figure 34. The electric field in the regions

between the sheets has magnitude: A. σ/εo

B. 2σ/3εo

C. σ/2εo

D. 2σ/εo

E. 0


34. A uniform electric field E = Eo j , where Eo is a positive constant, is set-up in a region of space. A frame is

placed in that region in such a way that its plane is perpendicular to the y-axis. Which of the following changes

would decrease the magnitude of the electric flux through the frame? A. Tilting the frame so that its plane is now in the yz-plane

B. Moving the frame vertically along the y-axis keeping parallel to the xz- plane

C. Rotating the frame in the xz-plane with respect to the y-axis

D. Sliding the frame sideways parallel to the z-axis within the xz-plane

E. Sliding the frame sideways parallel to the x-axis within the xz-plane

35. Consider a spherical shell of radius R and charge Q distributed uniformly on its surface. Find the radial

distance where the electric field due to the shell is half its maximum value.

36. In figure 37, a charge q is placed at the common center of two hemispheres A and B. The flux of the

electric field through hemisphere B is A. equal to the flux through hemisphere A

B. double the flux through hemisphere A

C. four times the flux through hemisphere A

D. zero

E. half the flux through hemisphere A

37. Figure 39 a, b and c, show the cross sections of three cylinders each carrying a uniform charge Q.

Concentric with each cylinder is a cylindrical Gaussian surface, all three with the same radius. Rank the

Gaussian surfaces according to the electric field at any point on the surface, GREATEST FIRST. A. All tie

B. a, b, c

C. b, c, a

D. c, b, a

E. a, c, b

38. A metallic sphere contains a cavity at the center as shown in figure 42. The outer surface of the sphere is

grounded by connecting a conducting wire between it and the earth. A negative point charge Q = −5.4 ×10-9 C is

placed inside the cavity of the sphere. What is the net electric flux through the outer surface of the metallic

sphere? A) 0

B) +6.1×102 N.m2/C

C) −6.1×102 N.m2/C

D) +3.1×102 N.m2/C

E) −3.1×102 N.m2/C


Figure 1 Figure 2 Figure 3



Figure 10 Figure 11 Figure 12 Figure 13




Figure 38 Figure 39


chapter gauss’ law 23 - kfupm...dr. m. f. al-kuhaili – phys 102 – chapter 23 page 1 phys102...

Documents