Gauss’s Law Problems

This section provides 100 problems to test your understanding of Gauss’s law, including electric flux calculations, field computations for symmetric charge distributions, conductors, and charged surfaces. Inspired by JEE Main, JEE Advanced, and NEET exam patterns, these problems are tailored for exam preparation, offering a mix of numerical, conceptual, and derivation-based challenges. NEET-style problems (66–100) are formatted as multiple-choice questions (MCQs) to match the exam’s objective format. Problems are organized by type to support progressive learning and build confidence in mastering electrostatics, a key topic for JEE/NEET success.

Numerical Problems

1. A uniform electric field $\overrightarrow{E}=600\hat{i}\text{N/C}$ passes through a square surface of side $0.3\text{m}$ in the yz-plane. Calculate the electric flux through the surface.

   • (a) $53.9{\text{N·m}}^2/\text{C}$
   • (b) $54.0{\text{N·m}}^2/\text{C}$
   • (c) $54.1{\text{N·m}}^2/\text{C}$
   • (d) $54.2{\text{N·m}}^2/\text{C}$

2. A point charge $q=4\mu \text{C}$ is at the center of a spherical Gaussian surface of radius $0.2\text{m}$. Calculate the electric flux through the surface (${ϵ}_0=8.85\times {10}^{-12}{\text{C}}^2/{\text{N·m}}^2$).

   • (a) $4.51\times {10}^5{\text{N·m}}^2/\text{C}$
   • (b) $4.52\times {10}^5{\text{N·m}}^2/\text{C}$
   • (c) $4.53\times {10}^5{\text{N·m}}^2/\text{C}$
   • (d) $4.54\times {10}^5{\text{N·m}}^2/\text{C}$

3. A charge $q=2\mu \text{C}$ is inside a cube of side $0.1\text{m}$. Calculate the electric flux through one face of the cube.

   • (a) $3.76\times {10}^4{\text{N·m}}^2/\text{C}$
   • (b) $3.77\times {10}^4{\text{N·m}}^2/\text{C}$
   • (c) $3.78\times {10}^4{\text{N·m}}^2/\text{C}$
   • (d) $3.79\times {10}^4{\text{N·m}}^2/\text{C}$

4. An infinite line charge has linear charge density $\lambda =3\times {10}^{-6}\text{C/m}$. Calculate the electric field at a distance $r=0.5\text{m}$ from the line ($k=9\times {10}^9{\text{N·m}}^2/{\text{C}}^2$).

   • (a) $1.07\times {10}^4\text{N/C}$
   • (b) $1.08\times {10}^4\text{N/C}$
   • (c) $1.09\times {10}^4\text{N/C}$
   • (d) $1.10\times {10}^4\text{N/C}$

5. An infinite plane sheet has surface charge density $\sigma =5\times {10}^{-6}{\text{C/m}}^2$. Calculate the electric field near the sheet.

   • (a) $2.82\times {10}^5\text{N/C}$
   • (b) $2.83\times {10}^5\text{N/C}$
   • (c) $2.84\times {10}^5\text{N/C}$
   • (d) $2.85\times {10}^5\text{N/C}$

6. A spherical shell of radius $R=0.1\text{m}$ has total charge $Q=6\mu \text{C}$. Calculate the electric field at $r=0.05\text{m}$ and $r=0.3\text{m}$.

   • (a) $0,6.00\times {10}^5\text{N/C}$
   • (b) $0,6.01\times {10}^5\text{N/C}$
   • (c) $0,6.02\times {10}^5\text{N/C}$
   • (d) $0,6.03\times {10}^5\text{N/C}$

7. A solid sphere of radius $R=0.2\text{m}$ has volume charge density $\rho =2\times {10}^{-6}{\text{C/m}}^3$. Calculate the electric field at $r=0.1\text{m}$.

   • (a) $3.76\times {10}^5\text{N/C}$
   • (b) $3.77\times {10}^5\text{N/C}$
   • (c) $3.78\times {10}^5\text{N/C}$
   • (d) $3.79\times {10}^5\text{N/C}$

8. A spherical conductor of radius $R=0.15\text{m}$ has charge $Q=8\mu \text{C}$. Calculate the electric field just outside the surface.

   • (a) $3.19\times {10}^6\text{N/C}$
   • (b) $3.20\times {10}^6\text{N/C}$
   • (c) $3.21\times {10}^6\text{N/C}$
   • (d) $3.22\times {10}^6\text{N/C}$

9. Two parallel infinite sheets have surface charge densities ${\sigma }_1=4\times {10}^{-6}{\text{C/m}}^2$ and ${\sigma }_2=-4\times {10}^{-6}{\text{C/m}}^2$. Calculate the electric field between the sheets.

   • (a) $4.51\times {10}^5\text{N/C}$
   • (b) $4.52\times {10}^5\text{N/C}$
   • (c) $4.53\times {10}^5\text{N/C}$
   • (d) $4.54\times {10}^5\text{N/C}$

10. A thick slab extends from $z=-0.03\text{m}$ to $z=0.03\text{m}$ with volume charge density $\rho =1\times {10}^{-6}{\text{C/m}}^3$. Calculate the electric field at $z=0.02\text{m}$.

    • (a) $2.25\times {10}^5\text{N/C}$
    • (b) $2.26\times {10}^5\text{N/C}$
    • (c) $2.27\times {10}^5\text{N/C}$
    • (d) $2.28\times {10}^5\text{N/C}$

11. A uniform field $\overrightarrow{E}=400\hat{i}\text{N/C}$ passes through a circular surface of radius $0.5\text{m}$ in the yz-plane. Calculate the electric flux.

    • (a) $314.0{\text{N·m}}^2/\text{C}$
    • (b) $314.1{\text{N·m}}^2/\text{C}$
    • (c) $314.2{\text{N·m}}^2/\text{C}$
    • (d) $314.3{\text{N·m}}^2/\text{C}$

12. A point charge $q=-3\mu \text{C}$ is at the center of a spherical surface of radius $0.4\text{m}$. Calculate the electric flux through the surface.

    • (a) $-3.38\times {10}^5{\text{N·m}}^2/\text{C}$
    • (b) $-3.39\times {10}^5{\text{N·m}}^2/\text{C}$
    • (c) $-3.40\times {10}^5{\text{N·m}}^2/\text{C}$
    • (d) $-3.41\times {10}^5{\text{N·m}}^2/\text{C}$

13. An infinite line charge has $\lambda =1\times {10}^{-6}\text{C/m}$. Calculate the electric field at $r=0.1\text{m}$.

    • (a) $1.79\times {10}^5\text{N/C}$
    • (b) $1.80\times {10}^5\text{N/C}$
    • (c) $1.81\times {10}^5\text{N/C}$
    • (d) $1.82\times {10}^5\text{N/C}$

14. An infinite plane sheet has $\sigma =2\times {10}^{-6}{\text{C/m}}^2$. Calculate the electric field near the sheet.

    • (a) $1.12\times {10}^5\text{N/C}$
    • (b) $1.13\times {10}^5\text{N/C}$
    • (c) $1.14\times {10}^5\text{N/C}$
    • (d) $1.15\times {10}^5\text{N/C}$

15. A spherical shell of radius $R=0.3\text{m}$ has $Q=9\mu \text{C}$. Calculate the electric field at $r=0.5\text{m}$.

    • (a) $3.23\times {10}^5\text{N/C}$
    • (b) $3.24\times {10}^5\text{N/C}$
    • (c) $3.25\times {10}^5\text{N/C}$
    • (d) $3.26\times {10}^5\text{N/C}$

16. A solid sphere of radius $R=0.4\text{m}$ has $\rho =3\times {10}^{-6}{\text{C/m}}^3$. Calculate the electric field at $r=0.2\text{m}$.

    • (a) $1.12\times {10}^5\text{N/C}$
    • (b) $1.13\times {10}^5\text{N/C}$
    • (c) $1.14\times {10}^5\text{N/C}$
    • (d) $1.15\times {10}^5\text{N/C}$

17. A spherical conductor of radius $R=0.2\text{m}$ has $Q = engaged in a rocket engine, a conductor plate has $\sigma =2\times {10}^{-5}{\text{C/m}}^2$. Calculate the electric field just outside the plate.

    • (a) $2.25\times {10}^6\text{N/C}$
    • (b) $2.26\times {10}^6\text{N/C}$
    • (c) $2.27\times {10}^6\text{N/C}$
    • (d) $2.28\times {10}^6\text{N/C}$

18. Two parallel sheets have ${\sigma }_1=3\times {10}^{-6}{\text{C/m}}^2$, ${\sigma }_2=3\times {10}^{-6}{\text{C/m}}^2$. Calculate the electric field between the sheets.

    • (a) $0\text{N/C}$
    • (b) $1\times {10}^5\text{N/C}$
    • (c) $2\times {10}^5\text{N/C}$
    • (d) $3\times {10}^5\text{N/C}$

19. A thick slab from $z=-0.05\text{m}$ to $z=0.05\text{m}$ has $\rho =2\times {10}^{-6}{\text{C/m}}^3$. Calculate the electric field at $z=0.04\text{m}$.

    • (a) $9.03\times {10}^5\text{N/C}$
    • (b) $9.04\times {10}^5\text{N/C}$
    • (c) $9.05\times {10}^5\text{N/C}$
    • (d) $9.06\times {10}^5\text{N/C}$

20. A charge $q=5\mu \text{C}$ is at the center of a spherical surface of radius $0.5\text{m}$. Calculate the electric flux through the surface.

    • (a) $5.64\times {10}^5{\text{N·m}}^2/\text{C}$
    • (b) $5.65\times {10}^5{\text{N·m}}^2/\text{C}$
    • (c) $5.66\times {10}^5{\text{N·m}}^2/\text{C}$
    • (d) $5.67\times {10}^5{\text{N·m}}^2/\text{C}$

21. A uniform field $\overrightarrow{E}=800\hat{i}\text{N/C}$ passes through a rectangular surface of dimensions $0.2\text{m}\times 0.3\text{m}$ in the yz-plane. Calculate the electric flux.

    • (a) $47.9{\text{N·m}}^2/\text{C}$
    • (b) $48.0{\text{N·m}}^2/\text{C}$
    • (c) $48.1{\text{N·m}}^2/\text{C}$
    • (d) $48.2{\text{N·m}}^2/\text{C}$

22. An infinite line charge has $\lambda =6\times {10}^{-6}\text{C/m}$. Calculate the electric field at $r=0.2\text{m}$.

    • (a) $5.39\times {10}^5\text{N/C}$
    • (b) $5.40\times {10}^5\text{N/C}$
    • (c) $5.41\times {10}^5\text{N/C}$
    • (d) $5.42\times {10}^5\text{N/C}$

23. An infinite plane sheet has $\sigma =1\times {10}^{-6}{\text{C/m}}^2$. Calculate the electric field near the sheet.

    • (a) $5.64\times {10}^4\text{N/C}$
    • (b) $5.65\times {10}^4\text{N/C}$
    • (c) $5.66\times {10}^4\text{N/C}$
    • (d) $5.67\times {10}^4\text{N/C}$

24. A spherical shell of radius $R=0.5\text{m}$ has $Q=10\mu \text{C}$. Calculate the electric field at $r=0.7\text{m}$.

    • (a) $1.83\times {10}^5\text{N/C}$
    • (b) $1.84\times {10}^5\text{N/C}$
    • (c) $1.85\times {10}^5\text{N/C}$
    • (d) $1.86\times {10}^5\text{N/C}$

25. A solid sphere of radius $R=0.1\text{m}$ has $\rho =4\times {10}^{-6}{\text{C/m}}^3$. Calculate the electric field at $r=0.05\text{m}$.

    • (a) $7.52\times {10}^5\text{N/C}$
    • (b) $7.53\times {10}^5\text{N/C}$
    • (c) $7.54\times {10}^5\text{N/C}$
    • (d) $7.55\times {10}^5\text{N/C}$

26. A spherical conductor of radius $R=0.3\text{m}$ has $Q=12\mu \text{C}$. Calculate the electric field just outside the surface.

    • (a) $1.33\times {10}^6\text{N/C}$
    • (b) $1.34\times {10}^6\text{N/C}$
    • (c) $1.35\times {10}^6\text{N/C}$
    • (d) $1.36\times {10}^6\text{N/C}$

27. Two parallel sheets have ${\sigma }_1=6\times {10}^{-6}{\text{C/m}}^2$, ${\sigma }_2=-2\times {10}^{-6}{\text{C/m}}^2$. Calculate the electric field between the sheets.

    • (a) $2.25\times {10}^5\text{N/C}$
    • (b) $2.26\times {10}^5\text{N/C}$
    • (c) $2.27\times {10}^5\text{N/C}$
    • (d) $2.28\times {10}^5\text{N/C}$

28. A thick slab from $z=-0.02\text{m}$ to $z=0.02\text{m}$ has $\rho =5\times {10}^{-6}{\text{C/m}}^3$. Calculate the electric field at $z=0.01\text{m}$.

    • (a) $5.64\times {10}^5\text{N/C}$
    • (b) $5.65\times {10}^5\text{N/C}$
    • (c) $5.66\times {10}^5\text{N/C}$
    • (d) $5.67\times {10}^5\text{N/C}$

29. A charge $q=7\mu \text{C}$ is inside a cube of side $0.2\text{m}$. Calculate the electric flux through one face.

    • (a) $1.31\times {10}^5{\text{N·m}}^2/\text{C}$
    • (b) $1.32\times {10}^5{\text{N·m}}^2/\text{C}$
    • (c) $1.33\times {10}^5{\text{N·m}}^2/\text{C}$
    • (d) $1.34\times {10}^5{\text{N·m}}^2/\text{C}$

30. An infinite line charge has $\lambda =8\times {10}^{-6}\text{C/m}$. Calculate the electric field at $r=0.4\text{m}$.

    • (a) $3.59\times {10}^5\text{N/C}$
    • (b) $3.60\times {10}^5\text{N/C}$
    • (c) $3.61\times {10}^5\text{N/C}$
    • (d) $3.62\times {10}^5\text{N/C}$

31. In a rocket ion engine, a charged plate has $\sigma =1\times {10}^{-5}{\text{C/m}}^2$. Calculate the electric field just outside the plate to guide ions.

    • (a) $1.12\times {10}^6\text{N/C}$
    • (b) $1.13\times {10}^6\text{N/C}$
    • (c) $1.14\times {10}^6\text{N/C}$
    • (d) $1.15\times {10}^6\text{N/C}$

32. A spherical shell of radius $R=0.2\text{m}$ has $Q=4\mu \text{C}$. Calculate the electric field at $r=0.1\text{m}$.

    • (a) $0\text{N/C}$
    • (b) $1\times {10}^5\text{N/C}$
    • (c) $2\times {10}^5\text{N/C}$
    • (d) $3\times {10}^5\text{N/C}$

33. A solid sphere of radius $R=0.5\text{m}$ has $\rho =1\times {10}^{-6}{\text{C/m}}^3$. Calculate the electric field at $r=0.6\text{m}$.

    • (a) $2.09\times {10}^5\text{N/C}$
    • (b) $2.10\times {10}^5\text{N/C}$
    • (c) $2.11\times {10}^5\text{N/C}$
    • (d) $2.12\times {10}^5\text{N/C}$

34. Two parallel sheets have ${\sigma }_1=5\times {10}^{-6}{\text{C/m}}^2$, ${\sigma }_2=1\times {10}^{-6}{\text{C/m}}^2$. Calculate the electric field outside the sheets.

    • (a) $3.38\times {10}^5\text{N/C}$
    • (b) $3.39\times {10}^5\text{N/C}$
    • (c) $3.40\times {10}^5\text{N/C}$
    • (d) $3.41\times {10}^5\text{N/C}$

35. A thick slab from $z=-0.04\text{m}$ to $z=0.04\text{m}$ has $\rho =3\times {10}^{-6}{\text{C/m}}^3$. Calculate the electric field at $z=0.05\text{m}$.

    • (a) $1.35\times {10}^6\text{N/C}$
    • (b) $1.36\times {10}^6\text{N/C}$
    • (c) $1.37\times {10}^6\text{N/C}$
    • (d) $1.38\times {10}^6\text{N/C}$

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Conceptual Problems

36. What does electric flux measure?

• (a) Charge enclosed
• (b) Flow of electric field lines through a surface
• (c) Electric field strength
• (d) Potential energy

37. What does Gauss’s law relate?

• (a) Electric field to potential
• (b) Electric flux to charge enclosed
• (c) Charge to distance
• (d) Field to energy

38. What is the key requirement for using Gauss’s law effectively?

• (a) High charge density
• (b) Symmetry in charge distribution
• (c) Small Gaussian surface
• (d) No symmetry

39. What happens to the electric field inside a spherical shell?

• (a) Increases with radius
• (b) Decreases with radius
• (c) Zero
• (d) Infinite

40. What is the unit of electric flux in SI units?

• (a) ${\text{N·m}}^2/\text{C}$
• (b) $\text{N/C}$
• (c) $\text{J}$
• (d) $\text{V}$

41. What does a zero electric field inside a conductor indicate?

• (a) No charges present
• (b) Charges on the surface
• (c) Charges inside the conductor
• (d) No field lines

42. What is the field direction just outside a conductor?

• (a) Parallel to the surface
• (b) Perpendicular to the surface
• (c) Random
• (d) Zero

43. What is the physical significance of $\frac{\sigma }{{ϵ}_0}$?

• (a) Electric field inside a conductor
• (b) Electric field just outside a conductor
• (c) Electric flux
• (d) Charge density

44. What does the field inside a solid sphere depend on?

• (a) Total charge
• (b) Distance from the center
• (c) Surface charge density
• (d) No dependence

45. What is the dimension of electric flux?

• (a) $[\text{M}{\text{L}}^3{\text{T}}^{-3}{\text{A}}^{-1}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

46. What does a zero flux through a closed surface indicate?

• (a) No electric field
• (b) No charge enclosed
• (c) Maximum field
• (d) No field lines

47. What is the significance of $\frac{\lambda }{2\pi {ϵ}_{0}r}$?

• (a) Field due to a point charge
• (b) Field due to an infinite line charge
• (c) Field due to a plane
• (d) Field inside a conductor

48. What happens to the field between two parallel sheets with opposite charges?

• (a) Zero
• (b) Fields add
• (c) Fields subtract
• (d) Fields cancel outside

49. What does the field inside a thick slab depend on?

• (a) Total charge
• (b) Distance from the center
• (c) Surface charge density
• (d) No dependence

50. How does Gauss’s law apply to rocket ion engines?

• (a) Calculates magnetic fields
• (b) Calculates electric fields for ion acceleration
• (c) Reduces charge
• (d) Increases distance

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Derivation Problems

51. Derive Gauss’s law from Coulomb’s law for a point charge.

52. Derive the electric field due to an infinite line charge using Gauss’s law.

53. Derive the electric field due to an infinite plane sheet using Gauss’s law.

54. Derive the electric field due to a spherical shell using Gauss’s law.

55. Derive the electric field due to a uniformly charged solid sphere using Gauss’s law.

56. Derive the electric field inside a conductor in electrostatic equilibrium.

57. Derive the electric field just outside a conductor surface.

58. Derive the electric field between two parallel charged sheets.

59. Derive the electric field inside a thick slab with volume charge density.

60. Derive the flux through a closed surface due to an external charge.

61. Derive the field due to a spherical conductor with a cavity containing a charge.

62. Derive the field outside a conductor near a point charge.

63. Derive the relation $\frac{Q_{\text{enc}}}{{ϵ}_0}$ for a complex charge distribution.

64. Derive the field due to a cylindrical shell of charge.

65. Derive the flux through a Gaussian surface with multiple charges inside and outside.

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NEET-style Conceptual Problems

66. What is the unit of surface charge density $\sigma$?

• (a) ${\text{C/m}}^2$
• (b) $\text{N/C}$
• (c) $\text{J}$
• (d) $\text{V}$

67. What does a negative electric flux through a surface indicate?

• (a) Field lines entering the surface
• (b) No charge enclosed
• (c) Maximum field
• (d) No field lines

68. Which symmetry is used for an infinite line charge?

• (a) Spherical
• (b) Cylindrical
• (c) Planar
• (d) No symmetry

69. What happens to the field inside a conductor with a cavity containing no charge?

• (a) Increases
• (b) Decreases
• (c) Zero
• (d) Infinite

70. What is the dimension of ${ϵ}_0$?

• (a) $[{\text{M}}^{-1}{\text{L}}^{-3}{\text{T}}^4{\text{A}}^2]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

71. What does the choice of Gaussian surface depend on?

• (a) Charge magnitude
• (b) Symmetry of the charge distribution
• (c) Field strength
• (d) Potential energy

72. What is the role of symmetry in Gauss’s law?

• (a) Increases field strength
• (b) Simplifies field calculations
• (c) Reduces charge
• (d) Increases distance

73. What happens to the field inside a spherical shell at $r=0$?

• (a) Maximum
• (b) Minimum
• (c) Zero
• (d) Infinite

74. Why does the field just outside a conductor depend on $\sigma$?

• (a) Due to symmetry
• (b) Due to Gauss’s law
• (c) Due to field lines
• (d) Due to charge quantization

75. What is the unit of linear charge density $\lambda$?

• (a) $\text{C/m}$
• (b) $\text{N/C}$
• (c) $\text{J}$
• (d) $\text{V}$

76. What does a constant field near an infinite plane indicate?

• (a) Field depends on distance
• (b) Field is independent of distance
• (c) Field is zero
• (d) Field is infinite

77. Which type of charge distribution produces a field proportional to $r$ inside?

• (a) Spherical shell
• (b) Infinite plane
• (c) Solid sphere
• (d) Line charge

78. What is the direction of the field between two parallel sheets with opposite charges?

• (a) From positive to negative
• (b) From negative to positive
• (c) Perpendicular to sheets
• (d) Zero

79. What does a pseudo-force do in a non-inertial frame for fields in conductors?

• (a) Affects perceived field
• (b) Affects charge distribution
• (c) Creates flux
• (d) Reduces field strength

80. What is the dimension of volume charge density $\rho$?

• (a) $[\text{A}\text{T}{\text{L}}^{-3}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

81. What is the role of Gauss’s law in rocket ion propulsion?

• (a) Reduces charge
• (b) Calculates fields for ion acceleration
• (c) Increases distance
• (d) Decreases field

82. What happens to the field inside a conductor with a cavity containing a charge?

• (a) Zero in the conductor material
• (b) Non-zero everywhere
• (c) Zero in the cavity
• (d) Infinite

83. Why does the field due to an infinite plane not depend on distance?

• (a) Due to symmetry
• (b) Due to charge quantization
• (c) Due to field lines
• (d) Due to work done

84. What is the significance of $\frac{\rho r}{3{ϵ}_0}$?

• (a) Field inside a spherical shell
• (b) Field inside a solid sphere
• (c) Field outside a conductor
• (d) Flux through a surface

85. What is the unit of ${ϵ}_0$?

• (a) ${\text{C}}^2/{\text{N·m}}^2$
• (b) ${\text{N·m}}^2/{\text{C}}^2$
• (c) $\text{J}$
• (d) $\text{V}$

86. What does a zero field between two parallel sheets indicate?

• (a) Opposite charges
• (b) Same charges of equal magnitude
• (c) No charges
• (d) Infinite charges

87. What is the physical significance of $\frac{Q_{\text{enc}}}{{ϵ}_0}$?

• (a) Electric field
• (b) Electric flux through a closed surface
• (c) Charge density
• (d) Potential energy

88. Why does the field inside a thick slab increase linearly?

• (a) Due to constant $\rho$ and increasing $Q_{\text{enc}}$
• (b) Due to symmetry
• (c) Due to field lines
• (d) Due to charge quantization

89. What is the dimension of $\sigma$?

• (a) $[\text{A}\text{T}{\text{L}}^{-2}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

90. How does Gauss’s law help in ion propulsion design?

• (a) Increases charge
• (b) Calculates fields for ion trajectories
• (c) Reduces field
• (d) Increases distance

91. What is the role of $Q_{\text{enc}}$ in Gauss’s law?

• (a) Determines field strength
• (b) Determines flux through the surface
• (c) Determines distance
• (d) Determines charge density

92. What does a field of $\frac{\sigma }{2{ϵ}_0}$ indicate?

• (a) Field due to a point charge
• (b) Field due to an infinite plane
• (c) Field inside a conductor
• (d) Field inside a sphere

93. What is the physical significance of $E(4\pi r^2)=\frac{Q}{{ϵ}_0}$?

• (a) Flux through a surface
• (b) Gauss’s law for a spherical surface
• (c) Field inside a conductor
• (d) Charge density

94. What is the dimension of $\lambda$?

• (a) $[\text{A}\text{T}{\text{L}}^{-1}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

95. Why does the field outside a conductor depend on total charge?

• (a) Due to symmetry
• (b) Due to Gauss’s law
• (c) Due to field lines
• (d) Due to charge quantization

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NEET-style Numerical Problems

96. A point charge $q=1\mu \text{C}$ is at the center of a spherical surface of radius $0.1\text{m}$. Calculate the electric flux through the surface.

• (a) $1.12\times {10}^5{\text{N·m}}^2/\text{C}$
• (b) $1.13\times {10}^5{\text{N·m}}^2/\text{C}$
• (c) $1.14\times {10}^5{\text{N·m}}^2/\text{C}$
• (d) $1.15\times {10}^5{\text{N·m}}^2/\text{C}$

97. An infinite line charge has $\lambda =2\times {10}^{-6}\text{C/m}$. Calculate the electric field at $r=0.3\text{m}$.

• (a) $1.19\times {10}^5\text{N/C}$
• (b) $1.20\times {10}^5\text{N/C}$
• (c) $1.21\times {10}^5\text{N/C}$
• (d) $1.22\times {10}^5\text{N/C}$

98. A spherical conductor of radius $R=0.1\text{m}$ has $Q=5\mu \text{C}$. Calculate the electric field just outside the surface.

• (a) $4.49\times {10}^6\text{N/C}$
• (b) $4.50\times {10}^6\text{N/C}$
• (c) $4.51\times {10}^6\text{N/C}$
• (d) $4.52\times {10}^6\text{N/C}$

99. Two parallel sheets have ${\sigma }_1=2\times {10}^{-6}{\text{C/m}}^2$, ${\sigma }_2=-2\times {10}^{-6}{\text{C/m}}^2$. Calculate the electric field between the sheets.

• (a) $2.25\times {10}^5\text{N/C}$
• (b) $2.26\times {10}^5\text{N/C}$
• (c) $2.27\times {10}^5\text{N/C}$
• (d) $2.28\times {10}^5\text{N/C}$

100. A solid sphere of radius $R=0.2\text{m}$ has $\rho =2\times {10}^{-6}{\text{C/m}}^3$. Calculate the electric field at $r=0.1\text{m}$.
     - (a) $3.76\times {10}^5\text{N/C}$
     - (b) $3.77\times {10}^5\text{N/C}$
     - (c) $3.78\times {10}^5\text{N/C}$
     - (d) $3.79\times {10}^5\text{N/C}$

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