Coulomb’s Law Problems

This section provides 100 problems to test your understanding of Coulomb’s law, including electric forces, vector analysis, superposition principle, equilibrium positions, and electric fields. 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. Two charges $q_1=+3\mu \text{C}$ and $q_2=-6\mu \text{C}$ are separated by $r=0.2\text{m}$ in vacuum. Calculate the force magnitude ($k=9\times {10}^9{\text{N·m}}^2/{\text{C}}^2$).

   • (a) $4.03\text{N}$
   • (b) $4.04\text{N}$
   • (c) $4.05\text{N}$
   • (d) $4.06\text{N}$

2. Two charges $q_1=+4\text{nC}$ and $q_2=+4\text{nC}$ are separated by $r=0.1\text{m}$ in vacuum. Calculate the force magnitude.

   • (a) $1.43\times {10}^{-5}\text{N}$
   • (b) $1.44\times {10}^{-5}\text{N}$
   • (c) $1.45\times {10}^{-5}\text{N}$
   • (d) $1.46\times {10}^{-5}\text{N}$

3. Two charges $q_1=+2\mu \text{C}$ and $q_2=-5\mu \text{C}$ are separated by $r=0.5\text{m}$ in water (${ϵ}_r=80$). Calculate the force magnitude.

   • (a) $0.0289\text{N}$
   • (b) $0.0290\text{N}$
   • (c) $0.0291\text{N}$
   • (d) $0.0292\text{N}$

4. A charge of $+10\mu \text{C}$ is created by removing electrons. How many electrons were removed? ($e=1.6\times {10}^{-19}\text{C}$)

   • (a) $6.24\times {10}^{13}$
   • (b) $6.25\times {10}^{13}$
   • (c) $6.26\times {10}^{13}$
   • (d) $6.27\times {10}^{13}$

5. Charges $q_1=+2\mu \text{C}$ at $(0,0)$ and $q_2=-3\mu \text{C}$ at $(0.4,0)$. Calculate the force on $q_1$ (vector form).

   • (a) $-0.843\hat{i}\text{N}$
   • (b) $-0.844\hat{i}\text{N}$
   • (c) $-0.845\hat{i}\text{N}$
   • (d) $-0.846\hat{i}\text{N}$

6. Charges $q_1=+5\mu \text{C}$ at $(0,0)$ and $q_2=+5\mu \text{C}$ at $(0,0.3)$. Calculate the force vector on $q_1$.

   • (a) $0.499\hat{j}\text{N}$
   • (b) $0.500\hat{j}\text{N}$
   • (c) $0.501\hat{j}\text{N}$
   • (d) $0.502\hat{j}\text{N}$

7. Charges $q_1=+3\mu \text{C}$ at $(0,0)$, $q_2=-2\mu \text{C}$ at $(0.2,0)$, $q_3=+4\mu \text{C}$ at $(0,0.2)$. Calculate the net force on $q_1$ (magnitude).

   • (a) $2.19\text{N}$
   • (b) $2.20\text{N}$
   • (c) $2.21\text{N}$
   • (d) $2.22\text{N}$

8. Charges $q_1=+q$ at $(0,0)$, $q_2=+q$ at $(a,0)$. Where should $q_3=-q$ be placed on the x-axis for zero net force?

   • (a) $x=0.49a$
   • (b) $x=0.50a$
   • (c) $x=0.51a$
   • (d) $x=0.52a$

9. Calculate the electric field at $(0,0.4)$ due to $q=+6\mu \text{C}$ at $(0,0)$.

   • (a) $3.37\times {10}^5\hat{j}\text{N/C}$
   • (b) $3.38\times {10}^5\hat{j}\text{N/C}$
   • (c) $3.39\times {10}^5\hat{j}\text{N/C}$
   • (d) $3.40\times {10}^5\hat{j}\text{N/C}$

10. Charges $q_1=+2\mu \text{C}$ at $(0.2,0)$, $q_2=-2\mu \text{C}$ at $(-0.2,0)$. Calculate the electric field at $(0,0.3)$ (magnitude).

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

11. A ring of charge (radius $R=0.1\text{m}$, total charge $Q=5\mu \text{C}$) lies in the xy-plane. Calculate the electric field on the axis at $z=0.1\text{m}$.

    • (a) $1.59\times {10}^6\text{N/C}$
    • (b) $1.60\times {10}^6\text{N/C}$
    • (c) $1.61\times {10}^6\text{N/C}$
    • (d) $1.62\times {10}^6\text{N/C}$

12. Two charges $q_1=+8\mu \text{C}$ and $q_2=-4\mu \text{C}$ are separated by $r=0.3\text{m}$ in vacuum. Calculate the force magnitude.

    • (a) $3.19\text{N}$
    • (b) $3.20\text{N}$
    • (c) $3.21\text{N}$
    • (d) $3.22\text{N}$

13. Charges $q_1=+3\mu \text{C}$ at $(0.1,0.1)$ and $q_2=-3\mu \text{C}$ at $(0,0)$. Calculate the force on $q_1$ (magnitude).

    • (a) $0.955\text{N}$
    • (b) $0.956\text{N}$
    • (c) $0.957\text{N}$
    • (d) $0.958\text{N}$

14. Charges $q_1=+q$, $q_2=+4q$ at $x=0$ and $x=a$. Where should $q_3=-q$ be placed for equilibrium?

    • (a) $x=0.32a$
    • (b) $x=0.33a$
    • (c) $x=0.34a$
    • (d) $x=0.35a$

15. Calculate the electric field at $(0.2,0)$ due to $q=-4\mu \text{C}$ at $(0,0)$.

    • (a) $-8.99\times {10}^5\hat{i}\text{N/C}$
    • (b) $-9.00\times {10}^5\hat{i}\text{N/C}$
    • (c) $-9.01\times {10}^5\hat{i}\text{N/C}$
    • (d) $-9.02\times {10}^5\hat{i}\text{N/C}$

16. Two charges $q_1=+5\mu \text{C}$ and $q_2=-5\mu \text{C}$ are separated by $r=0.4\text{m}$ in air (${ϵ}_r=1$). Calculate the force magnitude.

    • (a) $1.40\text{N}$
    • (b) $1.41\text{N}$
    • (c) $1.42\text{N}$
    • (d) $1.43\text{N}$

17. Charges $q_1=+2\mu \text{C}$ at $(0,0)$, $q_2=-3\mu \text{C}$ at $(0.5,0)$, $q_3=+1\mu \text{C}$ at $(0,0.5)$. Calculate the net force on $q_1$ (magnitude).

    • (a) $0.509\text{N}$
    • (b) $0.510\text{N}$
    • (c) $0.511\text{N}$
    • (d) $0.512\text{N}$

18. Calculate the electric field at $(0,0.5)$ due to $q=+8\mu \text{C}$ at $(0,0)$.

    • (a) $2.87\times {10}^5\hat{j}\text{N/C}$
    • (b) $2.88\times {10}^5\hat{j}\text{N/C}$
    • (c) $2.89\times {10}^5\hat{j}\text{N/C}$
    • (d) $2.90\times {10}^5\hat{j}\text{N/C}$

19. A line charge with $\lambda =2\times {10}^{-6}\text{C/m}$, length $L=0.2\text{m}$, lies on the x-axis. Calculate the electric field at $(0,0.1)$ (midpoint perpendicular).

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

20. Two charges $q_1=+6\mu \text{C}$ and $q_2=-3\mu \text{C}$ are separated by $r=0.2\text{m}$ in vacuum. Calculate the force magnitude.

    • (a) $4.03\text{N}$
    • (b) $4.04\text{N}$
    • (c) $4.05\text{N}$
    • (d) $4.06\text{N}$

21. Charges $q_1=+4\mu \text{C}$ at $(0.3,0)$, $q_2=-4\mu \text{C}$ at $(0,0)$. Calculate the force vector on $q_1$.

    • (a) $-1.599\hat{i}\text{N}$
    • (b) $-1.600\hat{i}\text{N}$
    • (c) $-1.601\hat{i}\text{N}$
    • (d) $-1.602\hat{i}\text{N}$

22. Charges $q_1=+q$ at $(0,0)$, $q_2=+q$ at $(a,0)$, $q_3=-2q$ at $(x,0)$. Find $x$ for equilibrium of $q_3$.

    • (a) $0.41a$
    • (b) $0.42a$
    • (c) $0.43a$
    • (d) $0.44a$

23. Calculate the electric field at $(0.1,0.1)$ due to $q=+3\mu \text{C}$ at $(0,0)$.

    • (a) $1.90\times {10}^5(\hat{i}+\hat{j})\text{N/C}$
    • (b) $1.91\times {10}^5(\hat{i}+\hat{j})\text{N/C}$
    • (c) $1.92\times {10}^5(\hat{i}+\hat{j})\text{N/C}$
    • (d) $1.93\times {10}^5(\hat{i}+\hat{j})\text{N/C}$

24. A ring of charge (radius $R=0.05\text{m}$, total charge $Q=2\mu \text{C}$) lies in the xy-plane. Calculate the electric field at $z=0.05\text{m}$.

    • (a) $1.27\times {10}^6\text{N/C}$
    • (b) $1.28\times {10}^6\text{N/C}$
    • (c) $1.29\times {10}^6\text{N/C}$
    • (d) $1.30\times {10}^6\text{N/C}$

25. Two charges $q_1=+1\mu \text{C}$ and $q_2=-2\mu \text{C}$ are separated by $r=0.1\text{m}$ in vacuum. Calculate the force magnitude.

    • (a) $1.79\text{N}$
    • (b) $1.80\text{N}$
    • (c) $1.81\text{N}$
    • (d) $1.82\text{N}$

26. Charges $q_1=+5\mu \text{C}$ at $(0,0)$, $q_2=-2\mu \text{C}$ at $(0.2,0.2)$, $q_3=+3\mu \text{C}$ at $(0.2,0)$. Calculate the net force on $q_1$ (magnitude).

    • (a) $1.58\text{N}$
    • (b) $1.59\text{N}$
    • (c) $1.60\text{N}$
    • (d) $1.61\text{N}$

27. Calculate the electric field at $(0,0.2)$ due to $q=-7\mu \text{C}$ at $(0,0)$.

    • (a) $-1.574\times {10}^6\hat{j}\text{N/C}$
    • (b) $-1.575\times {10}^6\hat{j}\text{N/C}$
    • (c) $-1.576\times {10}^6\hat{j}\text{N/C}$
    • (d) $-1.577\times {10}^6\hat{j}\text{N/C}$

28. A charge of $+15\mu \text{C}$ is created by removing electrons. How many electrons were removed? ($e=1.6\times {10}^{-19}\text{C}$)

    • (a) $9.37\times {10}^{13}$
    • (b) $9.38\times {10}^{13}$
    • (c) $9.39\times {10}^{13}$
    • (d) $9.40\times {10}^{13}$

29. Charges $q_1=+q$ at $(0,0)$, $q_2=+9q$ at $(a,0)$. Where should $q_3=-q$ be placed for equilibrium?

    • (a) $x=0.24a$
    • (b) $x=0.25a$
    • (c) $x=0.26a$
    • (d) $x=0.27a$

30. Two charges $q_1=+3\mu \text{C}$ and $q_2=-6\mu \text{C}$ are separated by $r=0.3\text{m}$ in a medium (${ϵ}_r=2$). Calculate the force magnitude.

    • (a) $1.79\text{N}$
    • (b) $1.80\text{N}$
    • (c) $1.81\text{N}$
    • (d) $1.82\text{N}$

31. In a rocket ion engine, charges $q_1=+2\mu \text{C}$ at $(0,0)$, $q_2=-3\mu \text{C}$ at $(0.1,0)$ steer a particle $q_3=+1\mu \text{C}$ at $(0,0.1)$. Calculate the net force on $q_3$ (magnitude).

    • (a) $2.47\text{N}$
    • (b) $2.48\text{N}$
    • (c) $2.49\text{N}$
    • (d) $2.50\text{N}$

32. Calculate the electric field at $(-0.2,0)$ due to $q=+5\mu \text{C}$ at $(0,0)$.

    • (a) $1.124\times {10}^6\hat{i}\text{N/C}$
    • (b) $1.125\times {10}^6\hat{i}\text{N/C}$
    • (c) $1.126\times {10}^6\hat{i}\text{N/C}$
    • (d) $1.127\times {10}^6\hat{i}\text{N/C}$

33. A ring of charge (radius $R=0.2\text{m}$, total charge $Q=10\mu \text{C}$) lies in the xy-plane. Calculate the electric field at $z=0.2\text{m}$.

    • (a) $1.99\times {10}^6\text{N/C}$
    • (b) $2.00\times {10}^6\text{N/C}$
    • (c) $2.01\times {10}^6\text{N/C}$
    • (d) $2.02\times {10}^6\text{N/C}$

34. Charges $q_1=+q$ at $(0,0)$, $q_2=+q$ at $(0,a)$, $q_3=-q$ at $(x,0)$. Find $x$ for equilibrium of $q_3$.

    • (a) $0.40a$
    • (b) $0.41a$
    • (c) $0.42a$
    • (d) $0.43a$

35. Charges $q_1=+4\mu \text{C}$ at $(0.2,0.2)$, $q_2=-2\mu \text{C}$ at $(0,0)$. Calculate the force on $q_1$ (magnitude).

    • (a) $0.449\text{N}$
    • (b) $0.450\text{N}$
    • (c) $0.451\text{N}$
    • (d) $0.452\text{N}$

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Conceptual Problems

36. What does Coulomb’s law describe?

• (a) Magnetic force between charges
• (b) Electric force between point charges
• (c) Gravitational force
• (d) Nuclear force

37. What is the direction of the force between two positive charges?

• (a) Attractive
• (b) Repulsive
• (c) No force
• (d) Perpendicular

38. What does the superposition principle state?

• (a) Forces are scalar quantities
• (b) Net force is the vector sum of individual forces
• (c) Forces cancel out
• (d) Forces are independent of distance

39. What happens to the force in a medium with ${ϵ}_r>1$?

• (a) Increases
• (b) Decreases
• (c) Remains the same
• (d) Becomes zero

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

• (a) Coulomb
• (b) Newton
• (c) Joule
• (d) Volt

41. What does a zero net force on a charge indicate?

• (a) No other charges present
• (b) Charge is in equilibrium
• (c) Charge is moving
• (d) Charge is neutral

42. What does the electric field represent?

• (a) Force per unit mass
• (b) Force per unit charge
• (c) Energy per unit charge
• (d) Charge per unit area

43. What is the physical significance of $k\frac{q}{r^2}$?

• (a) Electric force
• (b) Electric field magnitude
• (c) Electric potential
• (d) Charge density

44. What does charge quantization imply?

• (a) Charge is continuous
• (b) Charge is discrete, $q=ne$
• (c) Charge is zero
• (d) Charge is infinite

45. What is the dimension of electric force?

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

46. What does a negative force magnitude in Coulomb’s law indicate?

• (a) Repulsive force
• (b) Attractive force
• (c) No force
• (d) Perpendicular force

47. What is the significance of ${ϵ}_0$ in Coulomb’s law?

• (a) Permittivity of free space
• (b) Permittivity of medium
• (c) Charge density
• (d) Electric field

48. What happens to the force if the distance between charges doubles?

• (a) Increases by 4
• (b) Decreases by 4
• (c) Doubles
• (d) Halves

49. What does the electric field direction indicate for a positive charge?

• (a) Points inward
• (b) Points outward
• (c) Points perpendicular
• (d) No direction

50. How does Coulomb’s law apply to ion propulsion in rockets?

• (a) Calculates magnetic forces
• (b) Determines electric forces for steering charged particles
• (c) Reduces charge
• (d) Increases distance

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Derivation Problems

51. Derive the vector form of Coulomb’s law ${\overrightarrow{F}}_{1,2}=k\frac{q_1{q}_2}{r^2}{\hat{r}}_{12}$.

52. Derive the force in a medium $F_{\text{medium}}=\frac{F_{\text{vacuum}}}{{ϵ}_r}$.

53. Derive the electric field from Coulomb’s law $\overrightarrow{E}=k\frac{q}{r^2}\hat{r}$.

54. Derive the equilibrium position for a charge between two like charges.

55. Derive the net force on a charge due to multiple charges using the superposition principle.

56. Derive the electric field on the axis of a ring of charge.

57. Derive the force components in 2D for two charges.

58. Derive the charge quantization relation $q=ne$.

59. Derive the electric field due to a line charge at a perpendicular distance.

60. Derive the net electric field at a point due to multiple charges.

61. Derive the force magnitude in Coulomb’s law $F=k\frac{|q_1{q}_2|}{r^2}$.

62. Derive the equilibrium position for a charge in a non-linear arrangement.

63. Derive the relation between $k$ and ${ϵ}_0$ in Coulomb’s law.

64. Derive the superposition principle for electric fields.

65. Derive the force on a charge in a triangular arrangement of charges.

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NEET-style Conceptual Problems

66. What is the unit of electric field in SI units?

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

67. What does a positive electric field direction indicate for a negative charge?

• (a) Points away from the charge
• (b) Points toward the charge
• (c) No direction
• (d) Perpendicular

68. Which principle allows the calculation of net force from multiple charges?

• (a) Quantization
• (b) Superposition
• (c) Conservation
• (d) Equilibrium

69. What happens to the force if the charges are doubled?

• (a) Doubles
• (b) Halves
• (c) Quadruples
• (d) Remains the same

70. What is the dimension of Coulomb’s constant $k$?

• (a) $[\text{M}{\text{L}}^3{\text{T}}^{-4}{\text{A}}^{-2}]$
• (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 permittivity of free space ${ϵ}_0$ represent?

• (a) Charge density
• (b) Medium’s resistance to electric fields
• (c) Ability of vacuum to permit electric fields
• (d) Electric field strength

72. What is the role of vector addition in Coulomb’s law?

• (a) Determines magnitude only
• (b) Determines net force direction and magnitude
• (c) Reduces force
• (d) Increases distance

73. What happens to the electric field if the distance from the charge triples?

• (a) Increases by 9
• (b) Decreases by 9
• (c) Triples
• (d) Decreases by 3

74. Why does a medium reduce the force between charges?

• (a) Increases distance
• (b) Reduces permittivity
• (c) Polarization reduces effective field
• (d) Increases charge

75. What is the unit of force in Coulomb’s law?

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

76. What does a constant $k=\frac{1}{4\pi {ϵ}_0}$ indicate?

• (a) Charge quantization
• (b) Relation between force and permittivity
• (c) Electric field
• (d) Potential energy

77. Which type of force does Coulomb’s law describe?

• (a) Magnetic
• (b) Electric
• (c) Gravitational
• (d) Frictional

78. What is the direction of the electric field due to a negative charge?

• (a) Outward
• (b) Inward
• (c) Perpendicular
• (d) Random

79. What does a pseudo-force do in a non-inertial frame for charged particles?

• (a) Affects perceived electric force
• (b) Affects charge magnitude
• (c) Creates magnetic fields
• (d) Reduces field strength

80. What is the dimension of electric charge?

• (a) $[\text{A}\text{T}]$
• (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 Coulomb’s law in rocket ion propulsion?

• (a) Increases charge
• (b) Calculates forces for steering charged particles
• (c) Reduces field
• (d) Increases distance

82. What happens to the force if ${ϵ}_r$ increases?

• (a) Increases
• (b) Decreases
• (c) Remains constant
• (d) Becomes zero

83. Why does the force follow an inverse square law?

• (a) Due to charge quantization
• (b) Due to spherical symmetry of field
• (c) Due to medium effects
• (d) Due to vector addition

84. What is the significance of $k\frac{q_1{q}_2}{r^2}{\hat{r}}_{12}$?

• (a) Scalar force
• (b) Vector electric force
• (c) Electric field
• (d) Potential energy

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 electric field at a point indicate?

• (a) No charges present
• (b) Net field cancels out
• (c) Maximum force
• (d) No charge movement

87. What is the physical significance of $q=ne$?

• (a) Charge conservation
• (b) Charge quantization
• (c) Force calculation
• (d) Field strength

88. Why does the electric field point away from a positive charge?

• (a) Due to repulsion of a positive test charge
• (b) Due to attraction
• (c) Due to medium effects
• (d) Due to charge quantization

89. What is the dimension of electric field?

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

90. How does superposition help in ion propulsion systems?

• (a) Reduces charge
• (b) Calculates net force for particle steering
• (c) Increases field
• (d) Decreases distance

91. What is the role of distance in Coulomb’s law?

• (a) Linear dependence
• (b) Inverse square dependence
• (c) No dependence
• (d) Exponential dependence

92. What does a high ${ϵ}_r$ indicate?

• (a) Stronger force
• (b) Weaker force in the medium
• (c) No effect on force
• (d) Increased charge

93. What is the physical significance of $\frac{1}{4\pi {ϵ}_0}$?

• (a) Electric field
• (b) Coulomb’s constant
• (c) Charge density
• (d) Potential energy

94. What is the dimension of ${\overrightarrow{r}}_{12}$ in Coulomb’s law?

• (a) $[\text{L}]$
• (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 force depend on the product of charges?

• (a) Due to linear nature of electric forces
• (b) Due to inverse square law
• (c) Due to charge quantization
• (d) Due to medium effects

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NEET-style Numerical Problems

96. Two charges $q_1=+2\mu \text{C}$ and $q_2=-4\mu \text{C}$ are separated by $r=0.1\text{m}$ in vacuum. What is the force magnitude?

• (a) $7.19\text{N}$
• (b) $7.20\text{N}$
• (c) $7.21\text{N}$
• (d) $7.22\text{N}$

97. Charges $q_1=+3\mu \text{C}$ at $(0,0)$, $q_2=-3\mu \text{C}$ at $(0.2,0)$. What is the force on $q_1$ (magnitude)?

• (a) $2.02\text{N}$
• (b) $2.03\text{N}$
• (c) $2.04\text{N}$
• (d) $2.05\text{N}$

98. Calculate the electric field at $(0,0.3)$ due to $q=+5\mu \text{C}$ at $(0,0)$.

• (a) $4.99\times {10}^5\hat{j}\text{N/C}$
• (b) $5.00\times {10}^5\hat{j}\text{N/C}$
• (c) $5.01\times {10}^5\hat{j}\text{N/C}$
• (d) $5.02\times {10}^5\hat{j}\text{N/C}$

99. A charge of $+12\mu \text{C}$ is created by removing electrons. How many electrons were removed? ($e=1.6\times {10}^{-19}\text{C}$)

• (a) $7.49\times {10}^{13}$
• (b) $7.50\times {10}^{13}$
• (c) $7.51\times {10}^{13}$
• (d) $7.52\times {10}^{13}$

100. Charges $q_1=+q$ at $(0,0)$, $q_2=+q$ at $(a,0)$, $q_3=-q$ at $(x,0)$. Where is $q_3$ in equilibrium?
     - (a) $x=0.49a$
     - (b) $x=0.50a$
     - (c) $x=0.51a$
     - (d) $x=0.52a$

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