Electric Fields Problems

This section provides 100 problems to test your understanding of electric fields, including field calculations for point charges and charge distributions, electric field lines, and the motion of charges in 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. Calculate the electric field at $(0,0.3)$ due to a charge $q=+5\mu \text{C}$ at $(0,0)$ ($k=9\times {10}^9{\text{N·m}}^2/{\text{C}}^2$).

   • (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) $5.02\times {10}^5\hat{j}\text{N/C}$

2. A charge $q=-2\mu \text{C}$ is at $(0,0)$. Calculate the electric field at $(0.4,0)$.

   • (a) $-1.124\times {10}^5\hat{i}\text{N/C}$
   • (b) $-1.125\times {10}^5\hat{i}\text{N/C}$
   • (c) $-1.126\times {10}^5\hat{i}\text{N/C}$
   • (d) $-1.127\times {10}^5\hat{i}\text{N/C}$

3. Two charges $q_1=+3\mu \text{C}$ at $(0.2,0)$ and $q_2=-3\mu \text{C}$ at $(-0.2,0)$. Calculate the electric field at $(0,0.2)$ (magnitude).

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

4. A line charge with $\lambda =4\times {10}^{-6}\text{C/m}$, length $L=0.5\text{m}$, lies along the x-axis from $-0.25$ to $0.25$. Calculate the electric field at $(0,0.2)$ (magnitude).

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

5. A ring of charge (radius $R=0.1\text{m}$, total charge $Q=2\mu \text{C}$) lies in the xy-plane. Calculate the electric field on the z-axis at $z=0.1\text{m}$.

   • (a) $6.36\times {10}^5\text{N/C}$
   • (b) $6.37\times {10}^5\text{N/C}$
   • (c) $6.38\times {10}^5\text{N/C}$
   • (d) $6.39\times {10}^5\text{N/C}$

6. A disk of radius $R=0.2\text{m}$, surface charge density $\sigma =3\times {10}^{-6}{\text{C/m}}^2$, lies in the xy-plane. Calculate the electric field on the z-axis at $z=0.1\text{m}$ (${ϵ}_0=8.85\times {10}^{-12}{\text{C}}^2/{\text{N·m}}^2$).

   • (a) $6.27\times {10}^4\text{N/C}$
   • (b) $6.28\times {10}^4\text{N/C}$
   • (c) $6.29\times {10}^4\text{N/C}$
   • (d) $6.30\times {10}^4\text{N/C}$

7. An electron ($q=-1.6\times {10}^{-19}\text{C}$, $m=9.1\times {10}^{-31}\text{kg}$) is in a uniform field $\overrightarrow{E}=1000\hat{i}\text{N/C}$, starting at rest. Calculate its position after $t=2\text{ns}$.

   • (a) $-1.755\times {10}^{-4}\hat{i}\text{m}$
   • (b) $-1.756\times {10}^{-4}\hat{i}\text{m}$
   • (c) $-1.757\times {10}^{-4}\hat{i}\text{m}$
   • (d) $-1.758\times {10}^{-4}\hat{i}\text{m}$

8. A proton ($q=1.6\times {10}^{-19}\text{C}$, $m=1.67\times {10}^{-27}\text{kg}$) in $\overrightarrow{E}=500\hat{j}\text{N/C}$, with ${\overrightarrow{v}}_0=2\times {10}^4\hat{i}\text{m/s}$. Calculate the trajectory equation.

   • (a) $y=2.39\times {10}^2{x}^2$
   • (b) $y=2.40\times {10}^2{x}^2$
   • (c) $y=2.41\times {10}^2{x}^2$
   • (d) $y=2.42\times {10}^2{x}^2$

9. A charge $q=3\times {10}^{-6}\text{C}$ is in $\overrightarrow{E}=400\hat{i}\text{N/C}$, moving from $(0,0)$ to $(0.2,0.1)$. Calculate the work done by the field.

   • (a) $2.39\times {10}^{-4}\text{J}$
   • (b) $2.40\times {10}^{-4}\text{J}$
   • (c) $2.41\times {10}^{-4}\text{J}$
   • (d) $2.42\times {10}^{-4}\text{J}$

10. An electron in $\overrightarrow{E}=300\hat{j}\text{N/C}$, starting from rest. Calculate its velocity after $t=3\text{ns}$.

    • (a) $1.582\times {10}^5\hat{j}\text{m/s}$
    • (b) $1.583\times {10}^5\hat{j}\text{m/s}$
    • (c) $1.584\times {10}^5\hat{j}\text{m/s}$
    • (d) $1.585\times {10}^5\hat{j}\text{m/s}$

11. Calculate the electric field at $(0.1,0.1)$ due to $q=+4\mu \text{C}$ at $(0,0)$.

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

12. A line charge with $\lambda =1\times {10}^{-6}\text{C/m}$, length $L=0.6\text{m}$, lies along the x-axis from $-0.3$ to $0.3$. Calculate the electric field at $(0,0.1)$ (magnitude).

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

13. A ring of charge (radius $R=0.05\text{m}$, total charge $Q=1\mu \text{C}$) lies in the xy-plane. Calculate the electric field at $z=0.05\text{m}$.

    • (a) $6.36\times {10}^5\text{N/C}$
    • (b) $6.37\times {10}^5\text{N/C}$
    • (c) $6.38\times {10}^5\text{N/C}$
    • (d) $6.39\times {10}^5\text{N/C}$

14. A disk of radius $R=0.1\text{m}$, $\sigma =2\times {10}^{-6}{\text{C/m}}^2$, lies in the xy-plane. Calculate the electric field at $z=0.05\text{m}$.

    • (a) $6.27\times {10}^4\text{N/C}$
    • (b) $6.28\times {10}^4\text{N/C}$
    • (c) $6.29\times {10}^4\text{N/C}$
    • (d) $6.30\times {10}^4\text{N/C}$

15. A proton in $\overrightarrow{E}=200\hat{i}\text{N/C}$, ${\overrightarrow{v}}_0=3\times {10}^4\hat{j}\text{m/s}$. Calculate the trajectory equation.

    • (a) $y=1.56\times {10}^2{x}^2$
    • (b) $y=1.57\times {10}^2{x}^2$
    • (c) $y=1.58\times {10}^2{x}^2$
    • (d) $y=1.59\times {10}^2{x}^2$

16. Calculate the electric field at $(0,0.5)$ due to $q=-6\mu \text{C}$ at $(0,0)$.

    • (a) $-2.159\times {10}^5\hat{j}\text{N/C}$
    • (b) $-2.160\times {10}^5\hat{j}\text{N/C}$
    • (c) $-2.161\times {10}^5\hat{j}\text{N/C}$
    • (d) $-2.162\times {10}^5\hat{j}\text{N/C}$

17. Two charges $q_1=+4\mu \text{C}$ at $(0.1,0)$, $q_2=-4\mu \text{C}$ at $(-0.1,0)$. 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) $3\times {10}^5\text{N/C}$

18. A line charge with $\lambda =5\times {10}^{-6}\text{C/m}$, length $L=0.4\text{m}$, lies along the x-axis. Calculate the electric field at $(0,0.2)$ (magnitude).

    • (a) $2.24\times {10}^5\hat{j}\text{N/C}$
    • (b) $2.25\times {10}^5\hat{j}\text{N/C}$
    • (c) $2.26\times {10}^5\hat{j}\text{N/C}$
    • (d) $2.27\times {10}^5\hat{j}\text{N/C}$

19. A ring of charge (radius $R=0.2\text{m}$, $Q=4\mu \text{C}$) lies in the xy-plane. Calculate the electric field at $z=0.2\text{m}$.

    • (a) $7.98\times {10}^5\text{N/C}$
    • (b) $7.99\times {10}^5\text{N/C}$
    • (c) $8.00\times {10}^5\text{N/C}$
    • (d) $8.01\times {10}^5\text{N/C}$

20. A disk of radius $R=0.3\text{m}$, $\sigma =1\times {10}^{-6}{\text{C/m}}^2$, lies in the xy-plane. Calculate the electric field at $z=0.1\text{m}$.

    • (a) $2.88\times {10}^4\text{N/C}$
    • (b) $2.89\times {10}^4\text{N/C}$
    • (c) $2.90\times {10}^4\text{N/C}$
    • (d) $2.91\times {10}^4\text{N/C}$

21. An electron in $\overrightarrow{E}=400\hat{j}\text{N/C}$, starting from rest. Calculate its velocity after $t=1\text{ns}$.

    • (a) $7.02\times {10}^4\hat{j}\text{m/s}$
    • (b) $7.03\times {10}^4\hat{j}\text{m/s}$
    • (c) $7.04\times {10}^4\hat{j}\text{m/s}$
    • (d) $7.05\times {10}^4\hat{j}\text{m/s}$

22. A charge $q=2\times {10}^{-6}\text{C}$ in $\overrightarrow{E}=600\hat{i}\text{N/C}$, moves from $(0,0)$ to $(0.1,0.2)$. Calculate the work done.

    • (a) $1.19\times {10}^{-4}\text{J}$
    • (b) $1.20\times {10}^{-4}\text{J}$
    • (c) $1.21\times {10}^{-4}\text{J}$
    • (d) $1.22\times {10}^{-4}\text{J}$

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

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

24. A line charge with $\lambda =2\times {10}^{-6}\text{C/m}$, length $L=1\text{m}$, lies along the x-axis. Calculate the electric field at $(0,0.5)$ (magnitude).

    • (a) $7.19\times {10}^4\hat{j}\text{N/C}$
    • (b) $7.20\times {10}^4\hat{j}\text{N/C}$
    • (c) $7.21\times {10}^4\hat{j}\text{N/C}$
    • (d) $7.22\times {10}^4\hat{j}\text{N/C}$

25. A ring of charge (radius $R=0.15\text{m}$, $Q=3\mu \text{C}$) lies in the xy-plane. Calculate the electric field at $z=0.15\text{m}$.

    • (a) $7.98\times {10}^5\text{N/C}$
    • (b) $7.99\times {10}^5\text{N/C}$
    • (c) $8.00\times {10}^5\text{N/C}$
    • (d) $8.01\times {10}^5\text{N/C}$

26. A disk of radius $R=0.5\text{m}$, $\sigma =4\times {10}^{-6}{\text{C/m}}^2$, lies in the xy-plane. Calculate the electric field at $z=0.2\text{m}$.

    • (a) $7.49\times {10}^4\text{N/C}$
    • (b) $7.50\times {10}^4\text{N/C}$
    • (c) $7.51\times {10}^4\text{N/C}$
    • (d) $7.52\times {10}^4\text{N/C}$

27. A proton in $\overrightarrow{E}=100\hat{i}\text{N/C}$, ${\overrightarrow{v}}_0=5\times {10}^4\hat{j}\text{m/s}$. Calculate the trajectory equation.

    • (a) $y=5.22\times {10}^1{x}^2$
    • (b) $y=5.23\times {10}^1{x}^2$
    • (c) $y=5.24\times {10}^1{x}^2$
    • (d) $y=5.25\times {10}^1{x}^2$

28. Calculate the electric field at $(0.2,0.2)$ due to $q=-8\mu \text{C}$ at $(0,0)$.

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

29. Two charges $q_1=+5\mu \text{C}$ at $(0.3,0)$, $q_2=-5\mu \text{C}$ at $(-0.3,0)$. Calculate the electric field at $(0,0.4)$ (magnitude).

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

30. A line charge with $\lambda =3\times {10}^{-6}\text{C/m}$, length $L=0.8\text{m}$, lies along the x-axis. Calculate the electric field at $(0,0.4)$ (magnitude).

    • (a) $8.99\times {10}^4\hat{j}\text{N/C}$
    • (b) $9.00\times {10}^4\hat{j}\text{N/C}$
    • (c) $9.01\times {10}^4\hat{j}\text{N/C}$
    • (d) $9.02\times {10}^4\hat{j}\text{N/C}$

31. In a rocket ion engine, a disk (radius $R=0.1\text{m}$, $\sigma =5\times {10}^{-6}{\text{C/m}}^2$) creates a field at $z=0.05\text{m}$ to accelerate ions. Calculate the field magnitude.

    • (a) $1.04\times {10}^5\text{N/C}$
    • (b) $1.05\times {10}^5\text{N/C}$
    • (c) $1.06\times {10}^5\text{N/C}$
    • (d) $1.07\times {10}^5\text{N/C}$

32. A charge $q=1\times {10}^{-6}\text{C}$ in $\overrightarrow{E}=800\hat{i}\text{N/C}$, moves from $(0,0)$ to $(0.3,0.1)$. Calculate the work done.

    • (a) $2.39\times {10}^{-4}\text{J}$
    • (b) $2.40\times {10}^{-4}\text{J}$
    • (c) $2.41\times {10}^{-4}\text{J}$
    • (d) $2.42\times {10}^{-4}\text{J}$

33. An electron in $\overrightarrow{E}=200\hat{j}\text{N/C}$, starting from rest. Calculate its position after $t=4\text{ns}$.

    • (a) $2.81\times {10}^{-4}\hat{j}\text{m}$
    • (b) $2.82\times {10}^{-4}\hat{j}\text{m}$
    • (c) $2.83\times {10}^{-4}\hat{j}\text{m}$
    • (d) $2.84\times {10}^{-4}\hat{j}\text{m}$

34. A ring of charge (radius $R=0.1\text{m}$, $Q=5\mu \text{C}$) lies in the xy-plane. Calculate the electric field at $z=0.2\text{m}$.

    • (a) $9.98\times {10}^5\text{N/C}$
    • (b) $9.99\times {10}^5\text{N/C}$
    • (c) $1.00\times {10}^6\text{N/C}$
    • (d) $1.01\times {10}^6\text{N/C}$

35. A disk of radius $R=0.4\text{m}$, $\sigma =2\times {10}^{-6}{\text{C/m}}^2$, lies in the xy-plane. Calculate the electric field at $z=0.3\text{m}$.

    • (a) $4.19\times {10}^4\text{N/C}$
    • (b) $4.20\times {10}^4\text{N/C}$
    • (c) $4.21\times {10}^4\text{N/C}$
    • (d) $4.22\times {10}^4\text{N/C}$

---

Conceptual Problems

36. 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

37. What is the direction of the electric field due to a positive charge?

• (a) Toward the charge
• (b) Away from the charge
• (c) Perpendicular to the charge
• (d) No direction

38. What does the superposition principle state for electric fields?

• (a) Fields are scalar quantities
• (b) Net field is the vector sum of individual fields
• (c) Fields cancel out
• (d) Fields are independent of distance

39. What happens to the electric field if the distance from a point charge doubles?

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

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

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

41. 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

42. What do electric field lines represent?

• (a) Magnitude of the field
• (b) Direction of the field
• (c) Charge density
• (d) Potential energy

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 the density of electric field lines indicate?

• (a) Charge magnitude
• (b) Field strength
• (c) Distance from charge
• (d) Work done

45. 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) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

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

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

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

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

48. What happens to the field due to a charge distribution if the distance increases?

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

49. What does the motion of a charge in a uniform field resemble if ${\overrightarrow{v}}_0\perp \overrightarrow{E}$?

• (a) Linear motion
• (b) Parabolic motion
• (c) Circular motion
• (d) No motion

50. How do electric fields apply to rocket ion propulsion?

• (a) Reduce charge
• (b) Accelerate ions for thrust
• (c) Increase distance
• (d) Decrease field strength

---

Derivation Problems

51. Derive the electric field due to a point charge $\overrightarrow{E}=k\frac{q}{r^2}\hat{r}$.

52. Derive the superposition principle for electric fields ${\overrightarrow{E}}_{\text{net}}=\sum {\overrightarrow{E}}_i$.

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

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

55. Derive the electric field on the axis of a uniformly charged disk.

56. Derive the direction of electric field lines for a point charge.

57. Derive the motion of a charge in a uniform electric field (linear motion).

58. Derive the trajectory of a charge in a uniform field with ${\overrightarrow{v}}_0\perp \overrightarrow{E}$.

59. Derive the work done by an electric field $W=q\overrightarrow{E}\cdot \overrightarrow{d}$.

60. Derive the field line density relation to field strength.

61. Derive the electric field at a point due to a dipole.

62. Derive the field line pattern for a uniform electric field.

63. Derive the field due to two opposite charges (dipole approximation).

64. Derive the velocity of a charge in a uniform field starting from rest.

65. Derive the number of field lines proportional to charge magnitude.

---

NEET-style Conceptual Problems

66. What is the unit of work done by an electric field?

• (a) $\text{J}$
• (b) $\text{N/C}$
• (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 field from multiple charges?

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

69. What happens to the field if the charge doubles?

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

70. What is the dimension of electric field strength?

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

71. What does the direction of field lines indicate?

• (a) Charge magnitude
• (b) Field strength
• (c) Direction of force on a positive charge
• (d) Potential energy

72. What is the role of integration in field calculations for charge distributions?

• (a) Sums scalar fields
• (b) Sums vector field contributions
• (c) Reduces field strength
• (d) Increases distance

73. What happens to the field on the axis of a ring at $z=0$?

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

74. Why do field lines never cross?

• (a) Field is a scalar
• (b) Field direction is unique at each point
• (c) Charges repel
• (d) Field strength varies

75. What is the unit of acceleration of a charge in an electric field?

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

76. What does a uniform electric field indicate?

• (a) Constant field strength and direction
• (b) Variable field strength
• (c) Circular field lines
• (d) No field lines

77. Which type of motion does a charge exhibit in a uniform field with ${\overrightarrow{v}}_0=0$?

• (a) Parabolic
• (b) Linear
• (c) Circular
• (d) Oscillatory

78. What is the direction of motion of a negative charge in a uniform field?

• (a) Same as the field
• (b) Opposite to the field
• (c) Perpendicular to the field
• (d) Random

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

• (a) Affects perceived motion
• (b) Affects field strength
• (c) Creates field lines
• (d) Reduces charge

80. What is the dimension of work done by an electric field?

• (a) $[\text{M}{\text{L}}^2{\text{T}}^{-2}]$
• (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 electric fields in rocket ion propulsion?

• (a) Reduces charge
• (b) Accelerates ions for thrust
• (c) Increases distance
• (d) Decreases field

82. What happens to the field at the center of a uniformly charged ring?

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

83. Why do field lines start at positive charges?

• (a) Due to field direction outward
• (b) Due to charge quantization
• (c) Due to field strength
• (d) Due to work done

84. What is the significance of $\frac{\sigma }{2{ϵ}_0}$ for a disk at large $z$?

• (a) Field of an infinite sheet
• (b) Field of a point charge
• (c) Field of a ring
• (d) Potential energy

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

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

86. What does a zero work done by the field indicate?

• (a) No field present
• (b) Displacement perpendicular to field
• (c) Maximum field strength
• (d) No charge present

87. What is the physical significance of $k\int \frac{dq}{r^2}\hat{r}$?

• (a) Electric force
• (b) Electric field due to a distribution
• (c) Potential energy
• (d) Charge density

88. Why does a charge move parabolically in a uniform field?

• (a) Due to constant acceleration perpendicular to velocity
• (b) Due to circular motion
• (c) Due to field lines
• (d) Due to charge quantization

89. What is the dimension of linear charge density $\lambda$?

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

90. How do field lines help in ion propulsion design?

• (a) Increase charge
• (b) Visualize ion trajectories for thrust
• (c) Reduce field
• (d) Increase distance

91. What is the role of symmetry in field calculations?

• (a) Increases field strength
• (b) Cancels components to simplify calculations
• (c) Reduces charge
• (d) Increases distance

92. What does a high field line density indicate?

• (a) Weak field
• (b) Strong field
• (c) No field
• (d) Constant field

93. What is the physical significance of $\frac{qE}{m}$?

• (a) Electric field
• (b) Acceleration of a charge
• (c) Work done
• (d) Potential energy

94. What is the dimension of $\overrightarrow{E}\cdot \overrightarrow{d}$ in work calculations?

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

95. Why does the field due to a disk approach that of a point charge at large $z$?

• (a) Due to symmetry
• (b) Due to charge distribution behaving as a point
• (c) Due to field lines
• (d) Due to work done

---

NEET-style Numerical Problems

96. 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) $3.40\times {10}^5\hat{j}\text{N/C}$

97. A line charge with $\lambda =2\times {10}^{-6}\text{C/m}$, length $L=0.5\text{m}$, lies along the x-axis. Calculate the electric field at $(0,0.3)$ (magnitude).

• (a) $9.59\times {10}^4\hat{j}\text{N/C}$
• (b) $9.60\times {10}^4\hat{j}\text{N/C}$
• (c) $9.61\times {10}^4\hat{j}\text{N/C}$
• (d) $9.62\times {10}^4\hat{j}\text{N/C}$

98. A ring of charge (radius $R=0.1\text{m}$, $Q=4\mu \text{C}$) lies in the xy-plane. Calculate the electric field at $z=0.1\text{m}$.

• (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) $1.30\times {10}^6\text{N/C}$

99. A charge $q=2\times {10}^{-6}\text{C}$ in $\overrightarrow{E}=500\hat{i}\text{N/C}$, moves from $(0,0)$ to $(0.2,0.3)$. Calculate the work done.

• (a) $1.99\times {10}^{-4}\text{J}$
• (b) $2.00\times {10}^{-4}\text{J}$
• (c) $2.01\times {10}^{-4}\text{J}$
• (d) $2.02\times {10}^{-4}\text{J}$

100. An electron in $\overrightarrow{E}=100\hat{j}\text{N/C}$, starting from rest. Calculate its velocity after $t=5\text{ns}$.
     - (a) $8.77\times {10}^4\hat{j}\text{m/s}$
     - (b) $8.78\times {10}^4\hat{j}\text{m/s}$
     - (c) $8.79\times {10}^4\hat{j}\text{m/s}$
     - (d) $8.80\times {10}^4\hat{j}\text{m/s}$

Back to Chapter

Return to Electric Fields Chapter