Magnetic Fields Problems

This section provides 100 problems to test your understanding of magnetic fields, including calculations of magnetic fields using the Biot-Savart law and Ampere’s law, fields due to various current distributions, and their applications. 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 electromagnetism, a key topic for JEE/NEET success.

Numerical Problems

1. A wire carries a current $I=5\text{A}$ and has length $L=0.2\text{m}$ in a magnetic field $B=0.3\text{T}$ (perpendicular to the wire). Calculate the force on the wire.

   • (a) $0.299\text{N}$
   • (b) $0.300\text{N}$
   • (c) $0.301\text{N}$
   • (d) $0.302\text{N}$

2. A charge $q=3\mu \text{C}$ moves at $v=4\times {10}^5\text{m/s}$ in a magnetic field $B=0.2\text{T}$ (perpendicular to velocity). Calculate the magnetic force on the charge.

   • (a) $0.239\text{N}$
   • (b) $0.240\text{N}$
   • (c) $0.241\text{N}$
   • (d) $0.242\text{N}$

3. An infinite straight wire carries $I=10\text{A}$. Calculate the magnetic field at a distance $r=0.05\text{m}$ using the Biot-Savart law (${\mu }_0=4\pi \times {10}^{-7}\text{T·m/A}$).

   • (a) $3.99\times {10}^{-5}\text{T}$
   • (b) $4.00\times {10}^{-5}\text{T}$
   • (c) $4.01\times {10}^{-5}\text{T}$
   • (d) $4.02\times {10}^{-5}\text{T}$

4. A circular loop of radius $R=0.1\text{m}$ carries $I=2\text{A}$. Calculate the magnetic field at the center of the loop.

   • (a) $1.256\times {10}^{-5}\text{T}$
   • (b) $1.257\times {10}^{-5}\text{T}$
   • (c) $1.258\times {10}^{-5}\text{T}$
   • (d) $1.259\times {10}^{-5}\text{T}$

5. A solenoid with $n=1000\text{turns/m}$ carries $I=0.5\text{A}$. Calculate the magnetic field inside the solenoid using Ampere’s law.

   • (a) $6.282\times {10}^{-4}\text{T}$
   • (b) $6.283\times {10}^{-4}\text{T}$
   • (c) $6.284\times {10}^{-4}\text{T}$
   • (d) $6.285\times {10}^{-4}\text{T}$

6. A toroid with $N=500$ turns, mean radius $r=0.2\text{m}$, carries $I=1\text{A}$. Calculate the magnetic field inside the toroid.

   • (a) $4.99\times {10}^{-4}\text{T}$
   • (b) $5.00\times {10}^{-4}\text{T}$
   • (c) $5.01\times {10}^{-4}\text{T}$
   • (d) $5.02\times {10}^{-4}\text{T}$

7. A circular loop with $R=0.05\text{m}$, $I=3\text{A}$ is positioned at $x=0.05\text{m}$ on its axis. Calculate the magnetic field at that point.

   • (a) $2.26\times {10}^{-5}\text{T}$
   • (b) $2.27\times {10}^{-5}\text{T}$
   • (c) $2.28\times {10}^{-5}\text{T}$
   • (d) $2.29\times {10}^{-5}\text{T}$

8. A cylindrical conductor of radius $a=0.03\text{m}$ carries $I=15\text{A}$ uniformly. Calculate the magnetic field at $r=0.02\text{m}$ inside the cylinder.

   • (a) $3.33\times {10}^{-5}\text{T}$
   • (b) $3.34\times {10}^{-5}\text{T}$
   • (c) $3.35\times {10}^{-5}\text{T}$
   • (d) $3.36\times {10}^{-5}\text{T}$

9. An infinite current sheet has a surface current density $K=2000\text{A/m}$. Calculate the magnetic field on one side of the sheet.

   • (a) $1.256\times {10}^{-3}\text{T}$
   • (b) $1.257\times {10}^{-3}\text{T}$
   • (c) $1.258\times {10}^{-3}\text{T}$
   • (d) $1.259\times {10}^{-3}\text{T}$

10. A proton ($q=1.6\times {10}^{-19}\text{C}$, $v=3\times {10}^6\text{m/s}$) moves at ${45}^{\circ }$ to a magnetic field $B=0.1\text{T}$. Calculate the magnetic force.

    • (a) $3.39\times {10}^{-14}\text{N}$
    • (b) $3.40\times {10}^{-14}\text{N}$
    • (c) $3.41\times {10}^{-14}\text{N}$
    • (d) $3.42\times {10}^{-14}\text{N}$

11. A semi-infinite wire carries $I=6\text{A}$ and is observed at a perpendicular distance $r=0.06\text{m}$ from its end. Calculate the magnetic field.

    • (a) $4.99\times {10}^{-6}\text{T}$
    • (b) $5.00\times {10}^{-6}\text{T}$
    • (c) $5.01\times {10}^{-6}\text{T}$
    • (d) $5.02\times {10}^{-6}\text{T}$

12. A wire segment with $I=4\text{A}$, $dl=0.02\text{m}$, at $r=0.1\text{m}$ (perpendicular), produces a field $dB$. Calculate $dB$.

    • (a) $7.99\times {10}^{-9}\text{T}$
    • (b) $8.00\times {10}^{-9}\text{T}$
    • (c) $8.01\times {10}^{-9}\text{T}$
    • (d) $8.02\times {10}^{-9}\text{T}$

13. A circular loop with $R=0.08\text{m}$, $I=1.5\text{A}$ is observed at $x=0.06\text{m}$ on its axis. Calculate the magnetic field.

    • (a) $3.53\times {10}^{-6}\text{T}$
    • (b) $3.54\times {10}^{-6}\text{T}$
    • (c) $3.55\times {10}^{-6}\text{T}$
    • (d) $3.56\times {10}^{-6}\text{T}$

14. A solenoid with $n=800\text{turns/m}$ carries $I=0.4\text{A}$. Calculate the magnetic field inside.

    • (a) $4.01\times {10}^{-4}\text{T}$
    • (b) $4.02\times {10}^{-4}\text{T}$
    • (c) $4.03\times {10}^{-4}\text{T}$
    • (d) $4.04\times {10}^{-4}\text{T}$

15. A toroid with $N=2000$ turns, $r=0.5\text{m}$, carries $I=0.3\text{A}$. Calculate the magnetic field inside.

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

16. A cylindrical conductor of radius $a=0.04\text{m}$ carries $I=20\text{A}$ uniformly. Calculate the magnetic field at $r=0.05\text{m}$ (outside).

    • (a) $7.99\times {10}^{-5}\text{T}$
    • (b) $8.00\times {10}^{-5}\text{T}$
    • (c) $8.01\times {10}^{-5}\text{T}$
    • (d) $8.02\times {10}^{-5}\text{T}$

17. A current sheet has $K=1500\text{A/m}$. Calculate the magnetic field on one side.

    • (a) $9.42\times {10}^{-4}\text{T}$
    • (b) $9.43\times {10}^{-4}\text{T}$
    • (c) $9.44\times {10}^{-4}\text{T}$
    • (d) $9.45\times {10}^{-4}\text{T}$

18. A wire carries $I=7\text{A}$, $L=0.15\text{m}$ in $B=0.4\text{T}$ at ${60}^{\circ }$. Calculate the force on the wire.

    • (a) $0.363\text{N}$
    • (b) $0.364\text{N}$
    • (c) $0.365\text{N}$
    • (d) $0.366\text{N}$

19. A charge $q=5\mu \text{C}$ moves at $v=2\times {10}^5\text{m/s}$ in $B=0.25\text{T}$ at ${90}^{\circ }$. Calculate the force.

    • (a) $0.249\text{N}$
    • (b) $0.250\text{N}$
    • (c) $0.251\text{N}$
    • (d) $0.252\text{N}$

20. An infinite wire with $I=12\text{A}$ is at $r=0.03\text{m}$. Calculate $B$.

    • (a) $7.99\times {10}^{-5}\text{T}$
    • (b) $8.00\times {10}^{-5}\text{T}$
    • (c) $8.01\times {10}^{-5}\text{T}$
    • (d) $8.02\times {10}^{-5}\text{T}$

21. A loop with $R=0.02\text{m}$, $I=4\text{A}$ is at its center. Calculate $B$.

    • (a) $1.256\times {10}^{-4}\text{T}$
    • (b) $1.257\times {10}^{-4}\text{T}$
    • (c) $1.258\times {10}^{-4}\text{T}$
    • (d) $1.259\times {10}^{-4}\text{T}$

22. A solenoid with $n=1200\text{turns/m}$, $I=0.1\text{A}$. Calculate $B$ inside.

    • (a) $1.507\times {10}^{-4}\text{T}$
    • (b) $1.508\times {10}^{-4}\text{T}$
    • (c) $1.509\times {10}^{-4}\text{T}$
    • (d) $1.510\times {10}^{-4}\text{T}$

23. A toroid with $N=1000$ turns, $r=0.25\text{m}$, $I=0.5\text{A}$. Calculate $B$ inside.

    • (a) $3.99\times {10}^{-4}\text{T}$
    • (b) $4.00\times {10}^{-4}\text{T}$
    • (c) $4.01\times {10}^{-4}\text{T}$
    • (d) $4.02\times {10}^{-4}\text{T}$

24. A cylinder of radius $a=0.01\text{m}$ carries $I=8\text{A}$. Calculate $B$ at $r=0.005\text{m}$.

    • (a) $3.99\times {10}^{-5}\text{T}$
    • (b) $4.00\times {10}^{-5}\text{T}$
    • (c) $4.01\times {10}^{-5}\text{T}$
    • (d) $4.02\times {10}^{-5}\text{T}$

25. A current sheet with $K=500\text{A/m}$. Calculate $B$.

    • (a) $3.14\times {10}^{-4}\text{T}$
    • (b) $3.15\times {10}^{-4}\text{T}$
    • (c) $3.16\times {10}^{-4}\text{T}$
    • (d) $3.17\times {10}^{-4}\text{T}$

26. A finite wire from $x=-0.2\text{m}$ to $0.2\text{m}$, $I=3\text{A}$, at $y=0.1\text{m}$. Calculate $B$.

    • (a) $8.48\times {10}^{-6}\text{T}$
    • (b) $8.49\times {10}^{-6}\text{T}$
    • (c) $8.50\times {10}^{-6}\text{T}$
    • (d) $8.51\times {10}^{-6}\text{T}$

27. A loop with $R=0.06\text{m}$, $I=2\text{A}$, at $x=0.08\text{m}$. Calculate $B$.

    • (a) $1.45\times {10}^{-6}\text{T}$
    • (b) $1.46\times {10}^{-6}\text{T}$
    • (c) $1.47\times {10}^{-6}\text{T}$
    • (d) $1.48\times {10}^{-6}\text{T}$

28. A solenoid with $n=1500\text{turns/m}$, $I=0.2\text{A}$. Calculate $B$ inside.

    • (a) $3.76\times {10}^{-4}\text{T}$
    • (b) $3.77\times {10}^{-4}\text{T}$
    • (c) $3.78\times {10}^{-4}\text{T}$
    • (d) $3.79\times {10}^{-4}\text{T}$

29. A toroid with $N=800$ turns, $r=0.4\text{m}$, $I=0.6\text{A}$. Calculate $B$ inside.

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

30. A cylinder of radius $a=0.05\text{m}$ carries $I=25\text{A}$. Calculate $B$ at $r=0.06\text{m}$.

    • (a) $8.33\times {10}^{-5}\text{T}$
    • (b) $8.34\times {10}^{-5}\text{T}$
    • (c) $8.35\times {10}^{-5}\text{T}$
    • (d) $8.36\times {10}^{-5}\text{T}$

31. A spacecraft wire with $I=2\text{A}$, $L=0.1\text{m}$ in $B=0.05\text{T}$ (perpendicular). Calculate the force for navigation purposes.

    • (a) $0.0099\text{N}$
    • (b) $0.0100\text{N}$
    • (c) $0.0101\text{N}$
    • (d) $0.0102\text{N}$

32. An infinite wire with $I=15\text{A}$ at $r=0.02\text{m}$. Calculate $B$.

    • (a) $1.499\times {10}^{-4}\text{T}$
    • (b) $1.500\times {10}^{-4}\text{T}$
    • (c) $1.501\times {10}^{-4}\text{T}$
    • (d) $1.502\times {10}^{-4}\text{T}$

33. A loop with $R=0.04\text{m}$, $I=1\text{A}$, at $x=0.03\text{m}$. Calculate $B$.

    • (a) $2.09\times {10}^{-6}\text{T}$
    • (b) $2.10\times {10}^{-6}\text{T}$
    • (c) $2.11\times {10}^{-6}\text{T}$
    • (d) $2.12\times {10}^{-6}\text{T}$

34. A solenoid with $n=600\text{turns/m}$, $I=0.8\text{A}$. Calculate $B$ inside.

    • (a) $6.03\times {10}^{-4}\text{T}$
    • (b) $6.04\times {10}^{-4}\text{T}$
    • (c) $6.05\times {10}^{-4}\text{T}$
    • (d) $6.06\times {10}^{-4}\text{T}$

35. A toroid with $N=1200$ turns, $r=0.3\text{m}$, $I=0.4\text{A}$. Calculate $B$ inside.

    • (a) $3.19\times {10}^{-4}\text{T}$
    • (b) $3.20\times {10}^{-4}\text{T}$
    • (c) $3.21\times {10}^{-4}\text{T}$
    • (d) $3.22\times {10}^{-4}\text{T}$

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Conceptual Problems

36. What is the unit of magnetic field in SI units?

• (a) Tesla
• (b) Ampere
• (c) Ohm
• (d) Volt

37. What does the right-hand rule determine in the context of magnetic fields?

• (a) Direction of electric field
• (b) Direction of magnetic field due to a current
• (c) Direction of current flow
• (d) Direction of charge motion

38. What is the relationship between magnetic field and distance from an infinite straight wire?

• (a) $B\propto r$
• (b) $B\propto \frac{1}{r}$
• (c) $B\propto r^2$
• (d) $B\propto \frac{1}{r^2}$

39. What happens to the magnetic field at the center of a circular loop as the radius increases?

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

40. What does Ampere’s law relate?

• (a) Magnetic field to electric field
• (b) Magnetic field to enclosed current
• (c) Electric field to enclosed charge
• (d) Magnetic field to enclosed charge

41. What is the magnetic field inside an ideal solenoid?

• (a) Zero
• (b) Uniform and non-zero
• (c) Proportional to radius
• (d) Proportional to distance from the axis

42. What is the physical significance of ${\mu }_0$?

• (a) Permittivity of free space
• (b) Permeability of free space
• (c) Conductivity of free space
• (d) Resistivity of free space

43. What happens to the magnetic field outside an ideal solenoid?

• (a) Uniform and non-zero
• (b) Proportional to distance
• (c) Approximately zero
• (d) Infinite

44. What does the Biot-Savart law describe?

• (a) Magnetic field due to a static charge
• (b) Magnetic field due to a current element
• (c) Electric field due to a current
• (d) Electric field due to a magnetic field

45. What is the dimension of magnetic field $B$?

• (a) $[\text{M}{\text{T}}^{-2}{\text{A}}^{-1}]$
• (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 magnetic field inside a region indicate?

• (a) No current or magnetic sources nearby
• (b) Infinite current
• (c) Infinite magnetic field outside
• (d) No electric field

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

• (a) Magnetic field due to a circular loop
• (b) Magnetic field due to an infinite straight wire
• (c) Magnetic field inside a solenoid
• (d) Magnetic field inside a toroid

48. What happens to the magnetic field on the axis of a circular loop as you move away from the center?

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

49. What does the uniform magnetic field on either side of a current sheet indicate?

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

50. How do magnetic fields assist in spacecraft navigation systems?

• (a) Increase current flow
• (b) Detect orientation using magnetic sensors
• (c) Reduce resistance
• (d) Increase voltage

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Derivation Problems

51. Derive the magnetic force on a current-carrying wire in a uniform magnetic field $F=ILB\sin \theta$.

52. Derive the magnetic field due to an infinite straight wire using the Biot-Savart law $B=\frac{{\mu }_{0}I}{2\pi r}$.

53. Derive the magnetic field at the center of a circular loop $B=\frac{{\mu }_{0}I}{2R}$.

54. Derive the magnetic field due to an infinite straight wire using Ampere’s law $B=\frac{{\mu }_{0}I}{2\pi r}$.

55. Derive the magnetic field inside a solenoid using Ampere’s law $B={\mu }_{0}nI$.

56. Derive the magnetic field inside a toroid $B=\frac{{\mu }_{0}NI}{2\pi r}$.

57. Derive the magnetic field on the axis of a circular loop $B=\frac{{\mu }_{0}I{R}^2}{2(R^2+x^2{)}^{3/2}}$.

58. Derive the magnetic field inside a cylindrical conductor $B=\frac{{\mu }_{0}Ir}{2\pi a^2}$ for $r<a$.

59. Derive the magnetic field outside a cylindrical conductor $B=\frac{{\mu }_{0}I}{2\pi r}$ for $r>a$.

60. Derive the magnetic field due to an infinite current sheet $B=\frac{{\mu }_{0}K}{2}$.

61. Derive the magnetic field due to a semi-infinite straight wire using the Biot-Savart law.

62. Derive the magnetic field due to a finite straight wire $B=\frac{{\mu }_{0}I}{4\pi a}(\sin {\theta }_2-\sin {\theta }_1)$.

63. Derive the Biot-Savart law expression $d\overrightarrow{B}=\frac{{\mu }_0}{4\pi }\frac{I(d\overrightarrow{l}\times \hat{r})}{r^2}$.

64. Derive the magnetic field at a point due to a small current element using the Biot-Savart law.

65. Derive the direction of the magnetic field using the right-hand rule for a current-carrying wire.

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NEET-style Conceptual Problems

66. What is the unit of permeability of free space ${\mu }_0$?

• (a) $\text{T·m/A}$
• (b) $\text{N/A}$
• (c) $\text{V·m/A}$
• (d) $\text{A/m}$

67. What does a circular magnetic field line around a wire indicate?

• (a) Magnetic field due to a static charge
• (b) Magnetic field due to a current
• (c) Electric field due to a current
• (d) Electric field due to a charge

68. What is the relationship between magnetic field and current in a solenoid?

• (a) $B\propto \frac{1}{I}$
• (b) $B\propto I$
• (c) $B$ is independent of $I$
• (d) $B\propto I^2$

69. What happens to the magnetic field inside a toroid as the radius increases?

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

70. What is the dimension of ${\mu }_0$?

• (a) $[\text{M}\text{L}{\text{T}}^{-2}{\text{A}}^{-2}]$
• (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 magnetic field inside a cylindrical conductor depend on?

• (a) Distance from the axis
• (b) Total current only
• (c) Radius of the cylinder only
• (d) No dependence

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

• (a) Increases the magnetic field
• (b) Simplifies the calculation of the magnetic field
• (c) Reduces the current
• (d) Increases the resistance

73. What happens to the magnetic field outside a toroid?

• (a) Uniform and non-zero
• (b) Proportional to distance
• (c) Approximately zero
• (d) Infinite

74. Why does the magnetic field at the center of a circular loop depend on the radius?

• (a) Due to $B\propto \frac{1}{R}$
• (b) Due to increased current
• (c) Due to decreased current
• (d) Due to symmetry

75. What is the unit of surface current density $K$?

• (a) $\text{A/m}$
• (b) ${\text{A/m}}^2$
• (c) $\text{T}$
• (d) $\text{V}$

76. What does a constant magnetic field inside a solenoid indicate?

• (a) Non-uniform current
• (b) Uniform field along the axis
• (c) Zero field outside
• (d) Infinite field

77. Which type of current distribution produces a uniform magnetic field inside?

• (a) Straight wire
• (b) Circular loop
• (c) Solenoid
• (d) Current sheet

78. What is the direction of the magnetic field due to a current-carrying wire?

• (a) Along the wire
• (b) Perpendicular to the wire, circular around it
• (c) Random
• (d) Zero

79. What does a pseudo-force do in a non-inertial frame for magnetic field calculations?

• (a) Affects perceived field
• (b) Affects current distribution
• (c) Creates magnetic field
• (d) Reduces field

80. What is the dimension of $Id\overrightarrow{l}\times \hat{r}$ in the Biot-Savart law?

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

81. What is the role of magnetic fields in spacecraft navigation?

• (a) Increase current
• (b) Detect orientation using sensors
• (c) Reduce voltage
• (d) Increase resistance

82. What happens to the magnetic field inside a cylindrical conductor as the radius increases?

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

83. Why does the magnetic field due to a current sheet not depend on distance?

• (a) Due to infinite extent and symmetry
• (b) Due to increased current
• (c) Due to decreased current
• (d) Due to finite size

84. What is the significance of $\frac{{\mu }_{0}I{R}^2}{2(R^2+x^2{)}^{3/2}}$?

• (a) Magnetic field due to a straight wire
• (b) Magnetic field on the axis of a circular loop
• (c) Magnetic field inside a solenoid
• (d) Magnetic field inside a toroid

85. What is the unit of magnetic force?

• (a) Newton
• (b) Tesla
• (c) Ampere
• (d) Volt

86. What does a zero magnetic field at the center of a loop indicate?

• (a) No current
• (b) Infinite current
• (c) Infinite radius
• (d) No magnetic field outside

87. What is the physical significance of ${\mu }_{0}nI$?

• (a) Magnetic field due to a straight wire
• (b) Magnetic field inside a solenoid
• (c) Magnetic field on the axis of a loop
• (d) Magnetic field due to a current sheet

88. Why does the magnetic field outside a solenoid approach zero for an ideal solenoid?

• (a) Due to cancellation of fields
• (b) Due to increased current
• (c) Due to decreased current
• (d) Due to symmetry

89. What is the dimension of $\frac{{\mu }_{0}I}{r}$?

• (a) $[\text{M}{\text{T}}^{-2}{\text{A}}^{-1}]$
• (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 the magnetic field assist in spacecraft shielding?

• (a) Increases current
• (b) Deflects charged particles using magnetic fields
• (c) Reduces voltage
• (d) Increases resistance

91. What is the role of distance in the magnetic field due to a straight wire?

• (a) $B\propto r$
• (b) $B\propto \frac{1}{r}$
• (c) No dependence
• (d) Exponential dependence

92. What does a high magnetic field at the center of a loop indicate?

• (a) Large radius
• (b) Small radius or high current
• (c) No current
• (d) Infinite field

93. What is the physical significance of $\frac{{\mu }_{0}K}{2}$?

• (a) Magnetic field due to a straight wire
• (b) Magnetic field due to a current sheet
• (c) Magnetic field inside a solenoid
• (d) Magnetic field on the axis of a loop

94. What is the dimension of $\overrightarrow{B}\cdot d\overrightarrow{l}$ in Ampere’s law?

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

95. Why does the magnetic field inside a toroid depend on the radius?

• (a) Due to $B\propto \frac{1}{r}$
• (b) Due to symmetry
• (c) Due to field lines
• (d) Due to current quantization

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NEET-style Numerical Problems

96. A wire with $I=3\text{A}$, $L=0.25\text{m}$ in $B=0.2\text{T}$ (perpendicular). Calculate the force.

• (a) $0.149\text{N}$
• (b) $0.150\text{N}$
• (c) $0.151\text{N}$
• (d) $0.152\text{N}$

97. An infinite wire with $I=4\text{A}$ at $r=0.08\text{m}$. Calculate $B$.

• (a) $9.99\times {10}^{-6}\text{T}$
• (b) $1.00\times {10}^{-5}\text{T}$
• (c) $1.01\times {10}^{-5}\text{T}$
• (d) $1.02\times {10}^{-5}\text{T}$

98. A loop with $R=0.03\text{m}$, $I=2\text{A}$ at its center. Calculate $B$.

• (a) $4.18\times {10}^{-5}\text{T}$
• (b) $4.19\times {10}^{-5}\text{T}$
• (c) $4.20\times {10}^{-5}\text{T}$
• (d) $4.21\times {10}^{-5}\text{T}$

99. A solenoid with $n=400\text{turns/m}$, $I=1.2\text{A}$. Calculate $B$ inside.

• (a) $6.03\times {10}^{-4}\text{T}$
• (b) $6.04\times {10}^{-4}\text{T}$
• (c) $6.05\times {10}^{-4}\text{T}$
• (d) $6.06\times {10}^{-4}\text{T}$

100. A toroid with $N=600$ turns, $r=0.15\text{m}$, $I=0.5\text{A}$. Calculate $B$ inside.
     - (a) $3.99\times {10}^{-4}\text{T}$
     - (b) $4.00\times {10}^{-4}\text{T}$
     - (c) $4.01\times {10}^{-4}\text{T}$
     - (d) $4.02\times {10}^{-4}\text{T}$

Back to Chapter

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