JEE Main - Ampere’s law and applications to wires and solenoids Online Test (MCQ Quiz)

1. Ampere's law relates the magnetic field around a closed loop to the electric current passing through the loop. Mathematically, it is stated as:

A) ∮ B ⋅ dl = μ₀I_enc B) ∮ B ⋅ dl = ε₀I_enc C) ∮ E ⋅ dl = μ₀I_enc D) ∮ E ⋅ dl = ε₀I_enc

2. In Ampere's law, ∮ B ⋅ dl = μ₀I_enc, what does 'μ₀' represent?

A) The permittivity of free space B) The permeability of free space C) The charge density D) The electric field strength

3. In Ampere's law, ∮ B ⋅ dl = μ₀I_enc, what does 'I_enc' represent?

A) The total current enclosed by the loop B) The current flowing outside the loop C) The average current D) The induced current

4. Ampere's law is most useful for calculating the magnetic field when the symmetry of the problem allows for:

A) A spherical Amperian loop B) A rectangular Amperian loop C) An Amperian loop where the magnetic field is constant in magnitude and parallel to the loop D) An Amperian loop where the magnetic field is perpendicular to the loop

5. Consider a long straight wire carrying a current I. What is the magnitude of the magnetic field at a perpendicular distance r from the wire?

A) B = (μ₀I) / (2πr) B) B = (μ₀I) / (4πr) C) B = (2πr) / (μ₀I) D) B = (4πr) / (μ₀I)

6. The magnetic field lines around a long straight current-carrying wire are:

A) Radial B) Concentric circles centered on the wire C) Parallel to the wire D) Perpendicular to the wire

7. To determine the direction of the magnetic field around a straight current-carrying wire, one can use:

A) Fleming's Left-Hand Rule B) Fleming's Right-Hand Rule C) The Right-Hand Grip Rule D) The Right-Hand Thumb Rule

8. A solenoid is a coil of wire wound into a tightly packed helix. For an ideal, long solenoid, the magnetic field inside is approximately:

A) Uniform and parallel to the axis B) Non-uniform and strongest at the center C) Zero outside the solenoid D) Tangential to the circular cross-section

9. What is the magnitude of the magnetic field inside a long solenoid carrying current I, with n turns per unit length?

A) B = μ₀nI B) B = μ₀I / n C) B = I / (μ₀n) D) B = nI / μ₀

10. The magnetic field outside an ideal, long solenoid is approximately:

A) μ₀nI B) μ₀I / n C) Zero D) Strong and uniform

11. If the current in a long straight wire is doubled, the magnetic field at a given distance from the wire will:

A) Remain the same B) Be halved C) Be doubled D) Be quadrupled

12. If the distance from a long straight wire carrying current I is doubled, the magnetic field at that point will:

A) Remain the same B) Be halved C) Be doubled D) Be quadrupled

13. Consider a circular loop of radius R carrying current I. The magnetic field at the center of the loop is:

A) B = (μ₀I) / (2R) B) B = (μ₀I) / (4R) C) B = (2μ₀I) / R D) B = (4μ₀I) / R

14. To apply Ampere's law to a solenoid, we choose an Amperian loop that is:

A) A circle coaxial with the solenoid B) A rectangle with one side inside and one side outside the solenoid, parallel to the axis C) A rectangle perpendicular to the axis D) A circle perpendicular to the axis

15. If a solenoid is not long and ideal, the magnetic field:

A) Is uniform everywhere inside B) Is stronger near the ends than in the middle C) Is weaker near the ends than in the middle D) Is zero outside

16. What happens to the magnetic field inside a solenoid if the number of turns per unit length (n) is increased, while keeping the current (I) constant?

A) It decreases B) It increases C) It remains the same D) It becomes zero

17. What happens to the magnetic field inside a solenoid if the current (I) is increased, while keeping the number of turns per unit length (n) constant?

A) It decreases B) It increases C) It remains the same D) It becomes zero

18. Ampere's law is a consequence of:

A) Gauss's law for electricity B) Gauss's law for magnetism C) Faraday's law of induction D) Biot-Savart law

19. The unit of magnetic field (B) is Tesla (T). Which of the following is equivalent to Tesla?

A) Weber/meter² B) Weber-meter² C) Weber/meter D) Newton/(Ampere-meter)

20. A toroid is a solenoid bent into a circular shape. For a toroid with N turns and carrying current I, the magnetic field inside the toroid at a radius r is:

A) B = (μ₀NI) / (2πr) B) B = (μ₀NI) / r C) B = (μ₀NI) / (4πr) D) B = 0

21. The magnetic field inside a toroid is strongest where the windings are:

A) Widest apart B) Tightly packed C) Uniformly spaced D) Irregularly spaced

22. The magnetic field outside an ideal toroid is:

A) Strong and uniform B) Weak but non-uniform C) Zero D) Equal to the field of a straight solenoid

23. Ampere's law is applicable to which type of currents?

A) Only steady currents B) Only alternating currents C) Steady and alternating currents D) Displacement currents

24. If we consider an Amperian loop that encloses no net current, then the line integral of B around that loop is:

A) Non-zero B) Zero C) Dependent on the shape of the loop D) Equal to μ₀

25. For a current distribution with cylindrical symmetry, the magnetic field depends on:

A) The radial distance only B) The azimuthal angle only C) The axial distance only D) All three coordinates

26. A thin wire carries a current I. If the wire is bent into a circular loop of radius R, the magnetic field at the center is B_center. If it is bent into a square loop of side length L, the magnetic field at the center is B_square. Which statement is true?

A) B_center > B_square B) B_center < B_square C) B_center = B_square D) Cannot be determined without knowing current

27. What is the magnetic field at a point inside a long solenoid far from the ends, if the solenoid is carrying a current I and has n turns per unit length?

A) μ₀nI B) μ₀I/n C) nI/μ₀ D) 0

28. Consider two long straight wires placed parallel to each other, separated by a distance d, and carrying currents I₁ and I₂ in the same direction. The magnetic field at a point exactly midway between them is:

A) Zero B) Maximum C) Dependent on the direction of currents D) Dependent on the permeability of the medium

29. If two long straight wires carry currents in opposite directions, the magnetic field at a point midway between them is:

A) Zero B) Non-zero and directed perpendicular to the plane containing the wires C) Non-zero and directed parallel to the wires D) Non-zero and directed away from the wires

30. The magnetic field of a long straight wire is proportional to:

A) r B) 1/r C) r² D) 1/r²

31. Ampere's law is valid for:

A) Any shape of Amperian loop B) Only circular Amperian loops C) Only loops where B is constant D) Only loops where B is parallel to dl

32. What is the magnetic field at a distance r from the axis of a long solenoid, outside the solenoid?

A) μ₀nI B) μ₀nIr C) 0 D) μ₀nI/r

33. The magnetic field inside a toroid is:

A) Uniform B) Radial C) Circular, centered on the toroid axis D) Zero

34. If the current in a solenoid is reversed, the direction of the magnetic field inside the solenoid:

A) Remains the same B) Reverses C) Becomes zero D) Becomes tangential

35. Ampere's law is a macroscopic law, while Biot-Savart law is a microscopic law. Ampere's law can be derived from Biot-Savart law under conditions of:

A) High symmetry B) Low symmetry C) No symmetry D) Alternating currents

36. A current loop creates a magnetic field. If the current is doubled, the magnetic field at any point will:

A) Remain the same B) Be halved C) Be doubled D) Be quadrupled

37. What is the magnetic field at the center of a circular loop of radius R carrying current I, if the loop is made of wire with cross-sectional area A?

A) B = (μ₀I) / (2R) B) B = (μ₀I) / (2πR) C) B = (μ₀I) / (2A) D) The cross-sectional area does not affect the field at the center

38. Consider a long straight wire carrying current I. The magnetic field at a distance r is B. If the wire is hollow with inner radius r₁ and outer radius r₂, and the current flows uniformly through the cross-section, what is the field at r < r₁?

A) B = (μ₀I) / (2πr) B) B = (μ₀I r) / (2π(r₂² - r₁²)) C) B = (μ₀I r²) / (2π(r₂² - r₁²)) D) 0

39. For a hollow cylindrical conductor of inner radius r₁ and outer radius r₂ carrying a uniform current I, what is the magnetic field at a distance r such that r₁ < r < r₂?

A) B = (μ₀I) / (2πr) B) B = (μ₀I (r² - r₁²)) / (2πr(r₂² - r₁²)) C) B = (μ₀I (r₂² - r²)) / (2πr(r₂² - r₁²)) D) 0

40. The magnetic field lines inside a solenoid are:

A) Closed loops, but not necessarily circles B) Straight lines parallel to the axis C) Circles concentric with the axis D) Radial lines

41. Ampere's law is particularly useful for calculating magnetic fields in situations with:

A) Spherical symmetry B) Cylindrical symmetry C) Planar symmetry D) All of the above

42. The magnetic field at a point inside a long solenoid depends on:

A) The distance from the axis B) The position along the axis C) The current and the number of turns per unit length D) The radius of the solenoid

43. What is the magnetic flux through the surface enclosed by an Amperian loop if no net current passes through the loop?

A) Non-zero B) Zero C) Equal to μ₀ D) Cannot be determined

44. If the permeability of the medium inside a solenoid is μ instead of μ₀, the magnetic field inside becomes:

A) B = μnI B) B = μ₀nI C) B = (μ/μ₀)nI D) B = (μ₀/μ)nI

45. A long straight wire carries a current I. If a cylindrical surface of radius r is chosen as the Amperian loop, coaxial with the wire, the integral ∮ B ⋅ dl is:

A) μ₀I B) 2πr B C) 0 D) μ₀I / (2πr)

46. The magnetic field strength inside a solenoid is directly proportional to:

A) The current B) The square of the current C) The inverse of the current D) The inverse square of the current

47. Which of the following statements about Ampere's law is FALSE?

A) It applies to steady currents. B) It relates magnetic field to enclosed current. C) It is valid for any shape of Amperian loop. D) It is derived from Gauss's law for magnetism.

48. In a solenoid, the magnetic field lines are most densely packed:

A) At the center B) Near the ends C) Throughout the interior D) Outside the solenoid

49. Ampere's law is particularly useful when dealing with conductors carrying current that exhibit:

A) Random shapes B) High degree of symmetry C) Irregular current distribution D) Transient currents

Ampere’s law and applications to wires and solenoids - Online Test

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