JEE Main - Biot–Savart law and magnetic field of current elements Question Bank with Options

1. The magnetic field at a large distance x from the center of a circular loop of radius R carrying current I is proportional to:

A) 1/x

B) 1/x²

C) 1/x³

D) 1/x⁴

2. Which statement about the Biot-Savart law is incorrect?

A) It applies to steady currents.

B) It allows calculation of magnetic field from a current element.

C) The magnetic field is inversely proportional to the square of the distance.

D) The magnetic field is directly proportional to the sine of the angle between the current element and the position vector.

3. The magnetic field at a point P due to a current element Idl is zero when the angle between Idl and r is:

A) 0 degrees or 180 degrees

B) 90 degrees

C) 45 degrees

D) 270 degrees

4. The magnetic field produced by a current element is strongest when the angle between the current element vector and the position vector is:

A) 0 degrees

B) 90 degrees

C) 180 degrees

D) 45 degrees

5. The direction of the magnetic field dB due to a current element Idl is determined by:

A) The right-hand rule

B) The left-hand rule

C) Fleming's right-hand rule

D) Fleming's left-hand rule

6. The magnetic field at a point P due to a current element Idl is given by dB. If the current is reversed, the magnetic field dB will:

A) Reverse its direction

B) Remain unchanged

C) Become zero

D) Increase in magnitude

7. The Biot-Savart law is particularly useful for calculating magnetic fields from:

A) Symmetrical current distributions

B) Asymmetrical current distributions

C) Point charges

D) Electromagnetic waves

8. The magnetic field at the center of a current-carrying loop is proportional to:

A) The circumference of the loop

B) The diameter of the loop

C) The radius of the loop

D) The area of the loop

9. Which vector quantity is represented by the term Idl in the Biot-Savart law?

A) Velocity vector

B) Current density vector

C) Current element vector

D) Magnetic field vector

10. The magnetic field at the center of a current-carrying wire bent into a circle of radius R is independent of:

A) The current I

B) The radius R

C) The permeability of free space μ₀

D) The shape of the wire

11. If a current element is a loop, the Biot-Savart law is used to calculate the field by integrating over the entire loop:

A) dB = (μ₀ / 4π) * (Idl x r) / r³

B) dB = (μ₀ / 4π) * (Idl ⋅ r) / r³

C) dB = (μ₀ / 4π) * (Idl / r²)

D) dB = (μ₀ / 4π) * (Idl sinθ / r²)

12. The Biot-Savart law is a consequence of which fundamental principle?

A) Conservation of charge

B) Conservation of energy

C) Superposition principle

D) Newton's third law

13. For an infinitely long solenoid, the angles θ₁ and θ₂ in the formula (μ₀nI / 2) * (cosθ₁ - cosθ₂) approach:

A) 0° and 180° respectively

B) 0° and 0° respectively

C) 90° and 90° respectively

D) 0° and 90° respectively

14. What is the magnetic field at a point on the axis of a finite solenoid of length L and radius R, with n turns per unit length, carrying current I?

A) (μ₀nI / 2) * (cosθ₁ - cosθ₂)

B) (μ₀nI / 2) * (sinθ₁ - sinθ₂)

C) (μ₀nI / 2) * (tanθ₁ - tanθ₂)

D) (μ₀nI) * (cosθ₁ - cosθ₂)

15. The magnetic field at the center of a current-carrying hexagon of side 'a' is:

A) √3 μ₀I / (2πa)

B) 3√3 μ₀I / (2πa)

C) 6μ₀I / (2πa)

D) √3 μ₀I / (πa)

16. The magnetic field at the center of a current-carrying equilateral triangle of side 'a' is:

A) 3μ₀I / (2πa)

B) √3 μ₀I / (2πa)

C) μ₀I / (2πa)

D) 9μ₀I / (2πa)

17. What is the magnetic field at the center of a current-carrying loop shaped like a regular n-gon?

A) (nμ₀I / 2a) * tan(π/n)

B) (nμ₀I / 2a) * cot(π/n)

C) (nμ₀I / 2a) * sin(π/n)

D) (nμ₀I / 2a) * cos(π/n)

18. The magnetic field at the center of a semicircle of radius R carrying current I is:

A) μ₀I / R

B) μ₀I / (2R)

C) μ₀I / (4R)

D) πμ₀I / (2R)

19. For a finite straight wire of length L, the magnetic field at the end of the wire on the perpendicular bisector at distance r is:

A) (μ₀I / 4πr) * (1 / sqrt(1 + (2r/L)²))

B) (μ₀I / 2πr) * (1 / sqrt(1 + (2r/L)²))

C) (μ₀I / 4πr) * (1 / sqrt(1 + (L/2r)²))

D) (μ₀I / 4πr) * (L / sqrt(r² + (L/2)²))

20. The magnetic field produced by a finite straight wire of length L carrying current I at a point on its perpendicular bisector at a distance r from the midpoint is:

A) (μ₀I / 4πr) * (sin(φ₁/2) + sin(φ₂/2))

B) (μ₀I / 2πr) * (sin(φ₁) + sin(φ₂))

C) (μ₀I / 4πr) * (2 sin(θ))

D) (μ₀I / 4πr) * (L / sqrt(r² + (L/2)²))

21. Consider a current element Idl. The magnetic field dB at a distance r is zero when the point is located:

A) Along the line containing the current element

B) Perpendicular to the current element

C) At a distance equal to the length of the element

D) At the position of the element

22. The Biot-Savart law is derived from:

A) Gauss's Law for Magnetism

B) Ampere's Circuital Law

C) Maxwell's Equations

D) Lorentz Force Law

23. The magnetic field at a point on the axis of a circular loop is along:

A) The radius of the loop

B) The tangent to the loop

C) The axis of the loop

D) The perpendicular bisector of the loop

24. If the distance from a current element is doubled, the magnetic field produced by it will:

A) Halve

B) Double

C) Become one-fourth

D) Become one-eighth

25. If the current in a wire is doubled, the magnetic field produced by it will:

A) Halve

B) Double

C) Remain the same

D) Become four times

26. Which of the following quantities is NOT required to determine the magnetic field at a point using the Biot-Savart law?

A) The current flowing through the element

B) The length of the current element

C) The mass of the charge carriers

D) The distance from the element to the point

27. The unit of magnetic field is:

A) Tesla (T)

B) Ampere (A)

C) Weber (Wb)

D) Henry (H)

28. The Biot-Savart law is a fundamental law for calculating:

A) Electric potential

B) Magnetic field generated by steady currents

C) Electromagnetic induction

D) Magnetic force on a current-carrying conductor

29. In the formula dB = (μ₀ / 4π) * (Idl sinθ / r²), the term Idl represents:

A) The current intensity

B) The length of the wire

C) The vector product of current and length

D) The product of current and infinitesimal length vector

30. The magnetic field at the center of a current-carrying toroid is:

A) μ₀NI / (2πr)

B) μ₀NI / r

C) Zero

D) μ₀NI

31. The magnetic field outside a long solenoid is approximately:

A) μ₀nI

B) μ₀I

C) Zero

D) μ₀nI / 2

32. The magnetic field inside a long solenoid is:

A) Uniform and parallel to the axis

B) Non-uniform and parallel to the axis

C) Uniform and perpendicular to the axis

D) Zero

33. What is the magnetic field at the center of an infinite solenoid carrying current I with n turns per unit length?

A) μ₀nI

B) μ₀I

C) μ₀nI / 2

D) μ₀I / n

34. The magnetic field at the center of a current-carrying square loop of side length 'a' is:

A) 2μ₀I / (πa)

B) 4μ₀I / (πa)

C) μ₀I / (2πa)

D) √2 μ₀I / (πa)

35. For a circular loop, the magnetic field on the axis is maximum at:

A) The center of the loop (x=0)

B) Infinity (x→∞)

C) A distance R from the center

D) A distance R/2 from the center

36. The magnetic field on the axis of a circular loop of radius R carrying current I at a distance x from the center is:

A) (μ₀IR²) / (2(R² + x²)^(3/2))

B) (μ₀IR²) / (2(R² + x²))

C) (μ₀IR) / (2(R² + x²)^(3/2))

D) (μ₀IR²) / (R² + x²)^(3/2)

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

A) μ₀I / R

B) μ₀I / (2R)

C) μ₀I / (4R)

D) 2μ₀I / R

38. What is the direction of the magnetic field around a long straight wire carrying current, according to the right-hand rule?

A) Along the wire

B) Radially outwards from the wire

C) In concentric circles around the wire, perpendicular to the wire

D) Radially inwards towards the wire

39. The magnetic field due to a long straight wire carrying current I at a perpendicular distance r from the wire is given by:

A) μ₀I / (2πr)

B) μ₀I / r

C) 2πr / μ₀I

D) μ₀I / (4πr)

40. For a current element Idl, when is the magnetic field dB zero at a distance r?

A) When θ = 0° or θ = 180°

B) When θ = 90°

C) When θ = 45°

D) Always

41. For a current element Idl, when is the magnetic field dB maximum at a distance r?

A) When θ = 0°

B) When θ = 90°

C) When θ = 180°

D) When θ = 45°

42. The Biot-Savart law is applicable for:

A) Steady currents only

B) Time-varying currents only

C) Both steady and time-varying currents

D) Alternating currents only

43. What is the value of μ₀?

A) 4π × 10⁻⁷ T m/A

B) 8.85 × 10⁻¹² C²/N m²

C) 9 × 10⁹ N m²/C²

D) 1.6 × 10⁻¹⁹ C

44. The constant of proportionality in the Biot-Savart law in vacuum is:

A) μ₀ / 4π

B) μ₀

C) 1 / 4πε₀

D) ε₀ / 4π

45. The Biot-Savart law is analogous to which law in electrostatics?

A) Gauss's Law

B) Coulomb's Law

C) Ampere's Law

D) Faraday's Law

46. What is the direction of the magnetic field dB due to a current element Idl at a point P?

A) Parallel to Idl

B) Antiparallel to Idl

C) Perpendicular to both Idl and the position vector r

D) Perpendicular to Idl but parallel to r

47. In the Biot-Savart law, what does 'r' represent?

A) The length of the current element

B) The current flowing through the element

C) The distance from the current element to the point where the field is measured

D) The angle between the current element and the position vector

48. The Biot-Savart law states that the magnetic field dB produced by a current element Idl is proportional to:

A) Idl sin(theta) / r^2

B) Idl cos(theta) / r^2

C) Idl tan(theta) / r^2

D) Idl / r^2

49. What is the Biot-Savart law used to calculate?

A) Electric field due to a charge distribution

B) Magnetic field due to a current element

C) Force on a moving charge in a magnetic field

D) Magnetic flux through a surface

Biot–Savart law and magnetic field of current elements - Question Bank