A long solid cylindrical conductor of radius R carries a current uniformly distributed over its cross-section. The magnetic field at r = R/2 compared with that at the surface is:

A
one half
B
twice
C
zero
D
one quarter

Q46. AI-generated practice Single-correct MCQ Hard

A long hollow thin-walled metal tube carries a current along its length, uniformly distributed round its circumference. The magnetic field inside the tube (in the hollow region) is:

A
largest on the axis
B
uniform and non-zero
C
zero
Dμ₀I/(2πr)

Q47. AI-generated practice Single-correct MCQ Medium

The magnetic field outside an ideal toroid (at points not inside its windings) is:

Aμ₀NI/(2πr)
B
zero
Cμ₀nI
D
half of the field inside

Q48. AI-generated practice Single-correct MCQ Hard

A toroid has 500 turns and a mean radius of 10 cm. When it carries a current of 1 A, the field inside its core is (μ₀ = 4π × 10^-7 T m/A):

A5 × 10^-4 T
B3.1 × 10^-3 T
C1 × 10^-3 T
D6.3 × 10^-3 T

Q49. AI-generated practice Single-correct MCQ Easy

Two long solenoids have the same length and carry the same current, but one has twice as many turns as the other. The field inside the one with more turns is:

A
half as large
B
four times as large
C
twice as large
D
the same

Q50. AI-generated practice Single-correct MCQ Medium

Two long parallel wires, separated by 2d, carry equal currents I in opposite directions. The magnetic field midway between them is:

A
zero
Bμ₀I/(2πd)
Cμ₀I/(4πd)
Dμ₀I/(πd)

Q51. AI-generated practice Single-correct MCQ Hard

Two long parallel wires 10 cm apart carry currents of 5 A and 10 A in the same direction. The magnetic field at the point midway between them is (μ₀ = 4π × 10^-7 T m/A):

A
zero
B2 × 10^-5 T
C4 × 10^-5 T
D6 × 10^-5 T

Q52. AI-generated practice Single-correct MCQ Medium

Two long parallel wires 15 cm apart carry currents of 5 A and 10 A in the same direction. The magnetic field is zero at a point on the line joining them:

A
between the wires, 7.5 cm from each wire
B
between the wires, 5 cm from the 5 A wire
C
between the wires, 10 cm from the 5 A wire
D
outside the wires, 15 cm beyond the 5 A wire

Q53. AI-generated practice Single-correct MCQ Easy

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

A
spirals around the wire
B
straight lines parallel to the wire
C
radial lines starting from the wire
D
concentric circles centred on the wire

Q54. AI-generated practice Single-correct MCQ Hard

A long straight solid conductor of radius 2 cm carries a current of 4 A distributed uniformly over its cross-section. The magnetic field at a distance of 1 cm from its axis is (μ₀ = 4π × 10^-7 T m/A):

A8 × 10^-5 T
B1 × 10^-5 T
C4 × 10^-5 T
D2 × 10^-5 T

Q55. AI-generated practice Numerical value Easy

A long straight wire carries a current of 5 A. Take μ₀ = 4π × 10^-7 T m/A. If the magnetic field at a distance of 2 cm from it is x × 10^-5 T, find x.

Q56. AI-generated practice Numerical value Medium

A solenoid 50 cm long has 500 turns and carries a current of 2 A. Take μ₀ = 4π × 10^-7 T m/A. Find the magnetic field inside it in units of 10^-4 T, to the nearest integer.

Q57. AI-generated practice Numerical value Medium

A long solenoid must produce a field of 6.28 × 10^-3 T inside it with a current of 5 A. Take μ₀ = 4π × 10^-7 T m/A. Find the number of turns needed per centimetre of its length, to the nearest integer.

Q58. AI-generated practice Numerical value Hard

Two long parallel wires 20 cm apart carry currents of 6 A and 4 A in opposite directions. Take μ₀ = 4π × 10^-7 T m/A. If the magnetic field at the point midway between them is x × 10^-6 T, find x.

Q59. AI-generated practice Assertion–Reason Medium

Assertion (A): The magnetic field outside a long, closely wound solenoid is nearly zero.
Reason (R): The magnetic field inside a long solenoid is μ₀nI.

A
Both A and R are true and R is the correct explanation of A
B
Both A and R are true but R is not the correct explanation of A
C
A is true but R is false
D
A is false but R is true

Q60. AI-generated practice Assertion–Reason Hard

Assertion (A): The magnetic field inside a long hollow cylindrical conductor carrying a current along its length is zero.
Reason (R): Ampere's circuital law is valid only for symmetric current distributions.

A
Both A and R are true and R is the correct explanation of A
B
Both A and R are true but R is not the correct explanation of A
C
A is true but R is false
D
A is false but R is true