Question

A solenoid is 1 m long and 4 cm in diameter. It has five layers of windings of 1000 turns each and carries a current of 7 A. The magnetic field at the centre of the solenoid is

• A. \( 43.96 \times 10^{-3} \, \text{T} \)
• B. \( 49.6 \, \text{T} \)
• C. \( 43.96 \times 10^{-2} \, \text{T} \)
• D. \( 4.396 \times 10^{-2} \, \text{T} \)

Hint:

The magnetic field inside a solenoid is directly proportional to the number of turns per unit length and the current. The formula used for calculating this field is \( B = \mu_0 \frac{N}{L} I \).

Answer 1

The Correct Option is D

The magnetic field inside a solenoid is given by the formula: \[ B = \mu_0 \frac{N}{L} I \] where \( B \) is the magnetic field, \( \mu_0 \) is the permeability of free space (\( 4\pi \times 10^{-7} \, \text{T m/A} \)), \( N \) is the total number of turns, \( L \) is the length of the solenoid, and \( I \) is the current. The total number of turns is given by: \[ N = 5 \times 1000 = 5000 \, \text{turns} \] Substituting the values: \[ B = (4 \pi \times 10^{-7}) \frac{5000}{1} \times 7 \] \[ B = 4.396 \times 10^{-2} \, \text{T} \] Thus, the magnetic field at the center of the solenoid is \( 4.396 \times 10^{-2} \, \text{T} \).