Question

Find the magnetic field inside a solenoid having number of turns 7000, length 1m, and current 1 A.

• A. \(4\pi \times 10^{-7}\) T
• B. \(4\pi \times 10^{-5}\) T
• C. \(2 \times 10^{-3}\) T
• D. \(1 \times 10^{-3}\) T

Hint:

The magnetic field inside a solenoid depends on the number of turns per unit length and the current flowing through it. It can be calculated using \(B = \mu_0 n I\).

Answer 1

The Correct Option is B

The magnetic field inside a solenoid is given by the formula: \[ B = \mu_0 n I \] Where: - \(B\) is the magnetic field inside the solenoid, - \(\mu_0\) is the permeability of free space (\(4\pi \times 10^{-7}\) T·m/A), - \(n\) is the number of turns per unit length, - \(I\) is the current flowing through the solenoid. We are given: - Number of turns, \(N = 7000\), - Length of the solenoid, \(L = 1\) m, - Current, \(I = 1\) A. The number of turns per unit length \(n\) is: \[ n = \frac{N}{L} = \frac{7000}{1} = 7000 \, \text{turns/m} \] Substituting values into the formula: \[ B = 4\pi \times 10^{-7} \times 7000 \times 1 = 4\pi \times 10^{-5} \, \text{T} \] Thus, the magnetic field inside the solenoid is \(4\pi \times 10^{-5}\) T.