Question

A solenoid has the length 1 m and the area of cross section \(0.02\ \text{m}^2\). If no. of turns in the solenoid is 5000 then the self inductance of the solenoid is

• A. 0.2π henry
• B. 0.4π henry
• C. 0.2 henry
• D. 0.04π henry

Hint:

Use formula \(L = \frac{\mu_0 N^2 A}{l}\) for solenoids.
Cross-section area and total turns directly affect inductance.

Answer 1

The Correct Option is A

The formula for self inductance: \[ L = \frac{\mu_0 N^2 A}{l} \] Given: \[ N = 5000, \quad A = 0.02\ \text{m}^2, \quad l = 1\ \text{m}, \quad \mu_0 = 4\pi \times 10^{-7} \] \[ L = \frac{4\pi \times 10^{-7} \cdot (5000)^2 \cdot 0.02}{1} = 0.2\pi\ \text{H} \]