Question

A solenoid has length \( l \), number of turns \( N \), and area of cross-section \( A \). Its self-inductance \( L \) is:

• A. \( L = \frac{\mu_0 N^2 A}{l} \)
• B. \( L = \mu_0 N A \)
• C. \( L = \frac{\mu_0 N^2}{l} \)
• D. \( L = \frac{\mu_0^2 N A}{l} \)

Hint:

A long solenoid with more turns per unit length has higher self-inductance.

Answer 1

The Correct Option is A

The formula for the self-inductance of a solenoid is:
\[ L = \frac{\mu_0 N^2 A}{l} \] where:
- \( \mu_0 \) is the permeability of free space,
- \( N \) is the number of turns,
- \( A \) is the cross-sectional area,
- \( l \) is the length of the solenoid.