Inductance of a Long Solenoid

📊 advanced

$$L = \frac{\mu_0 N^2 A}{l}$$

Calculates the self-inductance of an air-core solenoid.

Variables & Units

$N$

Total number of turns

Unit: Integer

$A$

Cross-sectional area

Unit: $m^2$

$l$

Length of solenoid

Unit: Meter ($m$)

Key Information

📐 Derived From

Definition of inductance $L = N\Phi/I$ and Ampere's Law.

💡 Example

Finding $L$ for a coil with $1000$ turns, $10 cm$ length, $2 cm$ radius.

🔧 Applications

Radio frequency coils and power transformers.

⚠️ Constraints

Length $l$ must be much greater than radius.

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