Self-Inductance of a Solenoid

📊 intermediate

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

Calculates the inductance of a long solenoid.

Variables & Units

$L$

Self-inductance

Unit: Henry ($H$)

$N$

Total number of turns

Unit: Dimensionless

$A$

Cross-sectional area

Unit: $m^2$

$l$

Length of solenoid

Unit: Meter ($m$)

Key Information

📐 Derived From

Flux linkage $\Phi = LI$ and magnetic field $B = \mu_0 n I$.

💡 Example

Finding $L$ for a solenoid with 1000 turns and $10 cm$ length.

🔧 Applications

Radio tuning and power converters.

⚠️ Constraints

Length $l$ must be much greater than the radius.

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