Lesson 11 of 15
Solenoid Inductance
Inductance of a Solenoid
A solenoid is a coil of N turns wound over length l. When current flows, it creates a nearly uniform magnetic field inside. Its inductance is:
L = rac{mu_0 N^2 A}{l}
- L — inductance (henrys, H)
- H/m — permeability of free space
- N — total number of turns
- A — cross-sectional area (m²)
- l — length of the solenoid (m)
Why N²?
Each turn contributes to the field, and the total flux linkage is (flux per turn). Since flux per turn is also proportional to N (more turns = stronger field), inductance grows as .
Applications
Solenoids are the basis of inductors in filters and oscillators, electromagnets, transformers, and electric motors. Inductance opposes changes in current — a solenoid stores energy in its magnetic field.
Examples
| N | A (m²) | l (m) | L (H) |
|---|---|---|---|
| 1000 | 1×10⁻⁴ | 0.1 | 1.26e-03 |
| 100 | 1×10⁻⁴ | 0.1 | 1.26e-05 |
| 500 | 2×10⁻⁴ | 0.2 | 3.14e-04 |
| 200 | 5×10⁻⁴ | 0.5 | 5.03e-05 |
Your Task
Implement solenoid_inductance(N, A, l) returning inductance in henrys.
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