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Inductance of a solenoid
Intermediate
Depends on turns and geometry.
L = μ₀N²A/lL = μ₀N²A/l: grows as the square of turns and with an iron core by μ_r.
N = 1000, A = 10 cm², l = 0.2 m: 6.3 mH.
Doubling turns quadruples L.
In more detail
A long solenoid has inductance L = μ0N²A/l, where N is the number of turns, A is the cross-section and l is the length. It increases with the square of the number of turns.
Real-world uses
- Designing inductors with specific values for filters.
- Coils in motors and generators are designed with calculated inductance.
- Engineers designing a coil to filter a signal calculate its inductance from the number of turns and its length.
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Frequently asked questions
How can I increase inductance?
Add more turns, use a core with high permeability, or make the coil longer or narrower.
Does length affect it?
Yes, a longer coil has lower inductance for the same turns.
Why does inductance depend on N squared?
Doubling the turns doubles the flux per turn and doubles the number of turns, so the inductance rises by a factor of four.
Related topics in Magnetism & Induction
Eddy currents · Eddy current braking · Self-inductance · Energy in an inductor · Mutual inductance · Transformer