• Pixel-art sticker of Coilet, personifying Self-Inductance of a Solenoid, with the caption “Change My Current, I Push Back.”

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Coilet

Self-Inductance of a Solenoid Physics

\[L = \frac{\mu_0 N^2 A}{\ell}\]
$4.99 USD
$4.99 USD
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Meet Coilet, a long copper coil who pushes back against every change in his current. Inductance grows with the square of the turns: 500 turns, 1 cm² and 10 cm long give about 0.31 mH, so a 1 A change in 1 ms induces about 0.31 V. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Meet Coilet, a long copper coil who resists every change in the current flowing through him.

Current in a coil makes a magnetic field inside it. If the current changes, the field changes, and by Faraday's law that changing field induces a voltage in the same coil. That voltage always pushes against the change. This is self-inductance.

For a long solenoid with N turns, cross-section area A and length ℓ, the inductance is L = μ₀N²A/ℓ. It goes with the square of the number of turns, because more turns make more field and each turn also feels more of it.

A coil 10 cm long with 500 turns and an area of 1 cm² has L ≈ 0.31 mH. If its current changes by 1 A in 1 ms, it pushes back with about 0.31 V.

Inductors smooth out current in power supplies, filter signals in audio crossovers, and store the energy that makes a car's ignition coil fire.

Equations

\[L = \frac{\mu_0 N^2 A}{\ell}\]
SymbolMeaningUnit
\(L\) inductance \(\mathrm{H}\)
\(\mu_0\) vacuum permeability \(\mathrm{H/m}\)
\(N\) number of turns \(\mathrm{dimensionless}\)
\(A\) cross-section area \(\mathrm{m²}\)
\(\ell\) solenoid length \(\mathrm{m}\)

Sources

  1. OpenStax University Physics Vol. 2 — Self-Inductance and Inductors
  2. NIST CODATA — vacuum magnetic permeability μ₀

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