Magnetic Field of a Solenoid
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Constant used — built into this formula, no need to enter
Vacuum magnetic permeabilityLearning zone
Wind wire into a tight helix and the fields of all the turns add up inside while cancelling outside, leaving a remarkably uniform interior field that depends only on turns per length and current — not on the coil's diameter. A 20 cm coil of 1000 turns at 5 A produces μ₀ × 1000 × 5 / 0.2 ≈ 31 mT, several hundred times Earth's field. Wrap the same coil around an iron core and the field multiplies a thousandfold — the recipe for electromagnets, relays, and MRI bores (which swap iron for superconducting current).
Magnetic Field of a Solenoid
Where
- = Magnetic field
- = Number of turns
- = Current
- = Solenoid length
Missing one of these? Work it out first, then come back
- Magnetic field — Magnetic Flux (Φ = BA cos θ), Motional EMF (ε = BLv)
- Number of turns — Faraday's Law of Induction, Transformer Voltage Ratio
- Current — Ohm's Law, Electrical Power (P = VI)
- Solenoid length — Motional EMF (ε = BLv), Resistance of a Wire (R = ρL/A)