How to use it
- Choose a straight wire, a circular coil or a solenoid.
- Enter the current in amperes.
- Enter the size: the distance from the wire; the number of turns and the radius of a coil (and the distance along its axis, 0 for the centre); or the number of turns and length of a solenoid, with μr for its core (1 for air).
- Pick the length unit and read B in T, mT, µT and gauss, and H in A/m.
Formulas
μ₀ = 1.25663706212 × 10⁻⁶ N/A².
- Long straight wire: B = μ₀ I ÷ (2π r)
- N-turn circular coil on its axis: B = μ₀ N I R² ÷ (2 (R² + z²)^(3/2)); at the centre B = μ₀ N I ÷ (2R)
- Long solenoid: B = μr μ₀ N I ÷ ℓ = μr μ₀ n I
- Field strength: H = B ÷ (μr μ₀)
Worked example
A long wire carries 10 A. At 1 cm: B = 1.25663706 × 10⁻⁶ × 10 ÷ (2π × 0.01) = 0.0002 T = 200 µT = 2 G.
A coil of 100 turns, radius 5 cm, 10 A: B = μ₀ × 100 × 10 ÷ 0.1 = 12.566371 mT at the centre. 5 cm along the axis it drops to 4.442883 mT.
A solenoid with 1000 turns on 10 cm and 1 A: n = 10,000 turns per metre, B = μ₀ × 10,000 × 1 = 12.566371 mT, H = 10,000 A/m.
Tips
- The straight-wire formula needs a long wire: much longer than the distance r. Near the end of a short wire the field is weaker.
- The solenoid formula needs a long coil. For a coil about as long as it is wide the real field in the middle is noticeably lower.
- An iron core multiplies B by μr only until the iron saturates; this calculator assumes a constant μr.