Solenoid Magnetic Field Calculator
Calculate the magnetic field inside a solenoid from the number of turns, length, and current.
Uses the formula B = μ₀nI.
Magnetic Field
A solenoid is a coil of wire wound in a helix. When current flows through it, it creates a uniform magnetic field inside:
B = μ₀nI = μ₀NI/L
Where:
- B = Magnetic flux density (Tesla, T)
- μ₀ = Permeability of free space = 4π × 10⁻⁷ T·m/A ≈ 1.2566 × 10⁻⁶ T·m/A
- n = Turn density = N/L (turns per meter)
- N = Total number of turns
- I = Current through the wire (amperes)
- L = Length of the solenoid (meters)
Key observations:
- The field inside is uniform (same everywhere along the axis, well away from the ends)
- The field is proportional to both current and turns-per-meter
- Outside the solenoid, the field is nearly zero (it’s a good magnetic “shield”)
Inductance of a solenoid: L = μ₀N²A/ℓ = μ₀n²V where A is the cross-sectional area and V is the volume.
Reference values:
| Application | Typical B |
|---|---|
| Earth’s magnetic field | ~50 μT |
| Small electromagnet (lab) | 10–100 mT |
| MRI machine | 1.5–3 T |
| Strong research magnet | 20–45 T |
| Neutron star surface | 10⁸–10¹⁵ T |
Tip: Adding a ferromagnetic core (iron) multiplies B by the relative permeability μr — typically 100–10,000 for iron alloys.