Solenoid Magnetic Field Calculator

A solenoid is a length of wire wound tightly into a series of loops or turns, forming a cylindrical coil. When electric current flows through it, the solenoid generates a strong, nearly uniform magnetic field inside and a negligible field outside — behaving similarly to a bar magnet.

The magnetic field inside a long solenoid is given by B = μ × N × I / L, where μ is the permeability of the core material (μ₀ × μᵣ), N is the number of turns, I is the current in amperes, and L is the length of the solenoid in meters. For an air-core solenoid, μ₀ = 4π × 10⁻⁷ T·m/A.

Multiply the permeability of free space (μ₀ = 1.2566 × 10⁻⁶ T·m/A) by the relative permeability of the core, the number of turns, and the current. Then divide by the solenoid length. For example, a solenoid with 500 turns, 2 A current, 0.5 m length, and air core gives B = (4π × 10⁻⁷ × 500 × 2) / 0.5 ≈ 2.51 mT.

For an ideal, infinitely long solenoid, the magnetic field outside is essentially zero. In practice, real solenoids do have a small fringe field outside, but it is much weaker than the interior field. This is why solenoids are commonly used when a confined, strong magnetic field is needed.

Relative permeability (μᵣ) describes how much more easily a material supports the formation of a magnetic field compared to a vacuum. Air and vacuum have μᵣ = 1. Ferromagnetic materials like iron can have μᵣ in the thousands, dramatically amplifying the magnetic field inside the solenoid for the same current.

Using B = μ₀ × N × I / L = (4π × 10⁻⁷ × 100 × 0.1) / 0.1 ≈ 1.257 × 10⁻⁴ T (approximately 0.126 mT). This is for an air-core solenoid with a vacuum or air core (μᵣ = 1).

Moving electric charges (current) create magnetic fields around them. In a solenoid, the wire is wound so that the small individual magnetic fields from each loop all point in the same direction and add together. This constructive superposition creates a much stronger and more uniform magnetic field inside the coil than a single straight wire could produce.

Turn density (n = N/L) is the number of turns per unit length of the solenoid, measured in turns per meter. The magnetic field formula can also be written as B = μ × n × I. A higher turn density means more field-producing loops per meter, so the magnetic field increases proportionally with n.