A solenoid is a long, tightly wound coil of insulated wire. When current flows through it, it produces a strong, uniform magnetic field inside its core — behaving like a bar magnet.
For an ideal solenoid (very long compared to its diameter), the magnetic field inside is uniform and given by:
where:
The field is strongest and most uniform deep inside the solenoid. At the open ends, the field is approximately half the central value () as field lines begin to diverge.
To find the direction of the magnetic field (and identify the North pole) of a solenoid:
Curl the fingers of the right hand in the direction of conventional current flow around the solenoid. The extended thumb points toward the North pole, which is also the direction of inside.
Inserting a ferromagnetic core (e.g., soft iron) inside a current-carrying solenoid dramatically increases the magnetic field. This combination is called an electromagnet.
Magnetic permeability measures a material's ability to support a magnetic field within itself.
Relative permeability () is the ratio of the material's permeability to the permeability of free space:
| Material | Relative Permeability () |
|---|---|
| Air / Vacuum | |
| Soft Iron | – |
| Steel | – |
The magnetic field inside a solenoid with a ferromagnetic core is:
Because for iron, the field is greatly amplified.
| Feature | Air-Core Solenoid | Solenoid with Ferrous Core |
|---|---|---|
| Field Strength | Weaker | Hundreds–thousands of times stronger |
| Field Lines | Less concentrated, spread outside | Highly concentrated within core |
| Core |
Soft iron is the preferred core material for most electromagnets: