What Is a Solenoid?
When electric current flows through a wire, a magnetic field forms around it. A solenoid is a wire wound tightly in a long, thin coil. Because of this shape, running current through the solenoid produces a strong, nearly uniform magnetic field inside the coil and an extremely weak (essentially zero) field outside.
Solenoids appear in countless practical devices — from door locks and car starters to MRI machines and particle accelerators — because the magnetic field strength can be controlled simply by adjusting the current. They are also fundamental inductive elements in electronic circuits.
Solenoid Magnetic Field Equation
For a long (ideally infinite) solenoid the magnetic field inside is uniform and given by:
B = μ₀ · N · I / L
- B — Magnetic field strength (Tesla, T)
- μ₀ = 4π × 10⁻⁷ T·m/A ≈ 1.25664 × 10⁻⁶ T·m/A — Vacuum permeability (magnetic constant)
- N — Number of turns (complete coil loops)
- I — Electric current through the wire (Amperes)
- L — Total length of the solenoid (meters)
The ratio n = N / L is called the turn density (turns per meter). The formula simplifies to B = μ₀ · n · I.
How to Calculate the Magnetic Field of a Solenoid
- Count the total number of turns N in the solenoid.
- Measure or specify the electric current I (in mA, A, or kA).
- Measure the total length L of the solenoid (in mm, cm, m, inches, or feet).
- The calculator applies B = μ₀ × N × I / L and displays the result in Tesla (T), millitesla (mT), microtesla (μT), and Gauss (G).
The calculator supports both the metric (SI) system and the American system of measurement (inches and feet for length).
Unit Conversions
- 1 T = 1,000 mT = 1,000,000 μT = 10,000 G
- Earth's surface field ≈ 25–65 μT (0.25–0.65 G)
- Refrigerator magnet ≈ 5–10 mT
- MRI machine ≈ 1.5–7 T
Frequently Asked Questions
Why is the magnetic field zero outside an ideal solenoid?
At two diametrically opposite points on the coil the magnetic fields generated by the wire elements point in exactly opposite directions outside the solenoid, cancelling each other perfectly. Inside, those same fields add together, creating a strong, uniform field. Outside an ideal infinite solenoid, B = 0.
Does a real solenoid behave the same as an ideal one?
A finite-length solenoid has a slightly weaker field near its ends (fringing effects). The formula above is exact for an infinite solenoid and a very good approximation for real solenoids when the length is much greater than the diameter (L ≫ d).
How do I increase the magnetic field of a solenoid?
You can increase B by:
- Increasing the number of turns N (more coils = stronger field)
- Increasing the current I (higher current = stronger field)
- Decreasing the length L (shorter solenoid at same N = higher turn density)
- Adding a ferromagnetic core (iron core multiplies B by the relative permeability μᵣ, typically 100–10 000×)
What is vacuum permeability (μ₀)?
The vacuum permeability μ₀ = 4π × 10⁻⁷ T·m/A is a fundamental physical constant that relates magnetic field strength to the current that produces it in free space. It is sometimes called the magnetic constant or permeability of free space.