Campo Magnético Solenoide
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
B = μ₀·(N/L)·I
About this calculator
This calculator determines the magnetic field inside an ideal solenoid (long and tightly wound). The formula used is B = μ₀·(N/L)·I, where B is the magnetic field in teslas, μ₀ is the vacuum permeability (4π × 10⁻⁷ T·m/A), N is the number of turns, L is the solenoid length in meters, and I is the electrical current in amperes. The result is valid only for points near the center, away from the ends.
You can use this tool for designing electromagnets, coils for physics experiments, or sizing components such as relays and solenoid valves. For example, when designing an electromagnet to lift metal objects, you can estimate the required field and adjust the number of turns or current. Note that the formula assumes an ideal solenoid: no ferromagnetic core and uniform field inside.
Important considerations: the permeability μ₀ is for vacuum; if a material core is present, the field will be amplified by the relative permeability (μᵣ). Also, the long solenoid approximation fails if the length is less than 10 times the diameter. For short solenoids, the field at the ends is about half the central value. Ensure consistent units: length in meters and current in amperes.
Frequently asked questions
What is μ₀ and its value?
μ₀ is the vacuum magnetic permeability, a physical constant. Its value is 4π × 10⁻⁷ T·m/A, approximately 1.2566 × 10⁻⁶ T·m/A.
Does the formula work for solenoids with an iron core?
Not directly. For ferromagnetic cores, use B = μ₀·μᵣ·(N/L)·I, where μᵣ is the relative permeability of the material (e.g., iron ~200 to 5000).
What is the difference between an ideal and real solenoid?
An ideal solenoid is infinitely long with tightly packed turns, producing a uniform internal field and zero external field. Real solenoids have non-uniform fields at the ends and some external field.
Can I use this calculator for a short coil?
The formula is accurate only for long solenoids (length >> diameter). For short coils, the central field is lower than predicted; use corrections or numerical simulations.
How do I convert the field to gauss?
1 tesla = 10,000 gauss. Multiply the result in teslas by 10,000 to obtain the value in gauss.