Calculate the magnetic flux density (B) inside a solenoid based on its turns, length, current, and core material.
Last updated: March 2026 | By ForgeCalc Engineering
A solenoid is a long coil of wire that produces a uniform magnetic field inside its core when an electric current passes through it. The field is strongest and most uniform in the center of the solenoid.
The strength of the magnetic field (B) is directly proportional to the current (I) and the number of turns per unit length (n = N/l). Like inductance, the magnetic field can be greatly enhanced by using a core material with high magnetic permeability.
Where:
• B is the magnetic flux density (T)
• μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A)
• μ_r is the relative permeability of the core
• N is the total number of turns
• I is the current (A)
• l is the length of the solenoid (m)
One Tesla (T) is a very large unit of magnetic flux density. For context, the Earth's magnetic field is about 0.00005 T (50 μT), while a strong refrigerator magnet is about 0.005 T (5 mT).
Inside a long solenoid, the magnetic field lines are parallel and evenly spaced, creating a uniform field. Outside the solenoid, the field is very weak and quickly drops to zero.
Ferromagnetic materials like iron align their internal magnetic domains with the solenoid's field, effectively 'multiplying' the field strength by their relative permeability (μ_r).
An electromagnet is essentially a solenoid with a ferromagnetic core. It can be turned on and off by controlling the electric current, making it useful for lifting scrap metal, relays, and MRI machines.
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