Solenoid Magnetic Field

Formula

Description

Inside a long air-core solenoid the magnetic field is nearly uniform and equals the permeability times the number of turns per unit length times the current. Adding a ferromagnetic core multiplies the field by the relative permeability. This is the design equation for electromagnets, relays, inductors, and solenoid actuators.

Variables

• B — Axial flux density inside the solenoid (T)
• N — Total number of turns
• I — Current (A)
• l — Length of the solenoid (m)
• µ₀ = 4π×10⁻⁷ H/m —

Practical Notes

With a high-permeability core, replace µ₀ by µ₀·µr—the field can rise by thousands of times until the core saturates. The field outside an ideal long solenoid is essentially zero.