The Solenoid Formula

This inductance calculator applies L = μ₀μᵣN²A/l for a long solenoid, where μ₀ = 4π×10⁻⁷ H/m, N is the turns, A the cross-section, and l the length. Inductance scales with the square of the turns — doubling the windings quadruples the inductance.

Energy and Dynamics

An inductor stores ½LI² joules of magnetic energy, and an LR circuit charges with time constant τ = L/R. Both matter for switch-mode supplies, where the stored energy must be moved and the time constant sets the ripple and response.

Core Choices

Air cores are linear and lossless at high frequency; ferrite and iron cores multiply inductance by μr but saturate and heat at high currents or frequencies. Pick the core for the operating point, not just the room-temperature number.