The self-inductance of a long solenoid of length ℓ, area A, with n turns per unit length is approximately:

1. Total turns N = n ℓ; flux per turn Φ₁ = B A = (μ₀ n I) A. 2. Total flux linkage Λ = N Φ₁ = (n ℓ)(μ₀ n I A) = μ₀ n² ℓ A I. 3. So L = Λ / I = μ₀ n² A ℓ. _Source: syllabus Physics Ch 6 §6.8 Self-Inductance of a Solenoid_