The formula for the magnetic field inside an ideal long solenoid is B = μ₀ n I, where μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current. If the number of turns per unit length is increased to 2n while the current I remains the same, the new magnetic field B' will be B' = μ₀ (2n) I = 2 (μ₀ n I).