Two solenoids of equal number of turns having their length and the radii in the same ratio 1:2. The ratio of their self-inductance will be?

Self inductance of a solenoid, L = μ₀N²A/l = μ₀N²πr²/l
where l is the length of the solenoid, N is the total number of turns of the solenoid and A is the area of cross-section of the solenoid.
∴L₁/L₂ = (N₁/N₂)²(r₁/r₂)²(l₂/l₁)
Here, N₁ = N₂, l₁/l₂ = 1/2, r₁/r₂ = 1/2
∴L₁/L₂ = (1/2)²(2/1) = 1/2