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

Step-by-step solution

For solenoids, self inductance is given by, L= ₀ N^2 A l L₁ L₂ = ( r₁^2 l₁ ) ( r₂^2 l₂ ) = ( r₁^2 l₁ ) ( r₂^2 l₁ ) or L₁ L₂ = 1 2 ( r₁^2 l₁ / r₂^2 l₂ =1 / 2 )