How many meters of a thin wire are required to manufacture a solenoid of length `l_(0) = 100 cm` and inductance `L = 1.0 mH` if the solnoid's cross -sectional diameter is condiserably less than its length ?

Explanation

Given `L = mu_(0) n^(2) V = mu_(0) n^(2) l_(0) pi R^(2)`, where `R` is the radius of the solenoid
Thus, `n = sqrt((L)/(mu_(0) l_(0) pi)) (1)/(R)`
So, length of the wire required is,
`l = n l_(0) 2pi R = sqrt((4pi L l_(0))/(mu_(0))) = 1.10 km`