Find the inductance of a solenoid of length `l` whose winding is made of copper wire of mass `m`. The winding resistance is equal to `R`. The solenoid diameter is considerably less than its length.

Explanation

From the previous problem, we know that,
l' = length of the wire needed `= sqrt((L l 4pi)/(mu_(0)))`, where `l` = length of solenoid here.
Now, `R = (rho_(0) l')/(S)`, (where `S` = area of crossection of the wire, Also `m = rho S l'`)
Thus. `l' (R S)/(rho_(0)) = (R m)/(rho rho_(0) l')` or `l' = sqrt((Rm)/(rho rho_(0)))`
where `rho_(0)` = resistivity of copper and `rho` = its density.
Equating, `(Rm)/(rho rho_(0)) = (L l)/(mu_(0)//4pi)`
or, `L = (mu_(0))/(4pi) (m R)/(rho rho_(0) l)`