The length of a wire required to manufacture a solenoid of length `l` and self-induction `L` is (cross-sectional area is negligible)`

Options

A. `sqrt((2piLi)/(mu_0))`
B. `sqrt((mu_0Ll)/(4pi))`
C. `sqrt((4piLl)/(mu_0))`
D. `sqrt((mu_0Ll)/(2pi))`

Answer

C

Explanation

`L=(mu_0N^2A)/l`
if x is the length of the solenoid with r as radius
then `x=2pirN,A=pir^2`
`therefore L=mu_0((x^2)/(4pi^2r^2))(pir^2)/l[therefore N=x/(2pir)]`
`therefore x=sqrt((4piLl)/(mu_0))`