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((2pi Ll)/(mu_(0)))`
B. `sqrt((mu_(0) Ll)/(4 pi))`
C. `sqrt((4pi Ll)/(mu_(0)))`
D. `sqrt((mu_(0) Ll)/(2pi))`

Answer

C

Explanation

`L = (mu_(0)N^(2)A)/(l)`
If `x` is the length of the solenoid with `r` as radius, then `x = 2 pi rN, A = pi r^(2)`
`:. L = mu_(0) ((x^(2))/(4pi^(2) r^(2))) (pi r^(2))/(l) [ :. N = (x)/(2 pi r)]`
`:. x = sqrt((4pi L l)/(mu_(0)))`