The length of a thin wire required to manufacture a solenoid of length`l = 100 cm` and inductance `L = 1 mH`, if the solenoid's cross-sectional diameter is considerably less than its length is

Options

A. `1 km`
B. `0.10 km`
C. `0.010 km`
D. `10 km`

Answer

B

Explanation

Let `l_(1)` is the length of wire, then
`l_(1) = 2 pirN rArr Nr = (l_(1))/(2 pi) rArr L = (mu_(0) pi)/(l) (l_(1)^(2))/(4pi^(2))`
`rArr l_(1) = sqrt((Ll4pi)/(mu_(0))) = sqrt((10^(-3) xx 1xx 4pi)/(4 pi xx 10^(-7))) = 10^(2) m = 0.10 km`