A wire of fixed length is wound on a solenoid of length 'l' and radius 'r' . Its self inductiane is found to be Now if same wire is wound on a solenoid of length ad radius `(r)/(2)` then the self inductance will be

Options

A. `2L`
B. `L`
C. `4L`
D. `8L`

Answer

A

Explanation

`L = (mu_(0)N^(2)pi r^(2))/(l)` Length of wire `= N 2pir = `Constant `( = C`, suppose)
`:. L = mu_(0) ((C )/(2 pir))^(2) (pir^(2))/(l)`
`:. L prop (1)/(l)`
`:.` Self-inductance will become `2L`.