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

Answer

A

Explanation

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