A wire of fixed length is wound on a solenoid of length `l` and radius `r`. Its self-inductance is found to be `L`. Now, if the same wire is wound on a solenoid of length `l//2` and 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`.