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 same wire is wound on a solenoid of length l/2 and radius r/2 , then self inductance will be

ans: 2L

why not L/2

Self inductance is directly proportional to :
n2lr2
n is number of turns,
l is the length,
r is the radius.
SO THE LENGTH OF WIRE COMES OUT TO BE = 2*pie*r*n1
​L1 =k n1​2 l r2

Now if same wire is wound on a solenoid of length l/2 and radius r/2
then 
n2 = no of turns comes out to be =
2*pie*r*n1​/2*pie*r/2 = 2n1
so the correct answer is L/2
 

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