First slide
Inductance
Question

How much length of a very thin wire is required to obtain a solenoid of length  l0 and inductance L

Moderate
Solution

Suppose solenoid has N turns, each of radius r and length of wire is l. 

It’s self inductance  L=μ0N2Al0=μ0N2πr2l0 .... (i)
Also length of the wire  l=N×2πr

N2r2=l24π2.... (ii)
From equation (i) and (ii)  l=4πLloμo
 

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