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Q.

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

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a

2πLl0μ0

b

4πLl0μ02

c

4πLl0μ0

d

8πLl0μ0

answer is C.

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