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Q.

An air core solenoid has 1000 turns and is one metre long. Its cross - sectional area is 10cm². Its self - Inductance is

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a

2.56 mH

b

1.92 mH

c

1.26 mH

d

2.78 mH

answer is C.

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Detailed Solution

For solenoid, $B = μ_{0} ni = μ_{0} \frac{N_{i}}{l}$
$ϕ = NBA = N [μ_{0} \frac{N_{i}}{1}] A = μ_{0} \frac{N^{2} A}{1}$
Also $ϕ = Li ∴ L = \frac{μ_{0} N^{2} A}{1}$
So $L = 4 π \times 10^{- 7} \times \frac{(1000)^{2}}{1} \times 10 \times 10^{- 4} = 0 .0012566 H = 1 .26 mH$

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