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Q.

An air core solenoid has1000 turns and is one metre long. Its cross- sectional area is10 cm². 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, $B = μ_{0} ni = μ_{0} \frac{N}{l} i$
$ϕ = NBA = N [μ_{0} \frac{N}{l} i] A = μ_{0} \frac{N^{2} A}{l} i$
Also $ϕ = Li ∴ L = \frac{μ_{0} N^{2} A}{l}$
So $\begin{array}{l} L = 4 π \times 10^{- 7} \times \frac{(1000)^{2}}{1} \times 10 \times 10^{- 4} \end{array}$
$= 0 .0012566 H = 1 .26 mH$

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An air core solenoid has1000 turns and is one metre long. Its cross- sectional area is10 cm2. its self- inductance is