An air core solenoid has 1000 turns and is one metre long. Its cross sectional area is 10 ${cm}^{2}$ It's self- inductance is

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2.78 mH

2.56 mH

1.26 mH

1.92 mH

answer is C.

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Detailed Solution

$\begin{array}{rcl} ϕ & = & NAB = \frac{{NAμ}_{0} Ni}{l} \\ ϕ & = & Li \\ L & = & \frac{N^{2} {Aμ}_{0}}{l} = \frac{10^{6} x 10^{- 3} x 4 πx 10^{- 7}}{1} = 4 π \times 10^{- 4} = 12.56 \times 10^{- 4} H \end{array}$

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