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A short solenoid of length 4cm, radius 2cm and 100 turns is placed inside and on the axis of a long solenoid of length 80cm and 1500 turns, a current of 3A flows through the short solenoid. The mutual inductance of two solenoid is

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$3.52 \times 10^{- 3} H$

$2.96 \times 10^{- 4} H$

$5.3 \times 10^{- 5} H$

$8.3 \times 10^{- 5} H$

answer is A.

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Detailed Solution

$M = μ_{0} n_{1} n_{2} A l = 4 π \times 10^{- 7} (\frac{100}{4 \times 10^{- 2}}) (\frac{1500}{80 \times 10^{- 2}}) (π \times 4 \times 10^{- 4}) (4 \times 10^{- 2}) = 0.120 H$

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