Q138 / 170 · Manipal (MET) 2017 · Physics
A short solenoid of length 4 cm , radius 2 cm and 100 turns is placed inside and on the axis of a long solenoid of length 80 cm and 1500 turns. A current of 3 A flows through the short solenoid. The mutual inductance of two solenoids is
- Correct answerA$2.96 \times 10^{-4} \mathrm{H}$
- B$5.3 \times 10^{-5} \mathrm{H}$
- C$3.52 \times 10^{-3} \mathrm{H}$
- D$8.3 \times 10^{-5} \mathrm{H}$
Solution
$M_{21}=\frac{\mu_0 N_1 N_2 A_2}{l_1}$
$\therefore M_{21}=\frac{\left(4 \times 3.14 \times 10^{-7}\right) \times 1500 \times 100\times\left\{3.14\left(2 \times 10^{-2}\right)^2\right\}}{80 \times 10^{-4}}$
$M_{21}=2.96 \times 10^{-4} \mathrm{H}$
$\Rightarrow M_{12}=M_{21}=2.96 \times 10^{-4} \mathrm{H}$
Hence, the correct answer is option: 'A'.