Q 12-06-029JEE MainMedium
A long solenoid has $1000$ turns per metre and cross-section $10\ \text{cm}^2$. A $50$-turn coil is wound tightly round its middle. Find their mutual inductance, in microhenry, to the nearest whole number. ($\mu_0 = 4\pi \times 10^{-7}$ T m/A)
Numerical value type. Enter your answer.
Answer: 63
Concept. The solenoid's field $\mu_0nI$ passes through every turn of the outer coil: $M = \mu_0nN_2A$.
Step 1. Substitute. $A = 10\ \text{cm}^2 = 10^{-3}\ \text{m}^2$:
$$M = 4\pi \times 10^{-7} \times 1000 \times 50 \times 10^{-3} \approx 6.28 \times 10^{-5}\ \text{H} \approx 63\ \mu\text{H}$$
Answer. $63$.
Solution by Sreeraj P, M.Sc Physics