Q 12-06-084JEE MainJEE Main 2023 (6 Apr, Shift 2)Medium
Two concentric circular coils with radii $1\ \text{cm}$ and $1000\ \text{cm}$ and number of turns $10$ and $200$ respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be ______ $\times10^{-8}$ H. (Take $\pi^2=10$)
Numerical value type. Enter your answer.
Answer: 4
Field of the large coil at its centre: $B=\dfrac{\mu_0N_2I}{2R}$, uniform over the small coil.
$$M=\frac{\mu_0N_1N_2\pi r^2}{2R}=\frac{4\pi\times10^{-7}\times10\times200\times\pi\times10^{-4}}{2\times10}=\frac{4\pi^2\times2\times10^{-8}}{20}\times10=4\times10^{-8}\ \text{H}$$
Solution by Sreeraj P, M.Sc Physics