Two conducting circular loops of radii \(R_1\) and \(R_2\) are placed in the same plane with their centres coinciding. If \(R_1>>R_2\), the mutual inductance \(M\) between them will be directly proportional to:

A long solenoid of diameter \(0.1\) m has \(2 \times 10^4\) turns per meter. At the center of the solenoid, a coil of \(100\) turns and radius \(0.01\) m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to \(0\) A from \(4\) A in \(0.05\) s. If the resistance of the coil is \(10\pi^2~\Omega\), then the total charge flowing through the coil during this time is:
1. \(16~\mu \text{C}\)
2. \(32~\mu \text{C}\)
3. \(16\pi~\mu \text{C}\)
4. \(32\pi~\mu \text{C}\)

Two coils of self-inductance \(2~\text{mH}\) and \(8~\text{mH}\) are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is:
1. \(10~\text{mH}\)
2. \(6~\text{mH}\)
3. \(4~\text{mH}\)
4. \(16~\text{mH}\)

Two coils have a mutual inductance \(0.005\) H. The current changes in the first coil according to equation \(I=I_{0}\sin\omega t\) where \(I_{0}=2\) A and \(\omega=100\pi \) rad/s. The maximum value of emf in the second coil is:
1. \(4\pi\) V
2. \(3\pi\) V
3. \(2\pi\) V
4. \(\pi\) V