Metal rings $P$ and $Q$ are lying in the same plane, where current I is increasing steadily. The induced current in metal rings is shown correctly in figure

The length of solenoid is $$I$$ whose windings are made of material of density $$D$$ and resistivity $$\rho$$. The winding resistance is $$R$$. The inductance of solenoid is [$$m=$$ mass of winding wire, $$\mu_0=$$ permeability of free space]

A coil of $$n$$ turns and resistance $$R \Omega$$ is connected in series with a resistance $$\frac{R}{2}$$. The combination is moved for time $$t$$ second through magnetic flux $$\phi_1$$ to $$\phi_2$$. The induced current in the circuit is

2. Two coils have a mutual inductance of 0.01 H . The current in the first coil changes according to equation, $I=5 \sin 200 \pi t$. The maximum value of emf induced in the second coil is