Two coils have a mutual inductance of $$0.004 \mathrm{~H}$$. The current changes in the first coil according to equation $$\mathrm{I}=\mathrm{I}_0 \sin \omega \mathrm{t}$$, where $$\mathrm{I}_0=10 \mathrm{~A}$$ and $$\omega=50 ~\pi \mathrm{~rad} ~\mathrm{s}^{-1}$$. The maximum value of e.m.f. in the second coil in volt is

The magnetic flux through a circuit of resistance '$$R$$' changes by an amount $$\Delta \phi$$ in the time $$\Delta t$$. The total quantity of electric charge '$$Q$$' which passes during this time through any point of the circuit is

The self inductance '$$L$$' of a solenoid of length '$$l$$' and area of cross-section '$$\mathrm{A}$$', with a fixed number of turns '$$\mathrm{N}$$' increases as

A coil having effective area '$$A$$' is held with its plane normal to a magnitude field of induction '$$\mathrm{B}$$'. The magnetic induction is quickly reduced to $$25 \%$$ of its initial value in 1 second. The e.m.f. induced in the coil (in volt) will be