A coil of radius '$$r$$' is placed on another coil (whose radius is $$\mathrm{R}$$ and current flowing through it is changing) so that their centres coincide $$(\mathrm{R} \gg \mathrm{r})$$. If both the coils are coplanar then the mutual inductance between them is ( $$\mu_0=$$ permeability of free space)

When a current of $$1 \mathrm{~A}$$ is passed through a coil of 100 turns, the flux associated with it is $$2.5 \times 10^{-5} \mathrm{~Wb} /$$ turn. The self inductance of the coil in millihenry is

The mutual inductance of a pair of coils, each of '$$N$$' turns, is '$$M$$' henry. If a current of '$$I$$' ampere in one of the coils is brought to zero in '$$t$$' second, the e. m. f. induced per turn in the other coil in volt is

To manufacture a solenoid of length $$1 \mathrm{~m}$$ and inductance $$1 \mathrm{~mH}$$, the length of thin wire required is

(cross - sectional diameter of a solenoid is considerably less than the length)