A coil of radius '$$\mathrm{r}$$' is placed on another coil (whose radius is '$$\mathrm{R}$$' and current through it is changing) so that their centres coincide. ( $$R > r$$ ). If both coplanar, then the mutual inductance between them is proportional to

A metal wire of length $$2500 \mathrm{~m}$$ is kept in east-west direction, at a height of $$10 \mathrm{~m}$$ from the ground. If it falls freely on the ground then the current induced in the wire is (Resistance of wire $$=25 \sqrt{2} \Omega, \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$ and Earth's horizontal component of magnetic field $$\left.\mathrm{B}_{\mathrm{H}}=2 \times 10^{-5} \mathrm{~T}\right)$$

Two conducting wire loops are concentric and lie in the same plane. The current in the outer loop is clockwise and increasing with time. The induced current in the inner loop is

A straight conductor of length 0.6 M is moved with a speed of 10 ms$$^{-1}$$ perpendicular to magnetic field of induction 1.2 weber m$$^{-2}$$. The induced e.m.f. across the conductor is