The magnetic flux $$\phi$$ (in weber) linked with a closed circuit of resistance $$8 \Omega$$ varies with time (in seconds) as $$\phi=5 t^2-36 t+1$$. The induced current in the circuit at $$t=2 \mathrm{~s}$$ is __________ A.

A small square loop of wire of side $$l$$ is placed inside a large square loop of wire of side $$L\left(L=l^2\right)$$. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $$\sqrt{x} \times 10^{-7} \mathrm{H}$$, where $$x=$$ _________.

A ceiling fan having 3 blades of length $$80 \mathrm{~cm}$$ each is rotating with an angular velocity of 1200 $$\mathrm{rpm}$$. The magnetic field of earth in that region is $$0.5 \mathrm{G}$$ and angle of dip is $$30^{\circ}$$. The emf induced across the blades is $$\mathrm{N} \pi \times 10^{-5} \mathrm{~V}$$. The value of $$\mathrm{N}$$ is _________.

A horizontal straight wire $$5 \mathrm{~m}$$ long extending from east to west falling freely at right angle to horizontal component of earths magnetic field $$0.60 \times 10^{-4} \mathrm{~Wbm}^{-2}$$. The instantaneous value of emf induced in the wire when its velocity is $$10 \mathrm{~ms}^{-1}$$ is _________ $$\times 10^{-3} \mathrm{~V}$$.