A square loop of side $$2.0 \mathrm{~cm}$$ is placed inside a long solenoid that has 50 turns per centimetre and carries a sinusoidally varying current of amplitude $$2.5 \mathrm{~A}$$ and angular frequency $$700 ~\mathrm{rad} ~\mathrm{s}^{-1}$$. The central axes of the loop and solenoid coincide. The amplitude of the emf induced in the loop is $$x \times 10^{-4} \mathrm{~V}$$. The value of $$x$$ is __________.

$$ \text { (Take, } \pi=\frac{22}{7} \text { ) } $$

A 1 m long metal rod XY completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density 0.15 T. If the resistance of the circuit is 5$$\Omega$$, the force needed to move the rod in direction, as indicated, with a constant speed of 4 m/s will be ____________ 10$$^{-3}$$ N.

Two concentric circular coils with radii $$1 \mathrm{~cm}$$ and $$1000 \mathrm{~cm}$$, and number of turns 10 and 200 respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be ___________ $$\times 10^{-8} \mathrm{H}$$. (Take, $$\pi^{2}=10$$ )

As per the given figure, if $$\frac{\mathrm{dI}}{\mathrm{dt}}=-1 \mathrm{~A} / s$$ then the value of $$\mathrm{V}_{\mathrm{AB}}$$ at this instant will be ____________ $$\mathrm{V}$$.