A metallic cube of side $$15 \mathrm{~cm}$$ moving along $$y$$-axis at a uniform velocity of $$2 \mathrm{~ms}^{-1}$$. In a region of uniform magnetic field of magnitude $$0.5 \mathrm{~T}$$ directed along $$z$$-axis. In equilibrium the potential difference between the faces of higher and lower potential developed because of the motion through the field will be _________ mV.

The magnetic field B crossing normally a square metallic plate of area $$4 \mathrm{~m}^{2}$$ is changing with time as shown in figure. The magnitude of induced emf in the plate during $$\mathrm{t}=2 s$$ to $$\mathrm{t}=4 s$$, is __________ $$\mathrm{mV}$$.

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.