$A$ coil of resistance $250 \Omega$ is placed in a magnetic field. If the magnetic flux $(\phi)$ linked with the coil varies with time $t$ $(s)$ as $\phi = 50t^2 + 7$,the current in the coil at $t = 4 \ s$ is: (in $A$)

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

According to Faraday's law of electromagnetic induction:

$A$ vertical bar magnet is dropped from the shown position on the axis of a fixed metallic coil as shown in Fig-$I$. In Fig-$II$,the magnet is fixed and a horizontal coil is dropped. If the acceleration of the magnet and coil are $a_1$ and $a_2$ respectively,then:

$A$ magnetic field $B = 2t + 4t^{2}$ (where $t$ is time) is applied perpendicular to the plane of a circular wire of radius $r$ and resistance $R$. If all units are in $SI$, the electric charge that flows through the circular wire during $t = 0 \ s$ to $t = 2 \ s$ is:

$A$ square loop of side $10 \; cm$ and resistance $0.5 \; \Omega$ is placed vertically in the east-west plane. $A$ uniform magnetic field of $0.10 \; T$ is set up across the plane in the north-east direction. The magnetic field is decreased to zero in $0.70 \; s$ at a steady rate. Determine the magnitudes of induced emf and current during this time interval.