$A$ 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 $A$)

$A$ circular loop made of thin copper wire of mass $m$ is placed in a uniform magnetic field such that the plane of the loop is perpendicular to the magnetic field. If $d$ and $\rho$ are the density and resistivity of copper respectively and the magnetic field varies at a constant rate of $\frac{dB}{dt}$,then the induced current in the loop is . . . . . .

Magnetic flux (in $Wb$) linked with a closed loop varies with time $t$ (in $s$) as $\phi = 2t^2 + 1$. The magnitude of induced emf at $t = 1 \ s$ is $..... \ V$.

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

$A$ metallic ring is dropped down, keeping its plane perpendicular to a constant and horizontal magnetic field. The ring enters the region of magnetic field at $t = 0$ and completely emerges out at $t = T \, \text{sec}$. The current in the ring varies as

The total charge induced in a conducting loop when it is moved in a uniform magnetic field depends on