$A$ 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 across the plane in the north-east direction. The magnetic field decreases to zero at $0.70 \ s$ at a steady rate. Then the magnitude of the induced current during this time interval will be . . . . . . .

The magnetic flux passing perpendicular to the plane of the coil and directed into the paper is varying according to the relation $\phi = 3t^2 + 2t + 3$,where $\phi$ is in milliwebers $(mWb)$ and $t$ is in seconds $(s)$. The magnitude of the $emf$ induced in the loop when $t = 2 \ s$ is ...... $mV$.

$A$ coil having an area $2\,m^2$ is placed in a magnetic field which changes from $1\,Wb/m^2$ to $4\,Wb/m^2$ in an interval of $2$ seconds. The $e.m.f.$ induced in the coil will be......$V$.

$A$ coil of $n$ turns and resistance $R \Omega$ is connected in series with a resistance $R/4$. The combination is moved for time $t$ seconds through a magnetic flux change from $\phi_1$ to $\phi_2$. The induced current in the circuit is:

The flux linked with a coil at any instant $t$ is given by $\phi = 10t^2 - 50t + 250$. The induced $emf$ at $t = 3 \ s$ is ....... $V$.

$A$ current-carrying infinitely long wire is kept along the diameter of a circular wire loop,without touching it. The correct statement$(s)$ is (are):
$(A)$ The emf induced in the loop is zero if the current is constant.
$(B)$ The emf induced in the loop is finite if the current is constant.
$(C)$ The emf induced in the loop is zero if the current decreases at a steady rate.
$(D)$ The emf induced in the loop is finite if the current decreases at a steady rate.