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 is placed in a magnetic field $\vec{B}$ as shown below. $A$ current is induced in the coil because $\vec{B}$ is:

$A$ magnetic field of $2 \times 10^{-2} \, T$ acts at right angles to a coil of area $100 \, cm^2$ with $50$ turns. The average emf induced in the coil is $0.1 \, V$,when it is removed from the field in time $t$. The value of $t$ is $... \, sec$.

Two square wire frames $abcd$ and $efgh$ are placed in a uniformly decreasing magnetic field as shown in the figure. The direction of the induced current in both the loops is

An insulated copper wire of $100$ turns is wrapped around a wooden cylindrical core of the cross-sectional area $24\,cm^2$. The two ends of the wire are connected to a resistor. The total resistance in the circuit is $12\,\Omega$. If an externally applied uniform magnetic field in the core along its axis changes from $1.5\,T$ in one direction to $1.5\,T$ in the opposite direction,the charge flowing through a point in the circuit during the change of magnetic field will be $.........\,mC$.

The figure shows the north pole of a magnet moving away from a thick conducting loop containing a capacitor. The excess positive charge will arrive on