$A$ coil having an area $A_0$ is placed in a magnetic field which changes from $B_0$ to $4B_0$ in a time interval $t$. The $e.m.f.$ induced in the coil will be

The magnetic flux linked with a coil varies with time as $\Phi = 4t^2 + 3t + 7$. The magnitude of the induced e.m.f. at $t = 2 \ s$ is: (in $V$)

$A$ coil having $200$ turns has a surface area of $0.15 \ m^2$. $A$ magnetic field of strength $0.2 \ T$ applied perpendicular to this changes to $0.6 \ T$ in $0.4 \ s$,then the induced emf in the coil is . . . . . . $V$.

Two identical circular loops of metal wire are lying on a table without touching each other. $Loop-A$ carries a current which increases with time. In response,the $loop-B$

$A$ hundred turns of insulated copper wire are wrapped around an iron cylinder of area $1 \times 10^{-3} \ m^2$ and are connected to a resistor. The total resistance in the circuit is $10 \ \Omega$. If the longitudinal magnetic induction in the iron changes from $1 \ Wb/m^2$ in one direction to $1 \ Wb/m^2$ in the opposite direction,how much charge flows through the circuit?

An electron moves on a straight line path $XY$ as shown. The $abcd$ is a coil adjacent to the path of the electron. What will be the direction of current,if any,induced in the coil?