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

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 ....... $V$.

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 $loop-B$

$A$ coil of resistance $16 \Omega$ is placed with its plane perpendicular to a uniform magnetic field whose flux ($\phi$ in $10^{-3} \text{ Wb}$) changes with time ($t$ in seconds) as $\phi = 5t^2 + 4t + 2$. The induced current at time $t = 6 \text{ s}$ is: (in $\text{ mA}$)

Magnetic flux linked with the coil in weber is given by the equation $\phi = 5t^2 + 6t + 11$. The e.m.f. induced in the coil in the $5^{\text{th}}$ second will be (in $\text{ V}$)

The magnetic flux through a circuit of resistance $R$ changes by an amount $\Delta \phi$ in the time $\Delta t$. The total quantity of electric charge $Q$ which passes during this time through any point of the circuit is