The magnetic flux through a coil of resistance $R$ changes by an amount $\Delta \phi$ in time $\Delta t$. The total quantity of induced electric charge $Q$ is

The coil of a dynamo is rotating in a magnetic field. The developed induced $e.m.f.$ changes and the number of magnetic lines of force also changes. Which of the following conditions is correct?

The magnetic flux through a coil perpendicular to its plane and directed into the paper is varying according to the relation $\phi = (2t^2 + 4t + 6) \, mWb$. The $emf$ induced in the loop at $t = 4 \, s$ is ....... $V$.

The diagram below shows two circular loops of wire ($A$ and $B$) centred on and perpendicular to the $X$-axis and oriented with their planes parallel to each other. The $Y$-axis passes vertically through loop $A$ (dashed line). There is a current $I_B$ in loop $B$ as shown in the diagram. Possible actions which we might perform on loop $A$ are:
$(I)$ move $A$ to the right along $X$-axis closer to $B$
$(II)$ move $A$ to the left along $X$-axis away from $B$
$(III)$ as viewed from above,rotate $A$ clockwise about $Y$-axis
$(IV)$ as viewed from above,rotate $A$ anti-clockwise about $Y$-axis
Which of the actions will induce a current in $A$ only in the direction shown?

If magnetic flux $\phi = (3t^2 - 2t + 5) \ Wb$,then what is the induced emf at $t = 2 \ s$?

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 $B$: