$A$ 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 $... \, sec$.

$A$ uniform magnetic field $\vec{B}$ is perpendicular to the plane of a circular loop of diameter $10 \text{ cm}$ formed from a wire of diameter $2 \text{ mm}$ and resistivity $2 \times 10^{-8} \Omega \text{ m}$. If a current of $11 \text{ A}$ is to be induced in the loop, then the rate at which $\vec{B}$ is to be changed is: (in $\text{ T s}^{-1}$)

Magnetic flux $\phi$ (in weber) linked with a closed circuit of resistance $10\, \Omega$ varies with time $t$ (in seconds) as $\phi = 5t^2 - 4t + 1$. The induced electromotive force in the circuit at $t = 0.2\, s$ is ......... $V$.

The magnetic flux $\phi$ (in weber) linked with a closed circuit of resistance $8 \ \Omega$ varies with time (in seconds) as $\phi = 5t^2 - 36t + 1$. The induced current in the circuit at $t = 2 \ s$ is . . . . . . $A$.

Consider a magnet surrounded by a wire loop with an on/off switch $S$ as shown in the figure. If the switch is thrown from the off position (open circuit) to the on position (closed circuit), will a current flow in the circuit? Explain.

Magnetic flux (in weber) in a closed circuit of resistance $20\,\Omega$ varies with time $t(s)$ as $\phi = 8t^2 - 9t + 5$. The magnitude of the induced current at $t = 0.25\,s$ will be $...mA$.