The magnetic flux linked to a circular coil of radius $R$ is given by $\phi = 2t^3 + 4t^2 + 2t + 5 \; Wb$. The magnitude of the induced $emf$ in the coil at $t = 5 \; s$ is $.......... \; V$.

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 ......... $V$.

In the arrangement shown in the given figure,the current from $A$ to $B$ is increasing in magnitude. The induced current in the loop will

The magnetic flux linked with a coil satisfies the relation $\phi = 4t^2 + 6t + 9 \text{ Wb}$, where $t$ is the time in seconds. The emf induced in the coil at $t = 2 \text{ s}$ is (in $\text{ V}$)

$A$ long solenoid with $15$ turns per $cm$ has a small loop of area $2.0 \; cm^{2}$ placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from $2.0 \; A$ to $4.0 \; A$ in $0.1 \; s$, what is the induced $emf$ in the loop while the current is changing?

$A$ rectangular loop of length $2.5 \ m$ and width $2 \ m$ is placed at $60^{\circ}$ to a magnetic field of $4 \ T$. The loop is removed from the field in $10 \ s$. The average emf induced in the loop during this time is