Magnetic flux (in $Wb$) linked with a closed loop varies with time $t$ (in $s$) as $\phi = 2t^2 + 1$. The magnitude of induced emf at $t = 1 \ s$ is $..... \ V$.

Two identical coaxial circular loops carry current $i$ each circulating in the clockwise direction. If the loops are approaching each other,then

$A$ metallic ring is dropped down, keeping its plane perpendicular to a constant and horizontal magnetic field. The ring enters the region of magnetic field at $t = 0$ and completely emerges out at $t = T \, \text{sec}$. The current in the ring varies as

Assertion : Faraday's laws are consequences of conservation of energy.
Reason : In a purely resistive $A.C.$ circuit,the current lags behind the $e.m.f.$ in phase.

$A$ circular coil has $100$ turns,radius $3 \ cm$ and resistance $4 \Omega$. This coil is co-axial with a solenoid of $200$ turns/cm and diameter $4 \ cm$. If the solenoid current is decreased from $2 \ A$ to zero in $0.04 \ s$,then the current induced in the coil is

The direction of induced current is such that it opposes the very cause that has produced it. This is the law of