Faraday's laws are a consequence of the conservation of

$A$ coil of resistance $400\,\Omega$ is placed in a magnetic field. If the magnetic flux $\phi$ (in $Wb$) linked with the coil varies with time $t$ (in $s$) as $\phi = 50t^2 + 4$,the current in the coil at $t = 2\,s$ is $..........\,A$.

$A$ coil has an area $0.06 \ m^2$ and it has $600$ turns. After placing the coil in a magnetic field of strength $5 \times 10^{-5} \ Wb/m^2$,it is rotated through $90^{\circ}$ in $0.2 \ s$. The magnitude of average e.m.f induced in the coil is

Three resistances of magnitude $R$ each are connected in the form of an equilateral triangle of side $a$. The combination is placed in a magnetic field $B = B_0 e^{-\lambda t}$ perpendicular to its plane. The induced current in the circuit is given by:

$A$ coil having $100$ square loops each of side $10 \ cm$ is placed such that its plane is normal to a magnetic field,which is changing at a rate of $0.7 \ T \ s^{-1}$. The emf induced in the coil is (in $V$)

The magnetic flux through a coil of resistance $10\,\Omega$ is changed by $\Delta \phi$ in $0.1\,s$. The resulting current in the coil varies with time as shown in the figure. Then,the magnitude $\left| \Delta \phi \right|$ is equal to (in weber):