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

There are two square loops $A$ and $B$. When $A$ moves towards $B$,a current starts flowing in $B$ as shown in the figure,and the current in $B$ stops when $A$ stops moving. From this,we can infer that (Assume loop $B$ is at rest):

Three identical coils $C_1, C_2$ and $C_3$ are placed coaxially. $C_2$ is exactly midway between $C_1$ and $C_3$. $C_1$ carries current $I$ in an anti-clockwise direction, while $C_3$ carries current $I$ in a clockwise direction. An induced current flows through $C_2$ in a clockwise direction when:

The magnetic field in a coil of $100$ turns and $40 \text{ cm}^2$ area is increased from $1 \text{ T}$ to $6 \text{ T}$ in $2 \text{ s}$. The magnetic field is perpendicular to the coil. The $e.m.f.$ generated in it is $...... \text{ V}$.

The magnetic flux (in weber) in a closed circuit of resistance $20 \ \Omega$ varies with time $t$ (in seconds) according to the equation $\phi = 5t^2 - 6t + 9$. The magnitude of the induced current at $t = 0.2 \ s$ is: (in $A$)

State Lenz's law and prove that it is a specific representation of the law of conservation of energy.