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 $...mA$.

$A$ 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 e.m.f. induced in the coil is $0.1 \,V$, when it is removed from the field in time $t$. The value of $t$ is (in seconds): (in $s$)

$A$ coil of resistance $200 \Omega$ is placed in a magnetic field. If the magnetic flux $\phi$ (in weber) linked with the coil varies with time $t$ (in second) as per the equation $\phi = 50t^2 + 4$,then the current induced in the coil at a time $t = 2 \ s$ is (in $A$)

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

$A$ uniform magnetic field $B$ that is perpendicular to the plane of the page passes through the loops,as shown. The field is confined to a region of radius $a$,where $a < b$,and is changing at a constant rate. The induced $emf$ in the wire loop of radius $b$ is $\varepsilon$. What is the induced $emf$ in the wire loop of radius $2b$?

$A$ magnetic field $B = 2t + 4t^{2}$ (where $t$ is time) is applied perpendicular to the plane of a circular wire of radius $r$ and resistance $R$. If all units are in $SI$,the electric charge that flows through the circular wire during $t = 0 \ s$ to $t = 2 \ s$ is: