There are two stationary coils having mutual inductance $M,$ between them. The current in one of the coils is increasing with time as $I=Kt$ where $K$ is constant and $t$ is the time. The expression for the current in the other coil as a function of time $t,$ its resistance and inductance are $R$ and $L$ respectively is

Three loops $A, B$ and $C,$ and an observer is positioned as shown in the figure. As seen by the observer, constant current $l$ flows in middle loop $B$ in counter-clockwise direction and loop $B$ is moving towards observer with a velocity $v.$ The same observer would notice that

In the circuit shown below, the switch $S$ is closed at $t=0.$ Which of the following best represents the voltage across the inductor?

A semicircular wire of radius $R$ is moving in a magnetic field $B$ as shown in the figure. The emf (in $V$) induced across the wire is
(Given $BRV=8$ volt)

A square loop of side $a$ has resistance $R$ and lies at distance $a$ from an infinite straight wire carrying $I_0.$ Find the charge flown through the loop when the loop has turned through an angle of $120$ about an axis $AB$ as shown.