A uniform and constant magnetic field $B$ coming out of the plane of the paper exists in a rectangular region as shown in figure. $A$conducting rod $PQ$ is rotated about its mid-point $O$ with a uniform angular speed $\omega$ in the plane of the paper. The emf $E_{PQ}$ induced between $P$ and $Q$ is best represented by the graph

A conducting ring of radius a falls vertically downward with a velocity $v_0$ in a horizontal magnetic field $B.$ The potential difference between two points $P$ and $Q$ located symmetrically on both sides of the vertical will be

In the circuit shown in figure, the switch$\text{'}S\text{'}$ is closed at $t=0.$ After closing the switch, (in steady state), the value of current in the resistor $R_3$ as compared to the current through it before closing the switch

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