The loop shown moves with a constant velocity $V$ in a uniform magnetic field of magnetic induction $B$ directed into the paper. The potential difference between $P$ and $Q$ is:

$A$ conducting rod of length $L$ lies in the $XY$-plane and makes an angle $30^{\circ}$ with the $X$-axis. One end of the rod is initially at the origin. $A$ magnetic field exists in the region pointing along the positive $Z$-direction. The magnitude of the magnetic field varies with $y$ as $B = B_0 \left(\frac{y}{L}\right)^3$,where $B_0$ is a constant. At some instant,the rod starts moving with a velocity $v_0$ along the $X$-axis. The emf induced in the rod is

To measure a magnetic field between the magnetic poles of a loudspeaker, a small coil having $30$ turns and $2.5 \, cm^2$ area is placed perpendicular to the field and removed immediately. If the total charge flown through the coil is $7.5 \times 10^{-3} \, C$ and the total resistance of the wire and galvanometer is $0.3 \, \Omega$, then the magnitude of the magnetic field is

An infinitely long straight wire carrying current $I$,an open rectangular loop,and a conductor $C$ with a sliding connector are located in the same plane,as shown in the figure. The connector has length $l$ and resistance $R$. It slides to the right with a velocity $v$. The resistance of the conductor and the self-inductance of the loop are negligible. The induced current in the loop,as a function of separation $r$ between the connector and the straight wire,is:

$A$ conducting rod of mass $m$ and length $l$ is free to move without friction on two parallel long conducting rails,as shown in the figure. There is a resistance $R$ across the rails. In the entire space,there is a uniform magnetic field $B$ normal to the plane of the rod and rails. The rod is given an impulsive velocity $v_0$. What happens to the initial kinetic energy $\frac{1}{2} m v_0^2$?

$A$ simple pendulum with a bob of mass $m$ and a conducting wire of length $L$ swings under gravity through an angle $\theta$. The component of the Earth's magnetic field in the direction perpendicular to the swing is $B$. The maximum e.m.f. induced across the pendulum is ($g=$ acceleration due to gravity).