$A$ conducting rod is moving in a uniform magnetic field as shown in the diagram. Which end is at a lower potential?

$A$ rigid wire loop of square shape having side of length $L$ and resistance $R$ is moving along the $x$-axis with a constant velocity $v_0$ in the plane of the paper. At $t=0$,the right edge of the loop enters a region of length $3L$ where there is a uniform magnetic field $B$ into the plane of the paper,as shown in the figure. For sufficiently large $v_0$,the loop eventually crosses the region. Let $x$ be the location of the right edge of the loop. Let $v(x)$,$I(x)$,and $F(x)$ represent the velocity of the loop,current in the loop,and force on the loop,respectively,as a function of $x$. Counter-clockwise current is taken as positive. Which of the following schematic plot$(s)$ is(are) correct? (Ignore gravity)

$A$ metal disc rotates freely between the poles of a magnet in the direction indicated. Brushes $P$ and $Q$ make contact with the center (axle) and the edge of the disc,respectively. What current,if any,flows through $R$?

$A$ rod of length $20 \text{ cm}$ is rotating with an angular speed of $100 \text{ rps}$ in a magnetic field of strength $0.5 \text{ T}$ about one of its ends. What is the potential difference between the two ends of the rod? $(V)$

$A$ simple pendulum with a bob of mass $m$ and a conducting wire of length $L$ swings under gravity through an angle $2\theta$. The Earth's magnetic field component in the direction perpendicular to the swing is $B$. The maximum potential difference induced across the pendulum is

$A$ rectangular loop circuit has a sliding wire $PQ$ as shown in the figure. The loop is placed in a magnetic field $B$,perpendicular to its plane. The resistance of the wire $PQ$ is $R$. If the wire moves with constant velocity $v$,then find the current flowing in the wire $PQ$?