$A$ rod of length $1.0 \,m$ is rotated in a plane perpendicular to a uniform magnetic field of induction $0.25 \,T$ with a frequency of $12 \,rev/s$. The induced emf across the ends of the rod is (in $\,V$)

$A$ metal wire $PQ$ slides on parallel metallic rails having separation $0.25 \ m$,each having negligible resistance. There is a $2 \ \Omega$ resistor and $10 \ V$ battery as shown in the figure. There is a uniform magnetic field directed into the plane of the paper of magnitude $0.5 \ T$. $A$ force of $0.5 \ N$ to the left is required to keep the wire $PQ$ moving with constant speed to the right. With what speed is the wire $PQ$ moving? ..... $m/s$ (Neglect self-inductance of the loop)

$A$ conducting rod of length $l$ moves with a constant velocity $\upsilon$ perpendicular to a long,straight wire carrying a current $I$,as shown in the figure. Calculate the $emf$ generated between the ends of the rod.

$A$ 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 $R$?

$A$ 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)

$A$ square loop of side $20\, {cm}$ and resistance $1\, \Omega$ is moved towards the right with a constant speed ${v}_{0}$. The right arm of the loop is in a uniform magnetic field of $5\, {T}$. The field is perpendicular to the plane of the loop and is directed into it. The loop is connected to a network of resistors,each of value $4\, \Omega$. What should be the value of ${v}_{0}$ so that a steady current of $2\, {mA}$ flows in the loop?