$A$ wheel with $20$ metallic spokes,each $1 \,m$ long,is rotated with a speed of $120 \,rpm$ in a plane perpendicular to a magnetic field of $0.4 \,G$. The induced emf between the axle and the rim of the wheel will be $\left(1 \;G = 10^{-4} \;T \right)$.

$A$ coil has $1000$ turns and $500 \text{ cm}^2$ as its area. The plane of the coil is placed at right angles to a magnetic induction field of $2 \times 10^{-5} \text{ Wb/m}^2$. The coil is rotated through $180^{\circ}$ in $0.2 \text{ s}$. The average emf induced in the coil,in $\text{mV}$,is

$A$ rectangular loop $PQMN$ with a movable arm $PQ$ of length $12 \, cm$ and resistance $2 \, \Omega$ is placed in a uniform magnetic field of $0.1 \, T$ acting perpendicular to the plane of the loop as shown in the figure. The resistance of the arms $MN$, $NP$, and $MQ$ are negligible. The current induced in the loop when arm $PQ$ is moved with a velocity of $20 \, ms^{-1}$ is (in $ \, A$)

$A$ copper rod of mass $m$ slides under gravity on two smooth parallel rails,with separation $l$ and set at an angle of $\theta$ with the horizontal. At the bottom,the rails are joined by a resistance $R$. There is a uniform magnetic field $B$ normal to the plane of the rails,as shown in the figure. The terminal speed of the copper rod is

$A$ 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 bar is pulled with a constant speed $v$ on a smooth conducting rail. The region has a steady magnetic field of induction $B$ as shown in the figure. If the speed of the bar is doubled then the rate of heat dissipation will