$A$ conducting circular loop is placed in a uniform magnetic field of $0.4\,T$ with its plane perpendicular to the field. The radius of the loop starts expanding at a constant rate of $1\,mm/s$. The magnitude of the induced emf in the loop at an instant when the radius of the loop is $2\,cm$ will be $...........\,\mu V$.

$A$ conducting rod $PQ$ of length $L = 1.0 \, m$ is moving with a uniform speed $v = 2 \, m/s$ in a uniform magnetic field $B = 4.0 \, T$ directed into the paper. $A$ capacitor of capacity $C = 10 \, \mu F$ is connected as shown in the figure. Then:

$A$ metal disc of radius $R$ rotates with an angular velocity $\omega$ about an axis perpendicular to its plane passing through its centre in a magnetic field of induction $B$ acting perpendicular to the plane of the disc. The induced e.m.f. between the rim and axis of the disc is (magnitude only):

$A$ long solenoid with $2000$ turns per meter has a small loop of radius $3 \,cm$ placed inside the solenoid normal to its axis. If the current through the solenoid increases steadily from $1.5 \,A$ to $5.5 \,A$ in $\frac{\pi^2}{100} \,s$, the induced emf in the loop is (in $\,mV$)

$A$ 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

$A$ square metallic wire loop of side $0.1 \, m$ and resistance $1 \, \Omega$ is moved with a constant velocity in a magnetic field of $2 \, Wb/m^2$ as shown in the figure. The magnetic field is perpendicular to the plane of the loop, and the loop is connected to a network of resistances. What should be the velocity of the loop to have a steady current of $1 \, mA$ in the loop? (in $cm/sec$)