$A$ wire of length $1 \, m$ is moving at a speed of $2 \, ms^{-1}$ perpendicular to its length and a homogeneous magnetic field of $0.5 \, T$. The ends of the wire are joined to a circuit of resistance $6 \, \Omega$. The rate at which work is being done to keep the wire moving at constant speed 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

Two identical conductors $P$ and $Q$ are placed on two frictionless rails $R$ and $S$ in a uniform magnetic field directed into the plane. If $P$ is moved in the direction shown in the figure with a constant speed,then rod $Q$

$A$ $800$ turn coil of effective area $0.05\; m^{2}$ is kept perpendicular to a magnetic field $5 \times 10^{-5}\; T$. When the plane of the coil is rotated by $90^{\circ}$ around any of its coplanar axes in $0.1\; s$,the $emf$ induced in the coil will be.....$V$

$A$ $10\,m$ long horizontal wire extends from North-East to South-West. It is falling with a speed of $5.0\,m/s$,at right angles to the horizontal component of the earth's magnetic field,which is $0.3 \times 10^{-4}\,Wb/m^2$. The value of the induced $emf$ in the wire is:

$A$ certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field $B = 0.8 \, T$. When released,the radius of the loop starts shrinking at a constant rate of $dr/dt = -2 \, cm/s$. The induced emf in the loop at an instant when the radius of the loop is $r = 10 \, cm$ will be $........ mV$.