$A$ conductor loop of radius $R$ is present in a uniform magnetic field $B$ perpendicular to the plane of the ring. If the radius $R$ varies as a function of time $t$ as $R = R_0 + t$,the induced $e.m.f.$ in the loop is:

$A$ long metal bar of $30\,cm$ length is aligned along a north-south line and moves eastward at a speed of $10\,ms^{-1}$. $A$ uniform magnetic field of $4.0\,T$ points vertically downwards. If the south end of the bar has a potential of $0\,V$,the induced potential at the north end of the bar is.....$V$.

$A$ rectangular loop $PQRS$ is being pulled with a constant speed into a uniform transverse magnetic field by a force $F$ (as shown). The $e.m.f.$ induced in side $PS$ and the potential difference between points $P$ and $S$ respectively are (Resistance of the loop $= r$)

Two rails of a railway track,insulated from each other and the ground,are connected to a millivoltmeter. What is the reading of the voltmeter when a train travels with a speed of $180 \ km/hr$ along the track? Given that the vertical component of the Earth's magnetic field is $0.2 \times 10^{-4} \ Wb/m^2$ and the rails are separated by $1 \ m$.

$A$ conducting rod $AB$ of length $l = 1\,m$ is moving with a velocity $v = 4\,m/s$. The velocity vector makes an angle of $30^o$ with the length of the rod. $A$ uniform magnetic field $B = 2\,T$ exists in a direction perpendicular to the plane of motion. Then:

$A$ straight conductor of length $4 \,m$ moves at a speed of $10 \,m/s$. When the conductor makes an angle of $30^{\circ}$ with the direction of a magnetic field of induction $0.1 \,Wb/m^2$, the induced emf is: (in $\,V$)