Two metallic rings of radius $R$ are rolling on a metallic rod. $A$ magnetic field of magnitude $B$ is applied in the region. The magnitude of the potential difference between point $A$ and point $C$ on the two rings (as shown) will be:

$A$ 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 $\,V$)

$A$ metallic frame moves with constant velocity $v$ near an infinitely long current-carrying wire. At any instant,the induced $emf$ in sides $AD$ and $BC$ are $5\,V$ and $2\,V$ respectively. If the resistance of the frame is $6\,\Omega$,find the magnitude and direction of the induced current in it.

$A$ rectangular loop has a sliding connector $PQ$ of length $l$ and resistance $R \, \Omega$ and it is moving with a speed $v$ as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents $I_1, I_2$ and $I$ are:

$A$ thin semicircular conducting ring $(PQR)$ of radius $r$ is falling with its plane vertical in a horizontal magnetic field $B,$ as shown in the figure. The potential difference developed across the ring when its speed is $v,$ is

$A$ $2 \; m$ wire is moving with a velocity of $1 \; m/s$ perpendicular to a magnetic field of $0.5 \; Wb/m^2$. The induced e.m.f. in it will be $... \; V$.