$A$ 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

Derive the equation for the induced $emf$ in a rod of length $l$ sliding with velocity $v$ on a $U$-shaped frame placed perpendicular to a uniform magnetic field $B$.

$A$ wheel with radial metal spokes $1 \ m$ in length is rotated in a magnetic field of $0.5 \times 10^{-4} \ T$ normal to the plane of the wheel. If the induced emf between the rim and axle is $\pi / 3000 \ V$,then the rotational speed of the wheel in revolutions per minute is

$A$ circular coil of $500$ turns encloses an area of $0.04 \,m^2$. $A$ uniform magnetic field of induction $0.25 \,Wb/m^2$ is applied perpendicular to the plane of the coil. The coil is rotated by $90^o$ in $0.1 \,s$ at a constant angular velocity about one of its diameters. $A$ galvanometer of resistance $25 \,\Omega$ is connected in series with the coil. The total charge that will pass through the galvanometer is.......$C$

$A$ square loop $ABCD$ is moving with constant velocity $\vec{v}$ in a uniform magnetic field $\vec{B}$ which is perpendicular to the plane of paper and directed outward. The resistance of the coil is $R$. What is the rate of production of heat energy in the loop? [$L$ = length of side of the loop]

$A$ wire of length $1\,m$ is moving with a velocity of $8\,m/s$ at right angles to a magnetic field of $2\,T$. The magnitude of the induced emf between the ends of the wire will be $............\,V$.