$A$ wire loop enclosing a semi-circle of radius $R$ is located on the boundary of a uniform magnetic field of induction $\vec{B}$. At time $t=0$,the loop is set into rotation with angular velocity $\omega$ about its axis $0$,coinciding with a line of vector $\vec{B}$ on the boundary as shown in the figure. The emf induced in the loop is

$A$ metal rod of length $L$ rotates about one end at origin with a uniform angular velocity $\omega$. The magnetic field radially falls off as $B(r) = B_0 e^{-\lambda r}$; $\lambda$ being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is :

$A$ 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):

The arm $PQ$ of a rectangular conductor is moving from $x=0$ to $x=2b$ outwards and then inwards from $x=2b$ to $x=0$ as shown in the figure. $A$ uniform magnetic field perpendicular to the plane is acting from $x=0$ to $x=b$. Identify the graph showing the variation of different quantities with distance.

$A$ long horizontal metallic rod with length along the east-west direction is falling under gravity. The potential difference between its two ends will

$A$ 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.......$C$