$A$ metallic rod of length '$L$' is rotated with an angular speed of '$\omega$' normal to a uniform magnetic field '$B$' about an axis passing through one end of the rod,as shown in the figure. The induced emf will be:

$A$ uniform magnetic field of $0.4 \ \text{T}$ acts perpendicular to a circular copper disc $20 \ \text{cm}$ in radius. The disc is rotating with a uniform angular velocity of $10 \pi \ \text{rad s}^{-1}$ about an axis passing through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim (in $\text{V}$)? $(\pi = 3.14)$

The figure shows an apparatus suggested by Faraday to generate electric current from a flowing river. Two identical conducting plates of length $a$ and width $b$ are placed parallel facing one another on opposite sides of the river flowing with velocity $u$ at a distance $d$ apart. Now both the plates are connected by a load resistance $R$. Then the current through the load $R$ is: (Consider the vertical component of the magnetic field produced by the earth is $B_v$ and the resistivity of river water is $\rho$.)

$A$ rectangular coil of single turn,having area $A$,rotates in a uniform magnetic field $B$ with an angular velocity $\omega$ about an axis perpendicular to the field. If initially the plane of the coil is perpendicular to the field,then the average induced $e.m.f.$ when it has rotated through $90^{\circ}$ is

$A$ conducting rod is moving in a uniform magnetic field as shown in the diagram. Which end is at a lower potential?

$A$ conducting circular loop is placed in a uniform magnetic field,$B = 0.025 \, T$,with its plane perpendicular to the field. The radius of the loop is made to shrink at a constant rate of $1 \, mm \, s^{-1}$. The induced $emf$ when the radius is $2 \, cm$ is: