$A$ coil of area $80 \, cm^2$ and $50$ turns is rotating with $2000$ revolutions per minute about an axis perpendicular to a magnetic field of $0.05 \, T$. The maximum value of the e.m.f. developed in it is

$A$ coil of mean area $500 \ cm^2$ and having $1000$ turns is held with its plane perpendicular to a uniform magnetic field of $0.4 \ G$. If the coil is turned through $180^{\circ}$ in $\frac{1}{10} \ s$,then the average induced emf is $(1 \ G = 10^{-4} \ T)$. (in $V$)

$A$ conducting ring of radius $a$ is rotated about a point $O$ on its periphery as shown in the figure in a plane perpendicular to a uniform magnetic field $B$ which exists everywhere. The rotational velocity is $\omega$. Choose the correct statement$(s)$ related to the potential of the points $P, Q$ and $R$.

An $emf$ of $0.08\,V$ is induced in a metal rod of length $10\,cm$ held normal to a uniform magnetic field of $0.4\,T$,when it moves with a velocity of .......... $m/s$.

$A$ circular coil of radius $10\; cm$,$500$ turns,and resistance $2\; \Omega$ is placed with its plane perpendicular to the horizontal component of the Earth's magnetic field. It is rotated about its vertical diameter through $180^{\circ}$ in $0.25\; s$. Estimate the magnitudes of the emf and current induced in the coil. The horizontal component of the Earth's magnetic field at the place is $3.0 \times 10^{-5}\; T$.

Two conducting rings $P$ and $Q$ of radii $r$ and $2r$ rotate uniformly in opposite directions with centre of mass velocities $2v$ and $v$ respectively on a conducting surface $S$. There is a uniform magnetic field of magnitude $B$ perpendicular to the plane of the rings. The potential difference between the highest points of the two rings is