$A$ rod of length $80 \ cm$ rotates about its midpoint with a frequency of $10 \ rev/s$. The potential difference (in volts) between the two ends of the rod due to a magnetic field $B = 0.5 \ T$ directed perpendicular to the rod is:

$A$ small coil is introduced between the poles of an electromagnet so that its axis coincides with the magnetic field direction. The number of turns is $n$ and the cross-sectional area of the coil is $A$. When the coil turns through $180^o$ about its diameter,the charge flowing through the coil is $Q$. The total resistance of the circuit is $R$. What is the magnitude of the magnetic induction?

$A$ 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:

$A$ solid metal cube of edge length $2\, cm$ is moving in a positive $y-$ direction at a constant speed of $6\, m/s$. There is a uniform magnetic field of $0.1\, T$ in the positive $z-$ direction. The potential difference between the two faces of the cube perpendicular to the $x-$ axis is.....$mV$.

$A$ 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 $3.0 \times 10^{-5}\; T$.

$A$ 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: