$A$ cycle wheel of radius $0.5 \; m$ is rotated with a constant angular velocity of $10 \; rad/s$ in a region of magnetic field of $0.1 \; T$ which is perpendicular to the plane of the wheel. The $EMF$ generated between its centre and the rim is.....$V$

$A$ wire of length $1\, m$ is perpendicular to the $x-y$ plane. It is moved with velocity $\vec{v} = (3\hat{i} + 3\hat{j} + 2\hat{k})\, m/s$ through a region of uniform magnetic field $\vec{B} = (\hat{i} + 2\hat{j})\, T$. The potential difference between the ends of the wire is (in $V$):

$A$ cycle wheel contains $24$ spokes of $0.5 \, m$ length. It is rotated in a horizontal plane with $120 \, \text{revolution/min}$ in the presence of the Earth's magnetic field. If the total magnetic field of the Earth is $10^{-4} \, T$ (given $10^4 \, G = 1 \, T$), then find the dynamic $emf$ induced across the centre and the rim of the wheel (angle of dip is $30^{\circ}$).

The loop shown moves with a velocity $v$ in a uniform magnetic field of magnitude $B$,directed into the paper. The potential difference between $P$ and $Q$ is $e$. Then:

$A$ conducting rod of length $\ell$ moves with a velocity $V$ in a uniform magnetic field $B$ perpendicular to the plane of the rails. $A$ capacitor of capacitance $C$ is connected across the rails as shown. Find the charge on the capacitor due to the induced emf in the rod.

If we double the velocity of a rod moving in a uniform magnetic field, then the induced $emf$ will increase by how many times?