$A$ wire of length $10 \, cm$ translates in a direction making an angle of $60^\circ$ with its length. The plane of motion is perpendicular to a uniform magnetic field of $1.0 \, T$ that exists in the space. Find the $emf$ induced between the ends of the rod if the speed of translation is $20 \, cm/s$.

Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed $v$ in a uniform magnetic field $B$ directed into the plane of the paper (See figure). If charge densities $\sigma_1$ and $\sigma_2$ are induced on the left and right surfaces,respectively,of the sheet,then (ignore fringe effects):

$A$ metal disc of radius $30 \ cm$ rotates with a constant angular velocity $\omega = 100 \ rad/s$ about its axis. Find the magnitude of the potential difference between the centre and the rim of the disc if an external uniform magnetic field of induction $B = 4 \ mT$ is directed perpendicular to the disc. (in $mV$)

$A$ conductor of $3 \ m$ in length is moving perpendicularly to a magnetic field of $10^{-3} \ T$ with a speed of $10^2 \ m/s$. The $e.m.f.$ produced across the ends of the conductor will be ........ $V$.

$A$ circular coil of radius $8.0\; cm$ and $20$ turns is rotated about its vertical diameter with an angular speed of $50\; rad \;s^{-1}$ in a uniform horizontal magnetic field of magnitude $3.0 \times 10^{-2}\; T$. Obtain the maximum and average $emf$ induced in the coil. If the coil forms a closed loop of resistance $10\; \Omega,$ calculate the maximum value of current in the coil. Calculate the average power loss due to Joule heating. Where does this power come from?

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