$A$ current carrying circular loop is perpendicular to a magnetic field of induction $10^{-4} \, T$. If the radius of the loop starts shrinking at a uniform rate of $2 \, mm/s$, then the emf induced in the loop at the instant, when its radius is $20 \, cm$ will be (in $\pi \, \mu V$)

$A$ circular coil of $500$ turns encloses an area of $0.04 \,m^2$. $A$ uniform magnetic field of induction $0.25 \,Wb/m^2$ is applied perpendicular to the plane of the coil. The coil is rotated by $90^o$ in $0.1 \,s$ at a constant angular velocity about one of its diameters. $A$ galvanometer of resistance $25 \,\Omega$ is connected in series with the coil. The total charge that will pass through the galvanometer is.......$C$

$A$ rectangular loop with a sliding connector of length $10\, cm$ is situated in a uniform magnetic field perpendicular to the plane of the loop. The magnetic induction is $0.1\, T$ and the resistance of the connector is $1\, \Omega$. The sides $AB$ and $CD$ have resistances $2\, \Omega$ and $3\, \Omega$ respectively. Find the current in the connector during its motion with a constant velocity of $1\, m/s$.

$A$ metallic disc of radius $0.3 \ m$ is rotating with a constant angular speed of $60 \ rad \ s^{-1}$ in a plane perpendicular to a uniform magnetic field of $5 \times 10^{-2} \ T$. The emf induced between a point on the rim and the centre of the disc is: (in $V$)

$A$ 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?

$A$ 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 $mV$)