$A$ copper disc of radius $0.1 \ m$ rotates about an axis passing through its centre and perpendicular to its plane with $10 \ \text{revolutions per second}$ in a uniform transverse magnetic field of $0.1 \ T$. The emf induced across the radius of the disc is

$A$ metallic conductor of length $1 \; m$ rotates in a vertical plane parallel to the east-west direction about one of its ends with an angular velocity of $5 \; rad/s$. If the horizontal component of the Earth's magnetic field is $0.2 \times 10^{-4} \; T$,then the emf induced between the two ends of the conductor is .............

The figure shows a square loop of side $5 \ cm$ being moved towards the right at a constant speed of $1 \ cm/s$. The front edge enters the $20 \ cm$ wide magnetic field $(B = 0.6 \ T)$ at $t = 0$. Find the $emf$ induced in the loop at $(a) \ t = 2 \ s$,$(b) \ t = 10 \ s$,and $(c) \ t = 22 \ s$.

$A$ conducting square frame of side $a$ and a long straight wire carrying current $I$ are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity $V$. The $emf$ induced in the frame will be proportional to

$A$ small conducting loop of radius $a$ and resistance $r$ is pulled with velocity $v$ perpendicular to a long straight conductor carrying a current $i_0$. If a constant power $P$ is dissipated in the loop,find the variation of velocity $v$ of the loop as a function of $x$. Given that $x >> a$.

$A$ conducting rod of length $L = 0.1 \, m$ is moving with a uniform speed $v = 0.2 \, m/s$ on conducting rails in a magnetic field $B = 0.5 \, T$ as shown. On one side,the end of the rails is connected to a capacitor of capacitance $C = 20 \, \mu F$. Then the charges on the capacitor plates $A$ and $B$ are: