$A$ 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 $\pi \, \mu V$)

$A$ conducting rod $PQ$ of length $L = 1.0\, m$ is moving with a uniform speed $v = 20\, m/s$ in a uniform magnetic field $B = 4.0\, T$ directed into the paper. $A$ capacitor of capacity $C = 10\, \mu F$ is connected as shown in the figure. Then:

$A$ circular coil of radius $30 \ cm$,having $1$ turn and a resistance of ${\pi ^2} \ \Omega$,is placed in a magnetic field of $10^{-2} \ T$. The coil rotates about its diameter with a speed of $200 \ rpm$ in a direction perpendicular to the magnetic field. The value of the induced $AC$ current in the coil will be . . . . . . $mA$.

Kamla peddles a stationary bicycle. The pedals of the bicycle are attached to a $100$ turn coil of area $0.10 \; m^2$. The coil rotates at half a revolution per second and it is placed in a uniform magnetic field of $0.01 \; T$ perpendicular to the axis of rotation of the coil. What is the maximum voltage (in $V$) generated in the coil?

Consider the situation given in the figure. The wire $AB$ is slid on the fixed rails with a constant velocity $v$. If the wire $AB$ is replaced by a semicircular wire of the same length,the magnitude of the induced current will:

$A$ conducting rod,with a resistor of resistance $R$,is pulled with constant speed $v$ on a smooth conducting rail as shown in the figure. $A$ constant magnetic field $B$ is directed into the page. If the speed of the bar is doubled,by what factor does the rate of heat dissipation across the resistance $R$ change?