$A$ 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?

$A$ metallic rod of $1\; m$ length is rotated with a frequency of $50\; rev/s$,with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius $1\; m$,about an axis passing through the centre and perpendicular to the plane of the ring (Figure). $A$ constant and uniform magnetic field of $1\; T$ parallel to the axis is present everywhere. What is the $emf$ between the centre and the metallic ring?

$A$ conducting rod $AC$ of length $4l$ is rotated about a point $O$ in a uniform magnetic field $\vec B$ directed into the paper. $AO = l$ and $OC = 3l$. Then:

$A$ conducting circular loop is placed in the $X-Y$ plane in the presence of a magnetic field $\overrightarrow{B} = (3t^3 \hat{j} + 3t^2 \hat{k})$ in $SI$ units. If the radius of the loop is $1 \ m$,the induced emf in the loop at time $t = 2 \ s$ is $n\pi \ V$. The value of $n$ is:

$A$ train is moving with a speed of $30 \, m \, s^{-1}$ in the north-south direction on rails separated by $2 \, m$. If the vertical component of the Earth's magnetic field is $8 \times 10^{-5} \, T$,the induced $e.m.f.$ is: (in $, V$)

$A$ 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: