$A$ 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?

$A$ copper rod $AB$ of length $L$,pivoted at one end $A$,rotates at a constant angular velocity $\omega$,at right angles to a uniform magnetic field of induction $B$. The e.m.f. developed between the midpoint $C$ of the rod and end $B$ is

$A$ coil has $1000$ turns and $500 \text{ cm}^2$ as its area. The plane of the coil is placed at right angles to a magnetic induction field of $2 \times 10^{-5} \text{ Wb/m}^2$. The coil is rotated through $180^{\circ}$ in $0.2 \text{ s}$. The average emf induced in the coil,in $\text{mV}$,is

$A$ circular coil of radius $10\; cm$,$500$ turns,and resistance $2\; \Omega$ is placed with its plane perpendicular to the horizontal component of the Earth's magnetic field. It is rotated about its vertical diameter through $180^{\circ}$ in $0.25\; s$. Estimate the magnitudes of the emf and current induced in the coil. The horizontal component of the Earth's magnetic field at the place is $3.0 \times 10^{-5}\; T$.

$XPQY$ is a vertical smooth long loop having a total resistance $R$, where $PX$ is parallel to $QY$ and the separation between them is $l$. $A$ constant magnetic field $B$ perpendicular to the plane of the loop exists in the entire space. $A$ rod $CD$ of length $L$ $(L > l)$ and mass $m$ is made to slide down from rest under gravity as shown in the figure. The terminal speed acquired by the rod is . . . . . . $m/s$. ($g$ = acceleration due to gravity)

$A$ conducting rod $PQ$ of length $L = 1.0 \, m$ is moving with a uniform speed $v = 2 \, m/s$ 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: