In the given figure,in which direction should the rod be moved to induce an $emf$ between its two ends?

Derive the expression for the mechanical power required to move a conducting rod of length $l$ with a constant velocity $v$ in a uniform magnetic field $B$.

$A$ conducting rod $AB$ of length $l$ is projected on a frictionless frame $PSRQ$ with velocity $v_0$ in a uniform magnetic field $\vec{B}$ directed into the plane. The velocity of the rod after time $t$ is

$A$ rod of length $20 \text{ cm}$ is rotating with an angular speed of $100 \text{ rps}$ in a magnetic field of strength $0.5 \text{ T}$ about one of its ends. What is the potential difference between the two ends of the rod? $(V)$

$A$ conductor of length $l$ and mass $m$ can slide along a pair of vertical metal guides connected by a resistance $R$,as shown in the figure. Friction,resistance of the conductor,and guide rails are negligible. There exists a horizontal uniform magnetic field of strength $B$ normal to the plane of the page and directed outward. The terminal speed of fall under the influence of gravity is:

$A$ long straight wire carries a current,$I = 2 \text{ A}$. $A$ semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire,the rod,and the rails lie in the same horizontal plane,as shown in the figure. Two ends of the semi-circular rod are at distances $1 \text{ cm}$ and $4 \text{ cm}$ from the wire. At time $t = 0$,the rod starts moving on the rails with a speed $v = 3.0 \text{ m/s}$. $A$ resistor $R = 1.4 \text{ } \Omega$ and a capacitor $C_0 = 5.0 \text{ } \mu\text{F}$ are connected in series between the rails. At time $t = 0$,$C_0$ is uncharged. Which of the following statement$(s)$ is(are) correct? $\left[\mu_0 = 4\pi \times 10^{-7} \text{ SI units}, \ln 2 = 0.7\right]$
$(A)$ Maximum current through $R$ is $1.2 \times 10^{-6} \text{ A}$
$(B)$ Maximum current through $R$ is $3.8 \times 10^{-6} \text{ A}$
$(C)$ Maximum charge on capacitor $C_0$ is $8.4 \times 10^{-12} \text{ C}$
$(D)$ Maximum charge on capacitor $C_0$ is $2.4 \times 10^{-12} \text{ C}$