$A$ conducting rod of length $l$ moves with a constant velocity $\upsilon$ perpendicular to a long,straight wire carrying a current $I$,as shown in the figure. Calculate the $emf$ generated between the ends of the rod.

$A$ wire loop enclosing a semi-circle of radius $R$ is located on the boundary of a uniform magnetic field of induction $\vec{B}$. At time $t=0$,the loop is set into rotation with angular velocity $\omega$ about its axis $0$,coinciding with a line of vector $\vec{B}$ on the boundary as shown in the figure. The emf induced in the loop is

$A$ conducting wire of length $2500 \ m$ is kept in the east-west direction at a height of $10 \ m$ from the ground. If it falls freely to the ground,the induced current in the wire is (Resistance of wire $= 25 \sqrt{2} \ \Omega$,acceleration due to gravity $g = 10 \ m/s^2$,$B_H = 2 \times 10^{-5} \ T$). (in $A$)

$A$ 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 $2.4 \times 10^{-12} \text{ C}$

$A$ conducting rod $PQ$ of length $L = 1.0\, m$ is moving with 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:

An infinitely long straight wire carrying current $I$,an open rectangular loop,and a conductor $C$ with a sliding connector are located in the same plane,as shown in the figure. The connector has length $l$ and resistance $R$. It slides to the right with a velocity $v$. The resistance of the conductor and the self-inductance of the loop are negligible. The induced current in the loop,as a function of separation $r$ between the connector and the straight wire,is: