$A$ conducting rod $AB$ moves parallel to the $X-$ axis in a uniform magnetic field,which is directed perpendicular to the plane of motion (outwards). The end $A$ of the rod gets:

$A$ metallic wire loop of side $l = 0.1 \text{ m}$ and resistance $1 \Omega$ is moved with a constant velocity in a uniform magnetic field of $2 \text{ Wb m}^{-2}$ as shown in the figure. The magnetic field is perpendicular to the plane of the loop. The loop is connected to a network of resistors. The velocity of the loop required to have a steady current of $1 \text{ mA}$ in the loop is: (in $\text{ cm s}^{-1}$)

The wing span of an aeroplane is $20$ $m$. It is flying in a field where the vertical component of the Earth's magnetic field is $5 \times 10^{-5} \, T$,with a velocity of $360 \, km/h$. The potential difference produced between the wing tips will be ....... $V$.

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

$A$ metal wire of length $2500 \ m$ is kept in east-west direction,at a certain height from the ground. If it falls freely on the ground,then the current induced in the wire when its speed is $10 \ m/s$ is (Resistance of wire $= 25 \ \Omega$,$g = 10 \ m/s^2$ and Earth's horizontal component of magnetic field $B_{H} = 2 \times 10^{-5} \ T$). (in $A$)

$A$ rectangular loop has a sliding connector $PQ$ of length $2\ m$ and resistance $10\Omega$. It is moving with a speed $5\ m/s$ as shown. The set-up is placed in a uniform magnetic field $3\ T$ directed into the plane of the paper. Find the three currents $I_1$,$I_2$,and $I$.