$A$ simple pendulum made of a mass of $10 \ g$ and a metallic wire of length $10 \ cm$ is suspended vertically in a uniform magnetic field of $2 \ T$. The magnetic field direction is perpendicular to the plane of oscillations of the pendulum. If the pendulum is released from an angle of $60^{\circ}$ with the vertical, then the maximum induced $EMF$ between the point of suspension and the point of oscillation is . . . . . . $mV$. (Take $g = 10 \ m/s^2$)

$A$ rod of length $60 \ cm$ rotates with a uniform angular velocity $20 \ rad \ s^{-1}$ about its perpendicular bisector in a uniform magnetic field of $0.5 \ T$. The direction of the magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is . . . . . . $V$.

$A$ 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 $A$)

Two long parallel horizontal rails,a distance $l$ apart,each having a resistance $\lambda$ per unit length,are joined at one end by a resistance $R$. $A$ perfectly conducting rod $MN$ of mass $m$ is free to slide along the rails without friction. There is a uniform magnetic field of induction $B$ normal to the plane of the paper and directed into the paper. $A$ variable force $F$ is applied to the rod $MN$ such that,as the rod moves,a constant current $i$ flows through the circuit. The applied force $F$ as a function of distance $x$ of the rod from $R$ is:

$A$ 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:

$A$ rod of length $l$ is rotating in the plane of the paper with an angular speed $\omega$ about one of its ends,which is at a distance $a$ from an infinitely long conducting wire carrying current $i$ inwards the plane of the paper. Find the induced $emf$ in the rod at the instant as shown in the figure.