$A$ 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 $g = 10 \ m/s^2$)

The figure shows a square loop of side $5 \, cm$ being moved towards the right at a constant speed of $1 \, cm/s$. The front edge enters the $20 \, cm$ wide magnetic field at $t = 0$. Find the magnitude of the $emf$ induced in the loop at $(a) \, t = 2 \, s$, $(b) \, t = 10 \, s$, and $(c) \, t = 22 \, s$.

$A$ wire of length $1 \, m$ is moving at a speed of $2 \, m/s$ perpendicular to a homogeneous magnetic field of $0.5 \, T$. The ends of the wire are joined to a resistance of $6 \, \Omega$. The rate at which work is being done to keep the wire moving at that speed is:

$A$ rectangular loop of wire is placed in the $XY$-plane with its side of length $3 \,cm$ parallel to the $X$-axis and the side of length $4 \,cm$ parallel to the $Y$-axis. It is moving in the positive $X$-direction with the speed $10 \,cm/s$. $A$ magnetic field exists in the space with its direction parallel to the $Z$-axis. The field decreases by $2 \times 10^{-3} \,T/cm$ along the positive $X$-axis and increases in time by $2 \times 10^{-2} \,T/s$. The induced emf in the wire is

$A$ copper disc of radius $0.1 \ m$ is rotated about its centre with $10$ revolutions per second in a uniform magnetic field of $0.1 \ T$ with its plane perpendicular to the field. The e.m.f. induced across the radius of the disc is:

An aeroplane having a wing span of $30 \ m$ flies due north with a speed of $170 \ m/s$. If the vertical component of the Earth's magnetic field is $B = 3.6 \times 10^{-5} \ T$, the potential difference between the tips of the wings will be: (in $mV$)